Spacelike time-slice of an Isolated Horizon in a 3+1 spacetime with conformal decomposition. More...

#include <isol_hor.h>

Inheritance diagram for Lorene::Isol_hor:

Public Member Functions
	Isol_hor (Map_af &mpi, int depth_in=3)
	Standard constructor. More...

	Isol_hor (Map_af &mpi, const Scalar &lapse_in, const Scalar &psi_in, const Vector &shift_in, const Sym_tensor &aa_in, const Metric &gamt, const Sym_tensor &gamt_point, const Scalar &trK, const Scalar &trK_point, const Metric_flat &ff_in, int depth_in=3)
	Constructor from conformal decomposition. More...

	Isol_hor (const Isol_hor &)
	Copy constructor. More...

	Isol_hor (Map_af &mp, FILE *fich, bool partial_read, int depth_in=3)
	Constructor from a binary file. More...

virtual	~Isol_hor ()
	Destructor. More...

void	operator= (const Isol_hor &)
	Assignment to another Isol_hor. More...

const Map_af &	get_mp () const
	Returns the mapping (readonly). More...

Map_af &	set_mp ()
	Read/write of the mapping. More...

double	get_radius () const
	Returns the radius of the horizon. More...

void	set_radius (double rad)
	Sets the radius of the horizon to `rad` . More...

double	get_omega () const
	Returns the angular velocity. More...

void	set_omega (double ome)
	Sets the angular velocity to `ome` . More...

double	get_boost_x () const
	Returns the boost velocity in x-direction. More...

void	set_boost_x (double bo)
	Sets the boost velocity in x-direction to `bo` . More...

double	get_boost_z () const
	Returns the boost velocity in z-direction. More...

void	set_boost_z (double bo)
	Sets the boost velocity in z-direction to `bo` . More...

virtual const Scalar &	n_auto () const
	Lapse function $N_{auto}$ at the current time step `jtime`. More...

virtual const Scalar &	n_comp () const
	Lapse function $N_{comp}$ at the current time step `jtime`. More...

virtual const Scalar &	psi_auto () const
	Conformal factor $\Psi_{auto}$ at the current time step `jtime`. More...

virtual const Scalar &	psi_comp () const
	Conformal factor $\Psi_{comp}$ at the current time step `jtime`. More...

virtual const Vector &	dnn () const
	Covariant derivative of the lapse function $\overline\nabla_i N$ at the current time step `jtime`. More...

virtual const Vector &	dpsi () const
	Covariant derivative with respect to the flat metric of the conformal factor $\overline\nabla_i \Psi$ at the current time step `jtime`. More...

virtual const Vector &	beta_auto () const
	Shift function $\beta^i_{auto}$ at the current time step `jtime`. More...

virtual const Vector &	beta_comp () const
	Shift function $\beta^i_{comp}$ at the current time step `jtime`. More...

virtual const Sym_tensor &	aa_auto () const
	Conformal representation $A^{ij}_{auto}$ of the traceless part of the extrinsic curvature: Returns the value at the current time step `jtime`. More...

virtual const Sym_tensor &	aa_comp () const
	Conformal representation $A^{ij}_{comp}$ of the traceless part of the extrinsic curvature: Returns the value at the current time step `jtime`. More...

virtual const Scalar &	aa_quad () const
	Conformal representation $A^{ij}A_{ij}$ . More...

virtual const Metric &	tgam () const
	Conformal metric $\tilde\gamma_{ij} = \Psi^{-4} \gamma_{ij}$ Returns the value at the current time step (`jtime` ). More...

const Scalar	get_decouple () const
	Returns the function used to construct `tkij_auto` from `tkij_tot` . More...

void	n_comp (const Isol_hor &comp)
	Imports the part of N due to the companion hole `comp` . More...

void	psi_comp (const Isol_hor &comp)
	Imports the part of $\Psi$ due to the companion hole `comp` . More...

void	beta_comp (const Isol_hor &comp)
	Imports the part of $\beta^i$ due to the companion hole `comp`. More...

double	viriel_seul () const
	Computes the viriel error, that is the difference between the ADM and the Komar masses, calculated by the asymptotic behaviours of respectively $\Psi$ and N . More...

void	init_bhole ()
	Sets the values of the fields to : More...

void	init_met_trK ()
	Sets the 3-metric tilde to the flat metric and gamt_point, trK and trK_point to zero. More...

void	init_bhole_seul ()
	Initiates for a single black hole. More...

void	set_psi (const Scalar &psi_in)
	Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ . More...

void	set_nn (const Scalar &nn_in)
	Sets the lapse. More...

void	set_gamt (const Metric &gam_tilde)
	Sets the conformal metric to gam_tilde. More...

const Vector	radial_vect_hor () const
	Vector radial normal. More...

const Vector	tradial_vect_hor () const
	Vector radial normal tilde. More...

const Scalar	b_tilde () const
	Radial component of the shift with respect to the conformal metric. More...

const Scalar	darea_hor () const
	Element of area of the horizon. More...

double	area_hor () const
	Area of the horizon. More...

double	radius_hor () const
	Radius of the horizon. More...

double	ang_mom_hor () const
	Angular momentum (modulo) More...

double	mass_hor () const
	Mass computed at the horizon. More...

double	kappa_hor () const
	Surface gravity. More...

double	omega_hor () const
	Orbital velocity. More...

double	ang_mom_adm () const
	ADM angular Momentum. More...

Scalar	expansion () const
	Expansion of the outgoing null normal ( $\bf n + \bf s$ ) More...

void	init_data (int bound_nn, double lim_nn, int bound_psi, int bound_beta, int solve_lapse, int solve_psi, int solve_shift, double precis=1.e-12, double relax_nn=0.5, double relax_psi=0.5, double relax_beta=0.5, int niter=100)

void	init_data_loop (int bound_nn, double lim_nn, int bound_psi, int bound_beta, int solve_lapse, int solve_psi, int solve_shift, double precis=1.e-12, double precis_loop=1.e-12, double relax_nn=1., double relax_psi=1., double relax_beta=1., double relax_loop=1., int niter=100)

void	init_data_spher (int bound_nn, double lim_nn, int bound_psi, int bound_beta, int solve_lapse, int solve_psi, int solve_shift, double precis=1.e-12, double relax=1., int niter=100)

void	init_data_alt (int bound_nn, double lim_nn, int bound_psi, int bound_beta, int solve_lapse, int solve_psi, int solve_shift, double precis=1.e-12, double relax=1., int niter=100)

void	init_data_CTS_gen (int bound_nn, double lim_nn, int bound_psi, int bound_beta, int solve_lapse, int solve_psi, int solve_shift, double precis=1.e-12, double relax_nn=1., double relax_psi=1., double relax_beta=1., int niter=100, double a=1., double zeta=4.)

const Scalar	source_psi () const
	Source for $\Psi$ . More...

const Scalar	source_nn () const
	Source for `N`. More...

const Vector	source_beta () const
	Source for $\beta$ . More...

const Scalar	source_b_tilde () const
	Source for `b_tilde`. More...

const Vector	source_vector_b () const
	Source for `vector_b`. More...

const Valeur	boundary_psi_Dir_evol () const
	Dirichlet boundary condition for $\Psi$ (evolution) More...

const Valeur	boundary_psi_Neu_evol () const
	Neumann boundary condition for $\Psi$ (evolution) More...

const Valeur	boundary_psi_Dir_spat () const
	Dirichlet boundary condition for $\Psi$ (spatial) More...

const Valeur	boundary_psi_Neu_spat () const
	Neumann boundary condition for $\Psi$ (spatial) More...

const Valeur	boundary_psi_app_hor () const
	Neumann boundary condition for $\Psi$ (spatial) More...

const Valeur	boundary_psi_Dir () const
	Dirichlet boundary condition for $\Psi$ (spatial) More...

const Valeur	boundary_nn_Dir_kk () const
	Dirichlet boundary condition for `N` using the extrinsic curvature. More...

const Valeur	boundary_nn_Neu_kk (int nn=1) const
	Neumann boundary condition for `N` using the extrinsic curvature. More...

const Valeur	boundary_nn_Neu_Cook () const
	Neumann boundary condition for `N` using Cook's boundary condition. More...

const Valeur	boundary_nn_Dir_eff (double aa) const
	Dirichlet boundary condition for `N` (effectif) $\partial_r N + a N = 0$ . More...

const Valeur	boundary_nn_Dir_lapl (int mer=1) const
	Dirichlet boundary condition for `N` fixing the divergence of the connection form $\omega$ . More...

const Valeur	boundary_nn_Neu_eff (double aa) const
	Neumann boundary condition on nn (effectif) $\partial_r N + a N = 0$ . More...

const Valeur	boundary_nn_Dir (double aa) const
	Dirichlet boundary condition . More...

const Valeur	boundary_beta_r () const
	Component r of boundary value of $\beta$ . More...

const Valeur	boundary_beta_theta () const
	Component theta of boundary value of $\beta$ . More...

const Valeur	boundary_beta_phi (double om) const
	Component phi of boundary value of $\beta$ . More...

const Valeur	boundary_beta_x (double om) const
	Component x of boundary value of $\beta$ . More...

const Valeur	boundary_beta_y (double om) const
	Component y of boundary value of $\beta$ . More...

const Valeur	boundary_beta_z () const
	Component z of boundary value of $\beta$ . More...

const Valeur	beta_boost_x () const
	Boundary value for a boost in x-direction. More...

const Valeur	beta_boost_z () const
	Boundary value for a boost in z-direction. More...

const Vector	vv_bound_cart (double om) const
	Vector for boundary conditions in cartesian. More...

const Vector	vv_bound_cart_bin (double om, int hole=0) const
	Vector for boundary conditions in cartesian for binary systems. More...

const Valeur	boundary_vv_x (double om) const
	Component x of boundary value of . More...

const Valeur	boundary_vv_y (double om) const
	Component y of boundary value of . More...

const Valeur	boundary_vv_z (double om) const
	Component z of boundary value of . More...

const Valeur	boundary_vv_x_bin (double om, int hole=0) const
	Component x of boundary value of . More...

const Valeur	boundary_vv_y_bin (double om, int hole=0) const
	Component y of boundary value of . More...

const Valeur	boundary_vv_z_bin (double om, int hole=0) const
	Component z of boundary value of . More...

const Valeur	boundary_b_tilde_Neu () const
	Neumann boundary condition for `b_tilde`. More...

const Valeur	boundary_b_tilde_Dir () const
	Dirichlet boundary condition for `b_tilde`. More...

void	update_aa ()
	Conformal representation $A^{ij}$ of the traceless part of the extrinsic curvature: $A^{ij} = \Psi^4 \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ . More...

double	regularisation (const Vector &shift_auto, const Vector &shift_comp, double ang_vel)
	Corrects `shift_auto` in such a way that the total $A^{ij}$ is equal to zero in the horizon, which should ensure the regularity of $K^{ij}$ . More...

double	regularise_one ()
	Corrects the shift in the innermost shell, so that it remains ${\mathcal{C}}^2$ and that $A^{ij}$ equals zero on the horizon. More...

void	met_kerr_perturb ()
	Initialisation of the metric tilde from equation (15) of Dain (2002). More...

void	aa_kerr_ww (double mm, double aa)

double	axi_break () const
	Breaking of the axial symmetry on the horizon. More...

void	adapt_hor (double c_min, double c_max)

virtual void	sauve (FILE *fich, bool partial_save) const
	Total or partial saves in a binary file. More...

virtual void	set_psi_del_npsi (const Scalar &psi_in)
	Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ . More...

virtual void	set_psi_del_n (const Scalar &psi_in)
	Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ . More...

virtual void	set_npsi_del_psi (const Scalar &npsi_in)
	Sets the factor $N\Psi$ at the current time step (`jtime` ) and deletes the value of $\Psi$ . More...

virtual void	set_npsi_del_n (const Scalar &npsi_in)
	Sets the factor $N\Psi$ at the current time step (`jtime` ) and deletes the value of N. More...

virtual void	set_hh (const Sym_tensor &hh_in)
	Sets the deviation $h^{ij}$ of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ . More...

virtual void	set_hata (const Sym_tensor &hata_in)
	Sets the conformal representation $\hat{A}{ij}$ of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ . More...

virtual void	set_hata_TT (const Sym_tensor_tt &hata_tt)
	Sets the TT part of $\hat{A}^{ij}$ (see member `hata_evol` ). More...

virtual void	set_hata_from_XAB (Param par_bc=0x0, Param par_mat=0x0)
	Sets the conformal representation $\hat{A}{ij}$ of the traceless part of the extrinsic curvature from its potentials A, $\tilde{B}$ and . More...

virtual const Scalar &	nn () const
	Lapse function N at the current time step (`jtime` ) More...

virtual const Sym_tensor &	gam_dd () const
	Induced metric (covariant components $\gamma_{ij}$ ) at the current time step (`jtime` ) More...

virtual const Sym_tensor &	gam_uu () const
	Induced metric (contravariant components $\gamma^{ij}$ ) at the current time step (`jtime` ) More...

virtual const Sym_tensor &	k_dd () const
	Extrinsic curvature tensor (covariant components $K_{ij}$ ) at the current time step (`jtime` ) More...

virtual const Sym_tensor &	k_uu () const
	Extrinsic curvature tensor (contravariant components $K^{ij}$ ) at the current time step (`jtime` ) More...

virtual const Scalar &	A_hata () const
	Returns the potential A of $\hat{A}^{ij}$ . More...

virtual const Scalar &	B_hata () const
	Returns the potential $\tilde{B}$ of $\hat{A}^{ij}$ . More...

virtual const Scalar &	psi () const
	Conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ . More...

const Scalar &	psi4 () const
	Factor $\Psi^4$ at the current time step (`jtime` ). More...

const Scalar &	ln_psi () const
	Logarithm of $\Psi$ at the current time step (`jtime` ). More...

virtual const Scalar &	npsi () const
	Factor $N\Psi$ at the current time step (`jtime` ). More...

virtual const Sym_tensor &	hh (Param =0x0, Param =0x0) const
	Deviation $h^{ij}$ of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ . More...

virtual const Sym_tensor &	hata () const
	Conformal representation $\hat{A}^{ij}$ of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ . More...

virtual Sym_tensor	aa () const
	Conformal representation $A^{ij}$ of the traceless part of the extrinsic curvature: $A^{ij} = \Psi^4 \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ . More...

virtual const Scalar &	trk () const
	Trace K of the extrinsic curvature at the current time step (`jtime` ) More...

virtual const Vector &	hdirac () const
	Vector $H^i = {\cal D}_j \tilde\gamma^{ij}$ which vanishes in Dirac gauge. More...

virtual const Vector &	vec_X (int method_poisson=6) const
	Vector representing the longitudinal part of $\hat{A}^{ij}$ . More...

void	compute_X_from_momentum_constraint (const Vector &hat_S, const Sym_tensor_tt &hata_tt, int iter_max=200, double precis=1.e-12, double relax=0.8, int methode_poisson=6)
	Computes the vector from the conformally-rescaled momentum $\hat{S}^i = \Psi^6 S^i$ , using the momentum constraint. More...

virtual void	set_AB_hata (const Scalar &A_in, const Scalar &B_in)
	Sets the potentials A and $\tilde{B}$ of the TT part $\hat{A}^{ij}$ (see the documentation of `Sym_tensor` for details). More...

virtual void	initial_data_cts (const Sym_tensor &uu, const Scalar &trk_in, const Scalar &trk_point, double pdt, double precis=1.e-12, int method_poisson_vect=6, const char graph_device=0x0, const Scalar ener_dens=0x0, const Vector mom_dens=0x0, const Scalar trace_stress=0x0)
	Computes valid initial data by solving the constraint equations in the conformal thin-sandwich approach. More...

virtual double	adm_mass () const
	Returns the ADM mass (geometrical units) at the current step. More...

void	check_psi_dot (Tbl &tlnpsi_dot, Tbl &tdiff, Tbl &tdiff_rel) const
	Checks the $\frac{\partial}{\partial t} \ln\Psi$ relation. More...

void	set_scheme_order (int ord)
	Sets the order of the finite-differences scheme. More...

int	get_scheme_order () const
	Gets the order of the finite-differences scheme. More...

int	get_latest_j () const
	Gets the latest value of time step index. More...

const Evolution_std< double > &	get_time () const
	Gets the time coordinate t at successive time steps. More...

virtual const Vector &	beta () const
	shift vector $\beta^i$ at the current time step (`jtime` ) More...

const Metric &	gam () const
	Induced metric $\mathbf{\gamma}$ at the current time step (`jtime` ) More...

Tbl	check_hamiltonian_constraint (const Scalar *energy_density=0x0, ostream &ost=cout, bool verb=true) const
	Checks the level at which the hamiltonian constraint is verified. More...

Tbl	check_momentum_constraint (const Vector *momentum_density=0x0, ostream &ost=cout, bool verb=true) const
	Checks the level at which the momentum constraints are verified. More...

Tbl	check_dynamical_equations (const Sym_tensor strain_tensor=0x0, const Scalar energy_density=0x0, ostream &ost=cout, bool verb=true) const
	Checks the level at which the dynamical equations are verified. More...

void	save (const char *rootname) const
	Saves in a binary file. More...

Protected Member Functions
virtual ostream &	operator>> (ostream &) const
	Operator >> (virtual function called by the operator<<). More...

virtual void	del_deriv () const
	Deletes all the derived quantities. More...

void	set_der_0x0 () const
	Sets to `0x0` all the pointers on derived quantities. More...

Protected Attributes
Map_af &	mp
	Affine mapping. More...

int	nz
	Number of zones. More...

double	radius
	Radius of the horizon in LORENE's units. More...

double	omega
	Angular velocity in LORENE's units. More...

double	boost_x
	Boost velocity in x-direction. More...

double	boost_z
	Boost velocity in z-direction. More...

double	regul
	Intensity of the correction on the shift vector. More...

Evolution_std< Scalar >	n_auto_evol
	Values at successive time steps of the lapse function $N_{auto}$ . More...

Evolution_std< Scalar >	n_comp_evol
	Values at successive time steps of the lapse function $N_{comp}$ . More...

Evolution_std< Scalar >	psi_auto_evol
	Values at successive time steps of the conformal factor $\Psi_{auto}$ . More...

Evolution_std< Scalar >	psi_comp_evol
	Values at successive time steps of the lapse function $\Psi_{comp}$ . More...

Evolution_std< Vector >	dn_evol
	Values at successive time steps of the covariant derivative of the lapse with respect to the flat metric $\overline\nabla_i N$ . More...

Evolution_std< Vector >	dpsi_evol
	Values at successive time steps of the covariant derivative of the conformal factor $\overline\nabla_i \Psi$ . More...

Evolution_std< Vector >	beta_auto_evol
	Values at successive time steps of the shift function $\beta^i_{auto}$ . More...

Evolution_std< Vector >	beta_comp_evol
	Values at successive time steps of the shift function $\beta^i_{comp}$ . More...

Evolution_std< Sym_tensor >	aa_auto_evol
	Values at successive time steps of the components $A^{ij}_{auto}$ of the conformal representation of the traceless part of the extrinsic curvature: More...

Evolution_std< Sym_tensor >	aa_comp_evol
	Values at successive time steps of the components $A^{ij}_{comp}$ of the conformal representation of the traceless part of the extrinsic curvature: More...

Evolution_std< Sym_tensor >	aa_nn
	Values at successive time steps of the components $A^{ij}*2N$ . More...

Evolution_std< Scalar >	aa_quad_evol
	Values at successive time steps of the components $A^{ij}A_{ij}$ . More...

Metric	met_gamt
	3 metric tilde More...

Sym_tensor	gamt_point
	Time derivative of the 3-metric tilde. More...

Scalar	trK
	Trace of the extrinsic curvature. More...

Scalar	trK_point
	Time derivative of the trace of the extrinsic curvature. More...

Scalar	decouple
	Function used to construct $A^{ij}_{auto}$ from the total $A^{ij}$ . More...

const Metric_flat &	ff
	Pointer on the flat metric $f_{ij}$ with respect to which the conformal decomposition is performed. More...

Evolution_std< Scalar >	psi_evol
	Values at successive time steps of the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ . More...

Evolution_std< Scalar >	npsi_evol
	Values at successive time steps of the factor $N\Psi$ . More...

Evolution_std< Sym_tensor >	hh_evol
	Values at successive time steps of the components $h^{ij}$ . More...

Evolution_std< Sym_tensor >	hata_evol
	Values at successive time steps of the components $\hat{A}^{ij}$ . More...

Evolution_std< Scalar >	A_hata_evol
	Potential A associated with the symmetric tensor $\hat{A}^{ij}_{TT}$ . More...

Evolution_std< Scalar >	B_hata_evol
	Potential $\tilde{B}$ associated with the symmetric tensor $\hat{A}^{ij}_{TT}$ . More...

Metric *	p_tgamma
	Pointer on the conformal metric $\tilde\gamma_{ij}$ at the current time step (`jtime`) More...

Scalar *	p_psi4
	Pointer on the factor $\Psi^4$ at the current time step (`jtime`) More...

Scalar *	p_ln_psi
	Pointer on the logarithm of $\Psi$ at the current time step (`jtime`) More...

Vector *	p_hdirac
	Pointer on the vector $H^i = {\cal D}_j \tilde\gamma^{ij}$ (which vanishes in Dirac gauge), at the current time step (`jtime`). More...

Vector *	p_vec_X
	Pointer on the vector representing the longitudinal part of $\hat{A}^{ij}$ . More...

int	depth
	Number of stored time slices. More...

int	scheme_order
	Order of the finite-differences scheme for the computation of time derivatives. More...

int	jtime
	Time step index of the latest slice. More...

Evolution_std< double >	the_time
	Time label of each slice. More...

Evolution_std< Sym_tensor >	gam_dd_evol
	Values at successive time steps of the covariant components of the induced metric $\gamma_{ij}$ . More...

Evolution_std< Sym_tensor >	gam_uu_evol
	Values at successive time steps of the contravariant components of the induced metric $\gamma^{ij}$ . More...

Evolution_std< Sym_tensor >	k_dd_evol
	Values at successive time steps of the covariant components of the extrinsic curvature tensor $K_{ij}$ . More...

Evolution_std< Sym_tensor >	k_uu_evol
	Values at successive time steps of the contravariant components of the extrinsic curvature tensor $K^{ij}$ . More...

Evolution_std< Scalar >	n_evol
	Values at successive time steps of the lapse function N. More...

Evolution_std< Vector >	beta_evol
	Values at successive time steps of the shift vector $\beta^i$ . More...

Evolution_std< Scalar >	trk_evol
	Values at successive time steps of the trace K of the extrinsic curvature. More...

Evolution_full< Tbl >	adm_mass_evol
	ADM mass at each time step, since the creation of the slice. More...

Metric *	p_gamma
	Pointer on the induced metric at the current time step (`jtime`) More...

Friends
class	Bin_hor

Detailed Description

Spacelike time-slice of an Isolated Horizon in a 3+1 spacetime with conformal decomposition.

No gauge choice imposed. ()

Definition at line 254 of file isol_hor.h.

Constructor & Destructor Documentation

◆ Isol_hor() [1/4]

Lorene::Isol_hor::Isol_hor	(	Map_af &	mpi,
		int	depth_in = `3`
	)

Standard constructor.

Parameters

mpi	affine mapping
depth_in	number of stored time slices; this parameter is used to set the `scheme_order` member with `scheme_order` = `depth_in` - 1. `scheme_order` can be changed afterwards by the method `set_scheme_order(int)`.

Definition at line 179 of file isol_hor.C.

◆ Isol_hor() [2/4]

Lorene::Isol_hor::Isol_hor	(	Map_af &	mpi,
		const Scalar &	lapse_in,
		const Scalar &	psi_in,
		const Vector &	shift_in,
		const Sym_tensor &	aa_in,
		const Metric &	gamt,
		const Sym_tensor &	gamt_point,
		const Scalar &	trK,
		const Scalar &	trK_point,
		const Metric_flat &	ff_in,
		int	depth_in = `3`
	)

Constructor from conformal decomposition.

Parameters

mpi	affine mapping
lapse_in	lapse function N
psi_in	conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$
shift_in	shift vector
aa_in	conformal representation $A^{ij}$ of the traceless part of the extrinsic curvature: $A^{ij} = \Psi^4 \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$
gamt	3-metric tilde
gamt_point	time derivative of the 3-metric tilde
trK	trace K of the extrinsic curvature
trK_point	time derivative of the trace K of the extrinsic curvature
ff_in	reference flat metric with respect to which the conformal decomposition is performed
depth_in	number of stored time slices; this parameter is used to set the `scheme_order` member with `scheme_order` = `depth_in` - 1. `scheme_order` can be changed afterwards by the method `set_scheme_order(int)`.

Definition at line 196 of file isol_hor.C.

References Lorene::Metric::con(), Lorene::Metric_flat::con(), Lorene::Time_slice_conf::ff, Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice::jtime, met_gamt, Lorene::Time_slice::the_time, trK, and Lorene::Time_slice::trk_evol.

◆ Isol_hor() [3/4]

Lorene::Isol_hor::Isol_hor ( const Isol_hor & isolhor_in )

Copy constructor.

Definition at line 225 of file isol_hor.C.

◆ Isol_hor() [4/4]

Lorene::Isol_hor::Isol_hor	(	Map_af &	mp,
		FILE *	fich,
		bool	partial_read,
		int	depth_in = `3`
	)

Constructor from a binary file.

Parameters

mpi	affine mapping
fich	file containing the saved `isol_hor`
partial_read	indicates whether the full object must be read in file or whether the final construction is devoted to a constructor of a derived class
depth_in	number of stored time slices; this parameter is used to set the `scheme_order` member with `scheme_order` = `depth_in` - 1. `scheme_order` can be changed afterwards by the method `set_scheme_order(int)`.

Definition at line 256 of file isol_hor.C.

References beta_auto_evol, boost_x, boost_z, Lorene::Metric::con(), Lorene::Metric_flat::con(), Lorene::Time_slice::depth, Lorene::Time_slice_conf::ff, Lorene::fread_be(), gamt_point, Lorene::Map::get_bvect_spher(), Lorene::Map::get_mg(), Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice::jtime, met_gamt, mp, n_auto_evol, omega, psi_auto_evol, Lorene::Time_slice_conf::psi_evol, Lorene::Time_slice::the_time, trK, Lorene::Time_slice::trk_evol, and trK_point.

◆ ~Isol_hor()

Lorene::Isol_hor::~Isol_hor ( )

virtual

Destructor.

Definition at line 339 of file isol_hor.C.

Member Function Documentation

◆ A_hata()

const Scalar & Lorene::Time_slice_conf::A_hata ( ) const

virtualinherited

Returns the potential A of $\hat{A}^{ij}$ .

See the documentation of Sym_tensor for details. Returns the value at the current time step (jtime ).

Definition at line 667 of file time_slice_conf.C.

References Lorene::Time_slice_conf::A_hata_evol, Lorene::Time_slice_conf::hata_evol, Lorene::Time_slice::jtime, and Lorene::Time_slice::the_time.

◆ aa()

Sym_tensor Lorene::Time_slice_conf::aa ( ) const

virtualinherited

Conformal representation $A^{ij}$ of the traceless part of the extrinsic curvature: $A^{ij} = \Psi^4 \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .

Returns the value at the current time step (jtime ).

Definition at line 768 of file time_slice_conf.C.

References Lorene::Time_slice_conf::hata(), Lorene::Time_slice_conf::psi(), and Lorene::Time_slice_conf::psi4().

◆ aa_auto()

const Sym_tensor & Lorene::Isol_hor::aa_auto ( ) const

virtual

Conformal representation $A^{ij}_{auto}$ of the traceless part of the extrinsic curvature: Returns the value at the current time step jtime.

Definition at line 506 of file isol_hor.C.

References aa_auto_evol, and Lorene::Time_slice::jtime.

◆ aa_comp()

const Sym_tensor & Lorene::Isol_hor::aa_comp ( ) const

virtual

Conformal representation $A^{ij}_{comp}$ of the traceless part of the extrinsic curvature: Returns the value at the current time step jtime.

Definition at line 512 of file isol_hor.C.

References aa_comp_evol, and Lorene::Time_slice::jtime.

◆ aa_quad()

const Scalar & Lorene::Isol_hor::aa_quad ( ) const

virtual

Conformal representation $A^{ij}A_{ij}$ .

Returns the value at the current time step jtime.

Definition at line 887 of file isol_hor.C.

References Lorene::Time_slice_conf::aa(), aa_quad_evol, Lorene::contract(), Lorene::Time_slice::jtime, met_gamt, Lorene::Time_slice_conf::psi4(), and Lorene::Time_slice::the_time.

◆ adm_mass()

double Lorene::Time_slice_conf::adm_mass ( ) const

virtualinherited

Returns the ADM mass (geometrical units) at the current step.

Moreover this method updates adm_mass_evol if necessary.

Reimplemented from Lorene::Time_slice.

Reimplemented in Lorene::Tslice_dirac_max.

Definition at line 111 of file tslice_adm_mass.C.

References Lorene::Time_slice::adm_mass_evol, Lorene::Scalar::derive_con(), Lorene::Time_slice_conf::ff, Lorene::Vector::flux(), Lorene::Map::get_mg(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_nzone(), Lorene::Tbl::get_taille(), Lorene::Time_slice_conf::hdirac(), Lorene::Time_slice_conf::hh(), Lorene::Time_slice::jtime, Lorene::Time_slice_conf::psi(), Lorene::Tbl::set(), Lorene::Tbl::set_etat_qcq(), Lorene::Time_slice::the_time, Lorene::Tensor::trace(), and Lorene::Map::val_r().

◆ ang_mom_adm()

double Lorene::Isol_hor::ang_mom_adm ( ) const

ADM angular Momentum.

Definition at line 251 of file phys_param.C.

References Lorene::Time_slice_conf::gam_dd(), Lorene::Map_af::integrale_surface_infini(), Lorene::Time_slice_conf::k_dd(), mp, Lorene::Scalar::mult_rsint(), and Lorene::Time_slice_conf::trk().

◆ ang_mom_hor()

double Lorene::Isol_hor::ang_mom_hor ( ) const

Angular momentum (modulo)

Definition at line 181 of file phys_param.C.

References Lorene::contract(), darea_hor(), Lorene::Time_slice_conf::ff, Lorene::Metric::get_mp(), Lorene::Metric_flat::get_triad(), Lorene::Map_af::integrale_surface(), Lorene::Time_slice_conf::k_dd(), mp, radial_vect_hor(), radius, Lorene::Vector::set(), and Lorene::Scalar::std_spectral_base().

◆ area_hor()

double Lorene::Isol_hor::area_hor ( ) const

Area of the horizon.

Definition at line 160 of file phys_param.C.

References darea_hor(), Lorene::Map_af::integrale_surface(), mp, Lorene::Scalar::raccord(), and radius.

◆ axi_break()

double Lorene::Isol_hor::axi_break ( ) const

Breaking of the axial symmetry on the horizon.

Definition at line 1090 of file isol_hor.C.

References Lorene::contract(), darea_hor(), Lorene::Time_slice_conf::ff, Lorene::Time_slice::gam(), Lorene::Time_slice_conf::gam_uu(), Lorene::Metric::get_mp(), Lorene::Metric_flat::get_triad(), Lorene::Map_af::integrale_surface(), mp, radius_hor(), Lorene::Vector::set(), Lorene::Scalar::std_spectral_base(), and Lorene::Tensor::up_down().

◆ B_hata()

const Scalar & Lorene::Time_slice_conf::B_hata ( ) const

virtualinherited

Returns the potential $\tilde{B}$ of $\hat{A}^{ij}$ .

See the documentation of Sym_tensor_tt for details. Returns the value at the current time step (jtime ).

Definition at line 681 of file time_slice_conf.C.

References Lorene::Time_slice_conf::A_hata_evol, Lorene::Time_slice_conf::B_hata_evol, Lorene::Time_slice_conf::hata_evol, Lorene::Time_slice::jtime, and Lorene::Time_slice::the_time.

◆ b_tilde()

const Scalar Lorene::Isol_hor::b_tilde ( ) const

Radial component of the shift with respect to the conformal metric.

Definition at line 139 of file phys_param.C.

References Lorene::Time_slice::beta(), Lorene::contract(), Lorene::Tensor::down(), met_gamt, and Lorene::Metric::radial_vect().

◆ beta()

const Vector & Lorene::Time_slice::beta ( ) const

virtualinherited

shift vector $\beta^i$ at the current time step (jtime )

Definition at line 90 of file time_slice_access.C.

References Lorene::Time_slice::beta_evol, and Lorene::Time_slice::jtime.

◆ beta_auto()

const Vector & Lorene::Isol_hor::beta_auto ( ) const

virtual

Shift function $\beta^i_{auto}$ at the current time step jtime.

Definition at line 494 of file isol_hor.C.

References beta_auto_evol, and Lorene::Time_slice::jtime.

◆ beta_boost_x()

const Valeur Lorene::Isol_hor::beta_boost_x ( ) const

Boundary value for a boost in x-direction.

Definition at line 1147 of file bound_hor.C.

References boost_x, Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), mp, and Lorene::Mg3d::std_base_vect_cart().

◆ beta_boost_z()

const Valeur Lorene::Isol_hor::beta_boost_z ( ) const

Boundary value for a boost in z-direction.

Definition at line 1158 of file bound_hor.C.

References boost_z, Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), mp, and Lorene::Mg3d::std_base_vect_cart().

◆ beta_comp() [1/2]

const Vector & Lorene::Isol_hor::beta_comp ( ) const

virtual

Shift function $\beta^i_{comp}$ at the current time step jtime.

Definition at line 500 of file isol_hor.C.

References beta_comp_evol, and Lorene::Time_slice::jtime.

◆ beta_comp() [2/2]

void Lorene::Isol_hor::beta_comp ( const Isol_hor & comp )

Imports the part of $\beta^i$ due to the companion hole comp.

The total $\beta^i$ is then calculated.

Definition at line 715 of file isol_hor.C.

References beta_auto(), beta_comp(), beta_comp_evol, Lorene::Time_slice::beta_evol, Lorene::Vector::change_triad(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Time_slice::jtime, mp, and Lorene::Time_slice::the_time.

◆ boundary_b_tilde_Dir()

const Valeur Lorene::Isol_hor::boundary_b_tilde_Dir ( ) const

Dirichlet boundary condition for b_tilde.

Definition at line 1215 of file bound_hor.C.

References b_tilde(), Lorene::contract(), Lorene::Tensor::derive_cov(), Lorene::Time_slice_conf::ff, Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Scalar::inc_dzpuis(), met_gamt, mp, Lorene::Metric::radial_vect(), and Lorene::Scalar::std_spectral_base().

◆ boundary_b_tilde_Neu()

const Valeur Lorene::Isol_hor::boundary_b_tilde_Neu ( ) const

Neumann boundary condition for b_tilde.

Definition at line 1172 of file bound_hor.C.

References b_tilde(), Lorene::contract(), Lorene::Tensor::derive_cov(), Lorene::Scalar::derive_cov(), Lorene::Time_slice_conf::ff, Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Scalar::inc_dzpuis(), met_gamt, mp, Lorene::Metric::radial_vect(), and Lorene::Scalar::std_spectral_base().

◆ boundary_beta_phi()

const Valeur Lorene::Isol_hor::boundary_beta_phi ( double om ) const

Component phi of boundary value of $\beta$ .

Definition at line 981 of file bound_hor.C.

References Lorene::Valeur::base, Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Scalar::get_spectral_va(), mp, Lorene::Scalar::mult_rsint(), Lorene::Time_slice_conf::nn(), radial_vect_hor(), Lorene::Valeur::set(), Lorene::Scalar::std_spectral_base(), and Lorene::Scalar::val_grid_point().

◆ boundary_beta_r()

const Valeur Lorene::Isol_hor::boundary_beta_r ( ) const

Component r of boundary value of $\beta$ .

Definition at line 900 of file bound_hor.C.

References Lorene::Mg3d::get_angu(), Lorene::Valeur::get_base(), Lorene::Base_val::get_base_p(), Lorene::Base_val::get_base_r(), Lorene::Base_val::get_base_t(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Scalar::get_spectral_va(), mp, Lorene::Time_slice_conf::nn(), Lorene::norme(), radial_vect_hor(), Lorene::Valeur::set(), and Lorene::Scalar::val_grid_point().

◆ boundary_beta_theta()

const Valeur Lorene::Isol_hor::boundary_beta_theta ( ) const

Component theta of boundary value of $\beta$ .

Definition at line 941 of file bound_hor.C.

References Lorene::Mg3d::get_angu(), Lorene::Base_val::get_base_p(), Lorene::Base_val::get_base_r(), Lorene::Base_val::get_base_t(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), mp, Lorene::Time_slice_conf::nn(), radial_vect_hor(), Lorene::Valeur::set(), and Lorene::Scalar::val_grid_point().

◆ boundary_beta_x()

const Valeur Lorene::Isol_hor::boundary_beta_x ( double om ) const

Component x of boundary value of $\beta$ .

Definition at line 1024 of file bound_hor.C.

References Lorene::Vector::change_triad(), Lorene::Map::cosp, Lorene::Map::cost, Lorene::Time_slice::gam(), Lorene::Mg3d::get_angu(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Map::get_rot_phi(), mp, Lorene::Time_slice_conf::nn(), Lorene::Metric::radial_vect(), Lorene::Tensor::set(), Lorene::Mtbl::set_etat_qcq(), Lorene::Map::sinp, Lorene::Map::sint, Lorene::Mg3d::std_base_vect_cart(), Lorene::Scalar::val_grid_point(), and Lorene::Map::ya.

◆ boundary_beta_y()

const Valeur Lorene::Isol_hor::boundary_beta_y ( double om ) const

Component y of boundary value of $\beta$ .

Definition at line 1074 of file bound_hor.C.

References Lorene::Vector::change_triad(), Lorene::Map::cosp, Lorene::Map::cost, Lorene::Time_slice::gam(), Lorene::Mg3d::get_angu(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Map::get_rot_phi(), mp, Lorene::Time_slice_conf::nn(), Lorene::Metric::radial_vect(), Lorene::Tensor::set(), Lorene::Mtbl::set_etat_qcq(), Lorene::Map::sinp, Lorene::Map::sint, Lorene::Mg3d::std_base_vect_cart(), Lorene::Scalar::val_grid_point(), and Lorene::Map::xa.

◆ boundary_beta_z()

const Valeur Lorene::Isol_hor::boundary_beta_z ( ) const

Component z of boundary value of $\beta$ .

Definition at line 1124 of file bound_hor.C.

References Lorene::Vector::change_triad(), Lorene::Time_slice::gam(), Lorene::Mg3d::get_angu(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), mp, Lorene::Time_slice_conf::nn(), Lorene::Metric::radial_vect(), Lorene::Valeur::set(), and Lorene::Mg3d::std_base_vect_cart().

◆ boundary_nn_Dir()

const Valeur Lorene::Isol_hor::boundary_nn_Dir ( double aa ) const

Dirichlet boundary condition $ N = a $ .

Definition at line 650 of file bound_hor.C.

References Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), mp, Lorene::Time_slice_conf::nn(), Lorene::Valeur::set(), and Lorene::Scalar::val_grid_point().

◆ boundary_nn_Dir_eff()

const Valeur Lorene::Isol_hor::boundary_nn_Dir_eff ( double aa ) const

Dirichlet boundary condition for N (effectif) $\partial_r N + a N = 0$ .

Definition at line 589 of file bound_hor.C.

References Lorene::Scalar::dec_dzpuis(), Lorene::Scalar::derive_cov(), Lorene::Time_slice_conf::ff, Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), mp, Lorene::Time_slice_conf::nn(), Lorene::Valeur::set(), and Lorene::Scalar::val_grid_point().

◆ boundary_nn_Dir_kk()

const Valeur Lorene::Isol_hor::boundary_nn_Dir_kk ( ) const

Dirichlet boundary condition for N using the extrinsic curvature.

Definition at line 374 of file bound_hor.C.

References Lorene::contract(), Lorene::Time_slice_conf::ff, Lorene::Time_slice::gam(), Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Scalar::inc_dzpuis(), Lorene::Time_slice_conf::k_dd(), mp, Lorene::Time_slice_conf::nn(), Lorene::Valeur::set(), Lorene::Scalar::std_spectral_base(), and Lorene::Scalar::val_grid_point().

◆ boundary_nn_Dir_lapl()

const Valeur Lorene::Isol_hor::boundary_nn_Dir_lapl ( int mer = 1 ) const

Dirichlet boundary condition for N fixing the divergence of the connection form $\omega$ .

Definition at line 696 of file bound_hor.C.

References Lorene::Metric_flat::con(), Lorene::contract(), Lorene::Metric_flat::cov(), Lorene::Scalar::dec_dzpuis(), Lorene::Tensor::derive_con(), Lorene::Tensor::derive_cov(), Lorene::Scalar::derive_cov(), Lorene::Vector::divergence(), Lorene::Tensor::down(), Lorene::exp(), Lorene::Time_slice_conf::ff, Lorene::Time_slice::gam(), Lorene::Time_slice_conf::gam_uu(), Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Scalar::inc_dzpuis(), Lorene::Map_af::integrale_surface(), Lorene::Time_slice_conf::k_dd(), Lorene::Scalar::lapang(), Lorene::log(), met_gamt, mp, Lorene::Time_slice_conf::nn(), Lorene::Scalar::poisson_angu(), Lorene::pow(), Lorene::Time_slice_conf::psi(), Lorene::Map::r, Lorene::Metric::radial_vect(), radius, Lorene::Valeur::set(), Lorene::Scalar::set_dzpuis(), Lorene::Scalar::std_spectral_base(), Lorene::Time_slice_conf::trk(), Lorene::Tensor::up_down(), and Lorene::Scalar::val_grid_point().

◆ boundary_nn_Neu_Cook()

const Valeur Lorene::Isol_hor::boundary_nn_Neu_Cook ( ) const

Neumann boundary condition for N using Cook's boundary condition.

Definition at line 492 of file bound_hor.C.

References Lorene::contract(), Lorene::Scalar::derive_cov(), Lorene::Vector::divergence(), Lorene::Tensor::down(), Lorene::Time_slice_conf::ff, Lorene::Time_slice::gam(), Lorene::Time_slice_conf::gam_uu(), Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Scalar::inc_dzpuis(), Lorene::Time_slice_conf::k_dd(), Lorene::Scalar::lapang(), Lorene::log(), met_gamt, mp, Lorene::Time_slice_conf::nn(), Lorene::pow(), Lorene::Time_slice_conf::psi(), Lorene::Map::r, Lorene::Metric::radial_vect(), Lorene::Valeur::set(), Lorene::Scalar::std_spectral_base(), Lorene::Time_slice_conf::trk(), and Lorene::Scalar::val_grid_point().

◆ boundary_nn_Neu_eff()

const Valeur Lorene::Isol_hor::boundary_nn_Neu_eff ( double aa ) const

Neumann boundary condition on nn (effectif) $\partial_r N + a N = 0$ .

Definition at line 625 of file bound_hor.C.

References Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), mp, Lorene::Time_slice_conf::nn(), Lorene::Valeur::set(), and Lorene::Scalar::val_grid_point().

◆ boundary_nn_Neu_kk()

const Valeur Lorene::Isol_hor::boundary_nn_Neu_kk ( int nn = 1 ) const

Neumann boundary condition for N using the extrinsic curvature.

Definition at line 423 of file bound_hor.C.

References aa_auto(), Lorene::contract(), Lorene::Metric::cov(), Lorene::Scalar::derive_cov(), Lorene::Time_slice_conf::ff, Lorene::Time_slice::gam(), Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Scalar::inc_dzpuis(), Lorene::Time_slice_conf::k_dd(), kappa_hor(), met_gamt, mp, Lorene::Time_slice_conf::nn(), Lorene::Time_slice_conf::psi(), Lorene::Metric::radial_vect(), Lorene::Valeur::set(), Lorene::Scalar::std_spectral_base(), Lorene::Time_slice_conf::trk(), Lorene::Tensor::up_down(), and Lorene::Scalar::val_grid_point().

◆ boundary_psi_app_hor()

const Valeur Lorene::Isol_hor::boundary_psi_app_hor ( ) const

Neumann boundary condition for $\Psi$ (spatial)

Definition at line 300 of file bound_hor.C.

References Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), mp, Lorene::Time_slice_conf::psi(), radius, Lorene::Valeur::set(), and Lorene::Scalar::val_grid_point().

◆ boundary_psi_Dir()

const Valeur Lorene::Isol_hor::boundary_psi_Dir ( ) const

Dirichlet boundary condition for $\Psi$ (spatial)

Definition at line 327 of file bound_hor.C.

References Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), mp, Lorene::Time_slice_conf::psi(), Lorene::Scalar::std_spectral_base(), and Lorene::Scalar::val_grid_point().

◆ boundary_psi_Dir_evol()

const Valeur Lorene::Isol_hor::boundary_psi_Dir_evol ( ) const

Dirichlet boundary condition for $\Psi$ (evolution)

Definition at line 177 of file bound_hor.C.

References Lorene::Time_slice::beta(), Lorene::contract(), Lorene::Time_slice_conf::ff, Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), mp, Lorene::Time_slice_conf::nn(), Lorene::Time_slice_conf::psi(), Lorene::Time_slice_conf::trk(), and Lorene::Scalar::val_grid_point().

◆ boundary_psi_Dir_spat()

const Valeur Lorene::Isol_hor::boundary_psi_Dir_spat ( ) const

Dirichlet boundary condition for $\Psi$ (spatial)

Definition at line 234 of file bound_hor.C.

References Lorene::contract(), Lorene::Vector::divergence(), Lorene::Time_slice_conf::ff, Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Scalar::inc_dzpuis(), Lorene::Time_slice_conf::k_dd(), mp, Lorene::Time_slice_conf::psi(), Lorene::Scalar::std_spectral_base(), tradial_vect_hor(), Lorene::Time_slice_conf::trk(), and Lorene::Scalar::val_grid_point().

◆ boundary_psi_Neu_evol()

const Valeur Lorene::Isol_hor::boundary_psi_Neu_evol ( ) const

Neumann boundary condition for $\Psi$ (evolution)

Definition at line 206 of file bound_hor.C.

References Lorene::Time_slice::beta(), Lorene::Scalar::derive_cov(), Lorene::Vector::divergence(), Lorene::Time_slice_conf::ff, Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), mp, Lorene::Time_slice_conf::nn(), Lorene::Time_slice_conf::psi(), Lorene::Time_slice_conf::trk(), and Lorene::Scalar::val_grid_point().

◆ boundary_psi_Neu_spat()

const Valeur Lorene::Isol_hor::boundary_psi_Neu_spat ( ) const

Neumann boundary condition for $\Psi$ (spatial)

Definition at line 270 of file bound_hor.C.

References Lorene::contract(), Lorene::Scalar::derive_cov(), Lorene::Vector::divergence(), Lorene::Time_slice_conf::ff, Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Time_slice_conf::k_dd(), mp, Lorene::Time_slice_conf::psi(), tradial_vect_hor(), Lorene::Time_slice_conf::trk(), and Lorene::Scalar::val_grid_point().

◆ boundary_vv_x()

const Valeur Lorene::Isol_hor::boundary_vv_x ( double om ) const

Component x of boundary value of $ V^i $ .

Definition at line 1496 of file bound_hor.C.

References Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), mp, Lorene::Vector::set(), Lorene::Mg3d::std_base_vect_cart(), Lorene::Scalar::val_grid_point(), and vv_bound_cart().

◆ boundary_vv_x_bin()

const Valeur Lorene::Isol_hor::boundary_vv_x_bin	(	double	om,
		int	hole = `0`
	)		const

Component x of boundary value of $ V^i $ .

Definition at line 1575 of file bound_hor.C.

References Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), mp, Lorene::Vector::set(), Lorene::Mg3d::std_base_vect_cart(), Lorene::Scalar::val_grid_point(), and vv_bound_cart_bin().

◆ boundary_vv_y()

const Valeur Lorene::Isol_hor::boundary_vv_y ( double om ) const

Component y of boundary value of $ V^i $ .

Definition at line 1524 of file bound_hor.C.

References Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), mp, Lorene::Vector::set(), Lorene::Mg3d::std_base_vect_cart(), Lorene::Scalar::val_grid_point(), and vv_bound_cart().

◆ boundary_vv_y_bin()

const Valeur Lorene::Isol_hor::boundary_vv_y_bin	(	double	om,
		int	hole = `0`
	)		const

Component y of boundary value of $ V^i $ .

Definition at line 1602 of file bound_hor.C.

References Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), mp, Lorene::Vector::set(), Lorene::Mg3d::std_base_vect_cart(), Lorene::Scalar::val_grid_point(), and vv_bound_cart_bin().

◆ boundary_vv_z()

const Valeur Lorene::Isol_hor::boundary_vv_z ( double om ) const

Component z of boundary value of $ V^i $ .

Definition at line 1550 of file bound_hor.C.

References Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), mp, Lorene::Vector::set(), Lorene::Mg3d::std_base_vect_cart(), Lorene::Scalar::val_grid_point(), and vv_bound_cart().

◆ boundary_vv_z_bin()

const Valeur Lorene::Isol_hor::boundary_vv_z_bin	(	double	om,
		int	hole = `0`
	)		const

Component z of boundary value of $ V^i $ .

Definition at line 1628 of file bound_hor.C.

References Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), mp, Lorene::Vector::set(), Lorene::Mg3d::std_base_vect_cart(), Lorene::Scalar::val_grid_point(), and vv_bound_cart_bin().

◆ check_dynamical_equations()

Tbl Lorene::Time_slice::check_dynamical_equations	(	const Sym_tensor *	strain_tensor = `0x0`,
		const Scalar *	energy_density = `0x0`,
		ostream &	ost = `cout`,
		bool	verb = `true`
	)		const

inherited

Checks the level at which the dynamical equations are verified.

$\frac{\partial K_{ij}}{\partial t} - \pounds_{\mbox{\boldmath{$\beta $}}} K_{ij} = - D_i D_j N + N \left[ R_{ij} - 2 K_{ik} K^k_{\ j} + K K_{ij} + 4\pi \left( (S-E)\gamma_{ij} - 2 S_{ij} \right) \right]$

Parameters

strain_tensor	: a pointer on the strain_tensor $S_{ij}$ measured by the Eulerian observer of 4-velocity $\mbox{\boldmath{$n $}}$ ; if this is the null pointer, it is assumed that $S_{ij}$ = 0 (vacuum).
energy_density	: a pointer on the energy density E (see `check_hamiltonian_constraint`)
ost	: output stream for a formatted output of the result

Returns: Tbl 3D of size the number of domains times 3 times 3 (corresponding to the rank-2 tensor, with the symmetry in the components) containing the absolute ( if = 0 ) or the relative (in presence of matter) error in max version.

Definition at line 142 of file tslice_check_einstein.C.

References Lorene::Tensor::annule_domain(), Lorene::Tbl::annule_hard(), Lorene::Time_slice::beta(), Lorene::Metric::con(), Lorene::contract(), Lorene::Tensor::derive_con(), Lorene::Scalar::derive_con(), Lorene::Sym_tensor::derive_lie(), Lorene::Time_slice::gam(), Lorene::Tbl::get_dim(), Lorene::Map::get_mg(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_nzone(), Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd(), Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu(), Lorene::maxabs(), Lorene::Time_slice::nn(), Lorene::Tensor_sym::position(), Lorene::Metric::ricci(), Lorene::Time_slice::scheme_order, Lorene::Itbl::set(), Lorene::Tensor::trace(), Lorene::Time_slice::trk(), and Lorene::Tensor::up_down().

◆ check_hamiltonian_constraint()

Tbl Lorene::Time_slice::check_hamiltonian_constraint	(	const Scalar *	energy_density = `0x0`,
		ostream &	ost = `cout`,
		bool	verb = `true`
	)		const

inherited

Checks the level at which the hamiltonian constraint is verified.

$R + K^2 - K_{ij}K^{ij} = 16\pi E$

Parameters

energy_density	: a pointer on the energy density E measured by the Eulerian observer of 4-velocity $\mbox{\boldmath{$n $}}$ ; if this is the null pointer, it is assumed that E = 0 (vacuum).
ost	: output stream for a formatted output of the result

Returns: Tbl of size the number of domains containing the absolute ( if E = 0 ) or the relative (in presence of matter) error in max version.

Definition at line 82 of file tslice_check_einstein.C.

References Lorene::contract(), Lorene::Scalar::dec_dzpuis(), Lorene::Time_slice::gam(), Lorene::Time_slice::k_dd(), Lorene::Time_slice::k_uu(), Lorene::maxabs(), Lorene::Metric::ricci_scal(), and Lorene::Time_slice::trk().

◆ check_momentum_constraint()

Tbl Lorene::Time_slice::check_momentum_constraint	(	const Vector *	momentum_density = `0x0`,
		ostream &	ost = `cout`,
		bool	verb = `true`
	)		const

inherited

Checks the level at which the momentum constraints are verified.

$D_j K_i^{\ j} - D_i K = 8 \pi J_i$

Parameters

momentum_density	: a pointer on the momentum density measured by the Eulerian observer of 4-velocity $\mbox{\boldmath{$n $}}$ ; if this is the null pointer, it is assumed that = 0 (vacuum).
ost	: output stream for a formatted output of the result

Returns: Tbl 2D of size the number of domains times 3 (components)containing the absolute ( if = 0 ) or the relative (in presence of matter) error in max version.

Definition at line 112 of file tslice_check_einstein.C.

References Lorene::Scalar::derive_con(), Lorene::Sym_tensor::divergence(), Lorene::Time_slice::gam(), Lorene::Tensor::get_index_type(), Lorene::Time_slice::k_uu(), Lorene::maxabs(), and Lorene::Time_slice::trk().

◆ check_psi_dot()

void Lorene::Time_slice_conf::check_psi_dot	(	Tbl &	tlnpsi_dot,
		Tbl &	tdiff,
		Tbl &	tdiff_rel
	)		const

inherited

Checks the $\frac{\partial}{\partial t} \ln\Psi$ relation.

Parameters

tlnpsi_dot	[output] maximun value in each domain of $\left\| \frac{\partial}{\partial t} \ln\Psi \right\|$
tdiff	[output] maximum value in each domain of $\left\| \frac{\partial}{\partial t} \ln\Psi - \beta^i {\cal D}_i \ln \Psi - \frac{1}{6} ( {\cal D}_i \beta^i - N K) \right\|$
tdiff_rel	[output] relative error on the above relation in each domain.

Definition at line 907 of file time_slice_conf.C.

◆ compute_X_from_momentum_constraint()

void Lorene::Time_slice_conf::compute_X_from_momentum_constraint	(	const Vector &	hat_S,
		const Sym_tensor_tt &	hata_tt,
		int	iter_max = `200`,
		double	precis = `1.e-12`,
		double	relax = `0.8`,
		int	methode_poisson = `6`
	)

inherited

Computes the vector $ X^i $ from the conformally-rescaled momentum $\hat{S}^i = \Psi^6 S^i$ , using the momentum constraint.

Definition at line 840 of file time_slice_conf.C.

References Lorene::abs(), Lorene::contract(), Lorene::Tensor::get_index_type(), Lorene::max(), and Lorene::Vector::poisson().

◆ darea_hor()

const Scalar Lorene::Isol_hor::darea_hor ( ) const

Element of area of the horizon.

Definition at line 149 of file phys_param.C.

References Lorene::Time_slice_conf::gam_dd(), Lorene::sqrt(), and Lorene::Scalar::std_spectral_base().

◆ del_deriv()

void Lorene::Time_slice_conf::del_deriv ( ) const

protectedvirtualinherited

Deletes all the derived quantities.

Reimplemented from Lorene::Time_slice.

Definition at line 350 of file time_slice_conf.C.

References Lorene::Time_slice::del_deriv(), Lorene::Time_slice_conf::p_hdirac, Lorene::Time_slice_conf::p_ln_psi, Lorene::Time_slice_conf::p_psi4, Lorene::Time_slice_conf::p_tgamma, Lorene::Time_slice_conf::p_vec_X, and Lorene::Time_slice_conf::set_der_0x0().

◆ dnn()

const Vector & Lorene::Isol_hor::dnn ( ) const

virtual

Covariant derivative of the lapse function $\overline\nabla_i N$ at the current time step jtime.

Definition at line 482 of file isol_hor.C.

References dn_evol, and Lorene::Time_slice::jtime.

◆ dpsi()

const Vector & Lorene::Isol_hor::dpsi ( ) const

virtual

Covariant derivative with respect to the flat metric of the conformal factor $\overline\nabla_i \Psi$ at the current time step jtime.

Definition at line 488 of file isol_hor.C.

References dpsi_evol, and Lorene::Time_slice::jtime.

◆ expansion()

Scalar Lorene::Isol_hor::expansion ( ) const

Expansion of the outgoing null normal ( $\bf n + \bf s$ )

Definition at line 266 of file phys_param.C.

References Lorene::contract(), Lorene::Time_slice::gam(), Lorene::Time_slice_conf::k_dd(), and Lorene::Time_slice_conf::trk().

◆ gam()

const Metric & Lorene::Time_slice::gam ( ) const

inherited

Induced metric $\mathbf{\gamma}$ at the current time step (jtime )

Definition at line 98 of file time_slice_access.C.

References Lorene::Time_slice::gam_dd(), and Lorene::Time_slice::p_gamma.

◆ gam_dd()

const Sym_tensor & Lorene::Time_slice_conf::gam_dd ( ) const

virtualinherited

Induced metric (covariant components $\gamma_{ij}$ ) at the current time step (jtime )

Reimplemented from Lorene::Time_slice.

Definition at line 611 of file time_slice_conf.C.

References Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::jtime, Lorene::Time_slice_conf::psi4(), Lorene::Time_slice_conf::tgam(), and Lorene::Time_slice::the_time.

◆ gam_uu()

const Sym_tensor & Lorene::Time_slice_conf::gam_uu ( ) const

virtualinherited

Induced metric (contravariant components $\gamma^{ij}$ ) at the current time step (jtime )

Reimplemented from Lorene::Time_slice.

Definition at line 622 of file time_slice_conf.C.

References Lorene::Time_slice::gam_uu_evol, Lorene::Time_slice::jtime, Lorene::Time_slice_conf::psi4(), Lorene::Time_slice_conf::tgam(), and Lorene::Time_slice::the_time.

◆ get_boost_x()

double Lorene::Isol_hor::get_boost_x ( ) const

inline

Returns the boost velocity in x-direction.

Definition at line 445 of file isol_hor.h.

References boost_x.

◆ get_boost_z()

double Lorene::Isol_hor::get_boost_z ( ) const

inline

Returns the boost velocity in z-direction.

Definition at line 454 of file isol_hor.h.

References boost_z.

◆ get_decouple()

const Scalar Lorene::Isol_hor::get_decouple ( ) const

inline

Returns the function used to construct tkij_auto from tkij_tot .

Definition at line 519 of file isol_hor.h.

References decouple.

◆ get_latest_j()

int Lorene::Time_slice::get_latest_j ( ) const

inlineinherited

Gets the latest value of time step index.

Definition at line 346 of file time_slice.h.

References Lorene::Time_slice::jtime.

◆ get_mp()

const Map_af& Lorene::Isol_hor::get_mp ( ) const

inline

Returns the mapping (readonly).

Definition at line 418 of file isol_hor.h.

References mp.

◆ get_omega()

double Lorene::Isol_hor::get_omega ( ) const

inline

Returns the angular velocity.

Definition at line 436 of file isol_hor.h.

References omega.

◆ get_radius()

double Lorene::Isol_hor::get_radius ( ) const

inline

Returns the radius of the horizon.

Definition at line 426 of file isol_hor.h.

References radius.

◆ get_scheme_order()

int Lorene::Time_slice::get_scheme_order ( ) const

inlineinherited

Gets the order of the finite-differences scheme.

Definition at line 343 of file time_slice.h.

References Lorene::Time_slice::scheme_order.

◆ get_time()

const Evolution_std<double>& Lorene::Time_slice::get_time ( ) const

inlineinherited

Gets the time coordinate t at successive time steps.

Definition at line 349 of file time_slice.h.

References Lorene::Time_slice::the_time.

◆ hata()

const Sym_tensor & Lorene::Time_slice_conf::hata ( ) const

virtualinherited

Conformal representation $\hat{A}^{ij}$ of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .

Returns the value at the current time step (jtime ).

Definition at line 775 of file time_slice_conf.C.

References Lorene::Time_slice::beta(), Lorene::Sym_tensor::derive_lie(), Lorene::Vector::divergence(), Lorene::Time_slice_conf::ff, Lorene::Time_slice_conf::hata_evol, Lorene::Time_slice_conf::hh(), Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice::jtime, Lorene::Time_slice_conf::nn(), Lorene::Vector::ope_killing_conf(), Lorene::Time_slice_conf::psi(), Lorene::Time_slice_conf::psi4(), Lorene::Time_slice::scheme_order, and Lorene::Time_slice::the_time.

◆ hdirac()

const Vector & Lorene::Time_slice_conf::hdirac ( ) const

virtualinherited

Vector $H^i = {\cal D}_j \tilde\gamma^{ij}$ which vanishes in Dirac gauge.

Reimplemented in Lorene::Tslice_dirac_max.

Definition at line 818 of file time_slice_conf.C.

References Lorene::Time_slice_conf::ff, Lorene::Time_slice_conf::hh(), and Lorene::Time_slice_conf::p_hdirac.

◆ hh()

const Sym_tensor & Lorene::Time_slice_conf::hh	(	Param *	= `0x0`,
		Param *	= `0x0`
	)		const

virtualinherited

Deviation $h^{ij}$ of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ .

Returns the value at the current time step (jtime ).

Reimplemented in Lorene::Tslice_dirac_max.

Definition at line 761 of file time_slice_conf.C.

References Lorene::Time_slice_conf::hh_evol, and Lorene::Time_slice::jtime.

◆ init_bhole()

void Lorene::Isol_hor::init_bhole ( )

Sets the values of the fields to :

n_auto $= \frac{1}{2}-2\frac{a}{r}$
n_comp $= \frac{1}{2}$
psi_auto $= \frac{1}{2}+\frac{a}{r}$
psi_comp $= \frac{1}{2}$

a being the radius of the hole, the other fields being set to zero.

Definition at line 736 of file isol_hor.C.

References Lorene::Scalar::annule(), beta_auto_evol, beta_comp_evol, Lorene::Time_slice::beta_evol, dn_evol, dpsi_evol, Lorene::Time_slice_conf::ff, Lorene::Map::get_bvect_spher(), Lorene::Time_slice::jtime, mp, n_auto(), n_auto_evol, n_comp(), n_comp_evol, Lorene::Time_slice::n_evol, Lorene::Time_slice_conf::nn(), Lorene::Time_slice_conf::psi(), psi_auto(), psi_auto_evol, psi_comp(), psi_comp_evol, Lorene::Time_slice_conf::psi_evol, Lorene::Map::r, Lorene::Scalar::raccord(), radius, Lorene::Coord::set(), Lorene::Vector::set(), Lorene::Scalar::set_dzpuis(), Lorene::Tensor::set_etat_zero(), Lorene::Scalar::std_spectral_base(), and Lorene::Time_slice::the_time.

◆ init_bhole_seul()

void Lorene::Isol_hor::init_bhole_seul ( )

Initiates for a single black hole.

WARNING It supposes that the boost is zero and should only be used for an isolated black hole..

Definition at line 800 of file isol_hor.C.

References Lorene::Scalar::annule(), beta_auto_evol, beta_comp_evol, Lorene::Time_slice::beta_evol, dn_evol, dpsi_evol, Lorene::Time_slice_conf::ff, Lorene::Map::get_bvect_spher(), Lorene::Map::get_mg(), Lorene::Time_slice::jtime, mp, n_auto_evol, n_comp_evol, Lorene::Time_slice::n_evol, Lorene::Time_slice_conf::nn(), Lorene::Time_slice_conf::psi(), psi_auto_evol, psi_comp_evol, Lorene::Time_slice_conf::psi_evol, Lorene::Map::r, Lorene::Scalar::raccord(), radius, Lorene::Scalar::set_dzpuis(), Lorene::Scalar::set_etat_zero(), Lorene::Tensor::set_etat_zero(), Lorene::Scalar::set_outer_boundary(), Lorene::Scalar::std_spectral_base(), and Lorene::Time_slice::the_time.

◆ init_met_trK()

void Lorene::Isol_hor::init_met_trK ( )

Sets the 3-metric tilde to the flat metric and gamt_point, trK and trK_point to zero.

Definition at line 788 of file isol_hor.C.

References Lorene::Map::flat_met_spher(), gamt_point, met_gamt, mp, Lorene::Scalar::set_etat_zero(), Lorene::Tensor::set_etat_zero(), trK, and trK_point.

◆ initial_data_cts()

void Lorene::Time_slice_conf::initial_data_cts	(	const Sym_tensor &	uu,
		const Scalar &	trk_in,
		const Scalar &	trk_point,
		double	pdt,
		double	precis = `1.e-12`,
		int	method_poisson_vect = `6`,
		const char *	graph_device = `0x0`,
		const Scalar *	ener_dens = `0x0`,
		const Vector *	mom_dens = `0x0`,
		const Scalar *	trace_stress = `0x0`
	)

virtualinherited

Computes valid initial data by solving the constraint equations in the conformal thin-sandwich approach.

Parameters

uu	value of ${\tilde u}^{ij} = \partial h^{ij} /\partial t$ (freely specifiable data). This quantity must be trace-free with respect to the conformal metric $\tilde\gamma_{ij}$ , reflecting the unimodular character of $\tilde\gamma_{ij}$ .
trk_in	value of $K = K_i^{\ i}$ (freely specifiable data)
trk_point	value of $\partial K / \partial t$ (freely specifiable data)
pdt	time step, to be used in order to fill `depth` slices
precis	convergence threshold required to stop the iteration
method_poisson_vect	method to be used for solving vector Poisson equation (for the shift), see `Vector::poisson(double, const Metric_flat&, int) const`.
graph_device	name of type of graphical device: 0x0 (default value) will result in interactive choice; "/xwin" in X-Window display and "/n" in no output.
ener_dens	matter energy density E as measured by the Eulerian observer; this quantity is passed as a pointer, the null value of which (default) meaning E=0.
mom_dens	matter momentum density J as measured by the Eulerian observer; this quantity is passed as a pointer, the null value of which (default) meaning J=0.
trace_stress	trace of the matter stress S as measured by the Eulerian observer; this quantity is passed as a pointer, the null value of which (default) meaning S=0.

Reimplemented in Lorene::Tslice_dirac_max.

Definition at line 94 of file tslice_conf_init.C.

◆ k_dd()

const Sym_tensor & Lorene::Time_slice_conf::k_dd ( ) const

virtualinherited

Extrinsic curvature tensor (covariant components $K_{ij}$ ) at the current time step (jtime )

Reimplemented from Lorene::Time_slice.

Definition at line 633 of file time_slice_conf.C.

References Lorene::Time_slice::gam(), Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice_conf::k_uu(), and Lorene::Time_slice::the_time.

◆ k_uu()

const Sym_tensor & Lorene::Time_slice_conf::k_uu ( ) const

virtualinherited

Extrinsic curvature tensor (contravariant components $K^{ij}$ ) at the current time step (jtime )

Reimplemented from Lorene::Time_slice.

Definition at line 646 of file time_slice_conf.C.

References Lorene::Time_slice::gam(), Lorene::Time_slice_conf::hata(), Lorene::Time_slice::jtime, Lorene::Time_slice::k_uu_evol, Lorene::Time_slice_conf::psi(), Lorene::Time_slice_conf::psi4(), Lorene::Time_slice::the_time, and Lorene::Time_slice_conf::trk().

◆ kappa_hor()

double Lorene::Isol_hor::kappa_hor ( ) const

Surface gravity.

Definition at line 221 of file phys_param.C.

References ang_mom_hor(), Lorene::pow(), radius_hor(), and Lorene::sqrt().

◆ ln_psi()

const Scalar & Lorene::Time_slice_conf::ln_psi ( ) const

inherited

Logarithm of $\Psi$ at the current time step (jtime ).

Definition at line 722 of file time_slice_conf.C.

References Lorene::log(), Lorene::Time_slice_conf::p_ln_psi, Lorene::Time_slice_conf::psi(), and Lorene::Scalar::std_spectral_base().

◆ mass_hor()

double Lorene::Isol_hor::mass_hor ( ) const

Mass computed at the horizon.

Definition at line 209 of file phys_param.C.

References ang_mom_hor(), Lorene::pow(), radius_hor(), and Lorene::sqrt().

◆ met_kerr_perturb()

void Lorene::Isol_hor::met_kerr_perturb ( )

Initialisation of the metric tilde from equation (15) of Dain (2002).

The determinant of this conformal metric is not one.

Definition at line 898 of file isol_hor.C.

References Lorene::Metric::con(), Lorene::Metric_flat::con(), Lorene::Metric::cov(), Lorene::Metric::determinant(), Lorene::Time_slice_conf::ff, Lorene::Time_slice::gam(), Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice::jtime, met_gamt, Lorene::norme(), Lorene::pow(), set_psi(), Lorene::Scalar::std_spectral_base(), and Lorene::Time_slice::the_time.

◆ n_auto()

const Scalar & Lorene::Isol_hor::n_auto ( ) const

virtual

Lapse function $N_{auto}$ at the current time step jtime.

Definition at line 458 of file isol_hor.C.

References Lorene::Time_slice::jtime, and n_auto_evol.

◆ n_comp() [1/2]

const Scalar & Lorene::Isol_hor::n_comp ( ) const

virtual

Lapse function $N_{comp}$ at the current time step jtime.

Definition at line 464 of file isol_hor.C.

References Lorene::Time_slice::jtime, and n_comp_evol.

◆ n_comp() [2/2]

void Lorene::Isol_hor::n_comp ( const Isol_hor & comp )

Imports the part of N due to the companion hole comp .

The total N is then calculated.

It also imports the covariant derivative of N and construct the total $\nabla_i N$ .

Definition at line 580 of file isol_hor.C.

References Lorene::Tensor::dec_dzpuis(), Lorene::Scalar::derive_cov(), Lorene::Time_slice_conf::ff, Lorene::Map::get_bvect_cart(), Lorene::Scalar::import(), Lorene::Time_slice::jtime, mp, n_auto(), n_comp_evol, Lorene::Time_slice::n_evol, Lorene::Tensor::set_etat_qcq(), Lorene::Scalar::std_spectral_base(), and Lorene::Time_slice::the_time.

◆ nn()

const Scalar & Lorene::Time_slice_conf::nn ( ) const

virtualinherited

Lapse function N at the current time step (jtime )

Reimplemented from Lorene::Time_slice.

Definition at line 594 of file time_slice_conf.C.

References Lorene::Time_slice::jtime, Lorene::Time_slice::n_evol, Lorene::Time_slice_conf::npsi_evol, Lorene::Time_slice_conf::psi_evol, and Lorene::Time_slice::the_time.

◆ npsi()

const Scalar & Lorene::Time_slice_conf::npsi ( ) const

virtualinherited

Factor $N\Psi$ at the current time step (jtime ).

Definition at line 735 of file time_slice_conf.C.

References Lorene::Time_slice::jtime, Lorene::Time_slice::n_evol, Lorene::Time_slice_conf::npsi_evol, Lorene::Time_slice_conf::psi_evol, and Lorene::Time_slice::the_time.

◆ omega_hor()

double Lorene::Isol_hor::omega_hor ( ) const

Orbital velocity.

Definition at line 236 of file phys_param.C.

References ang_mom_hor(), Lorene::pow(), radius_hor(), and Lorene::sqrt().

◆ operator=()

void Lorene::Isol_hor::operator= ( const Isol_hor & isolhor_in )

Assignment to another Isol_hor.

Definition at line 346 of file isol_hor.C.

References aa_auto_evol, aa_comp_evol, aa_nn, aa_quad_evol, beta_auto_evol, beta_comp_evol, boost_x, boost_z, decouple, dn_evol, dpsi_evol, gamt_point, met_gamt, mp, n_auto_evol, n_comp_evol, nz, omega, Lorene::Time_slice_conf::operator=(), psi_auto_evol, psi_comp_evol, radius, regul, trK, and trK_point.

◆ operator>>()

ostream & Lorene::Isol_hor::operator>> ( ostream & flux ) const

protectedvirtual

Operator >> (virtual function called by the operator<<).

Reimplemented from Lorene::Time_slice_conf.

Definition at line 381 of file isol_hor.C.

References Lorene::Time_slice_conf::adm_mass(), ang_mom_adm(), ang_mom_hor(), area_hor(), boost_x, boost_z, mass_hor(), omega_hor(), Lorene::Time_slice_conf::operator>>(), and radius.

◆ psi()

const Scalar & Lorene::Time_slice_conf::psi ( ) const

virtualinherited

Conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .

$\Psi$ is defined by

$\Psi := \left( \frac{\det\gamma_{ij}}{\det f_{ij}} \right) ^{1/12}$

Returns the value at the current time step (jtime ).

Definition at line 696 of file time_slice_conf.C.

References Lorene::Time_slice::jtime, Lorene::Time_slice::n_evol, Lorene::Time_slice_conf::npsi_evol, Lorene::Time_slice_conf::psi_evol, and Lorene::Time_slice::the_time.

◆ psi4()

const Scalar & Lorene::Time_slice_conf::psi4 ( ) const

inherited

Factor $\Psi^4$ at the current time step (jtime ).

Definition at line 710 of file time_slice_conf.C.

References Lorene::Time_slice_conf::p_psi4, Lorene::pow(), Lorene::Time_slice_conf::psi(), and Lorene::Scalar::std_spectral_base().

◆ psi_auto()

const Scalar & Lorene::Isol_hor::psi_auto ( ) const

virtual

Conformal factor $\Psi_{auto}$ at the current time step jtime.

Definition at line 470 of file isol_hor.C.

References Lorene::Time_slice::jtime, and psi_auto_evol.

◆ psi_comp() [1/2]

const Scalar & Lorene::Isol_hor::psi_comp ( ) const

virtual

Conformal factor $\Psi_{comp}$ at the current time step jtime.

Definition at line 476 of file isol_hor.C.

References Lorene::Time_slice::jtime, and psi_comp_evol.

◆ psi_comp() [2/2]

void Lorene::Isol_hor::psi_comp ( const Isol_hor & comp )

Imports the part of $\Psi$ due to the companion hole comp .

The total $\Psi$ is then calculated.

It also imports the covariant derivative of $\Psi$ and construct the total $\nabla_i \Psi$ .

Definition at line 672 of file isol_hor.C.

References Lorene::Tensor::dec_dzpuis(), Lorene::Scalar::derive_cov(), Lorene::Time_slice_conf::ff, Lorene::Map::get_bvect_cart(), Lorene::Scalar::import(), Lorene::Time_slice::jtime, mp, psi_auto(), psi_comp_evol, Lorene::Time_slice_conf::psi_evol, Lorene::Tensor::set_etat_qcq(), Lorene::Scalar::std_spectral_base(), and Lorene::Time_slice::the_time.

◆ radial_vect_hor()

const Vector Lorene::Isol_hor::radial_vect_hor ( ) const

Vector radial normal.

Definition at line 98 of file phys_param.C.

References Lorene::Time_slice_conf::ff, Lorene::Time_slice_conf::gam_uu(), Lorene::Metric::get_mp(), Lorene::Metric_flat::get_triad(), Lorene::Vector::set(), Lorene::sqrt(), and Lorene::Vector::std_spectral_base().

◆ radius_hor()

double Lorene::Isol_hor::radius_hor ( ) const

Radius of the horizon.

Definition at line 170 of file phys_param.C.

References area_hor(), and Lorene::pow().

◆ regularisation()

double Lorene::Isol_hor::regularisation	(	const Vector &	shift_auto,
		const Vector &	shift_comp,
		double	ang_vel
	)

Corrects shift_auto in such a way that the total $A^{ij}$ is equal to zero in the horizon, which should ensure the regularity of $K^{ij}$ .

WARNING : this should only be used for a black hole in a binary system Bin_hor.

Parameters

comp	[input]: the part of $\beta^i$ generated by the companion hole.

Definition at line 91 of file regularisation.C.

References Lorene::Cmp::annule(), Lorene::Tensor::annule_domain(), Lorene::Scalar::annule_hard(), beta_auto_evol, Lorene::Valeur::c, Lorene::Vector::change_triad(), Lorene::Valeur::coef_i(), Lorene::diffrelmax(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_mg(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Map::get_rot_phi(), Lorene::Scalar::get_spectral_va(), Lorene::Tensor::get_triad(), Lorene::Scalar::import(), Lorene::Time_slice::jtime, Lorene::norme(), nz, Lorene::pow(), Lorene::Vector::set(), Lorene::Valeur::set_etat_c_qcq(), Lorene::Scalar::set_spectral_va(), Lorene::Vector::std_spectral_base(), and Lorene::Time_slice::the_time.

◆ regularise_one()

double Lorene::Isol_hor::regularise_one ( )

Corrects the shift in the innermost shell, so that it remains ${\mathcal{C}}^2$ and that $A^{ij}$ equals zero on the horizon.

return the relative difference between the shift before and after the regularisation.

WARNING this should only be used for an isolated black hole.

Definition at line 186 of file regularisation.C.

References Lorene::Time_slice::beta(), boost_x, Lorene::Vector::change_triad(), Lorene::Valeur::coef_i(), Lorene::Map::get_bvect_cart(), mp, omega, Lorene::Vector::set(), Lorene::Valeur::set_etat_c_qcq(), Lorene::Scalar::set_spectral_va(), Lorene::Map::x, and Lorene::Map::y.

◆ sauve()

void Lorene::Isol_hor::sauve	(	FILE *	fich,
		bool	partial_save
	)		const

virtual

Total or partial saves in a binary file.

Parameters

fich	binary file
partial_save	indicates whether the whole object must be saved.

Reimplemented from Lorene::Time_slice_conf.

Definition at line 404 of file isol_hor.C.

References beta_auto_evol, boost_x, boost_z, Lorene::Metric::con(), Lorene::Time_slice::depth, Lorene::fwrite_be(), gamt_point, Lorene::Time_slice::jtime, met_gamt, n_auto_evol, omega, psi_auto_evol, Lorene::Time_slice_conf::psi_evol, Lorene::Time_slice_conf::sauve(), Lorene::Scalar::sauve(), Lorene::Tensor_sym::sauve(), trK, and trK_point.

◆ save()

void Lorene::Time_slice::save ( const char * rootname ) const

inherited

Saves in a binary file.

The saved data is sufficient to restore the whole time slice via the constructor from file.

Parameters

rootname root for the file name; the current time step index will be appended to it.

Definition at line 464 of file time_slice.C.

References Lorene::Time_slice::beta(), Lorene::Time_slice::depth, Lorene::fwrite_be(), Lorene::Map::get_mg(), Lorene::Tensor::get_mp(), Lorene::Tensor::get_triad(), Lorene::Time_slice::jtime, Lorene::Time_slice::nn(), Lorene::Base_vect::sauve(), Lorene::Time_slice::sauve(), Lorene::Mg3d::sauve(), and Lorene::Map::sauve().

◆ set_AB_hata()

void Lorene::Time_slice_conf::set_AB_hata	(	const Scalar &	A_in,
		const Scalar &	B_in
	)

virtualinherited

Sets the potentials A and $\tilde{B}$ of the TT part $\hat{A}^{ij}$ (see the documentation of Sym_tensor for details).

Sets the value at the current time step (jtime ).

Definition at line 894 of file time_slice_conf.C.

References Lorene::Time_slice_conf::A_hata_evol, Lorene::Time_slice_conf::B_hata_evol, Lorene::Time_slice_conf::hata_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu_evol, and Lorene::Time_slice::the_time.

◆ set_boost_x()

void Lorene::Isol_hor::set_boost_x ( double bo )

inline

Sets the boost velocity in x-direction to bo .

Definition at line 449 of file isol_hor.h.

References boost_x.

◆ set_boost_z()

void Lorene::Isol_hor::set_boost_z ( double bo )

inline

Sets the boost velocity in z-direction to bo .

Definition at line 458 of file isol_hor.h.

References boost_z.

◆ set_der_0x0()

void Lorene::Time_slice_conf::set_der_0x0 ( ) const

protectedinherited

Sets to 0x0 all the pointers on derived quantities.

Definition at line 364 of file time_slice_conf.C.

References Lorene::Time_slice_conf::p_hdirac, Lorene::Time_slice_conf::p_ln_psi, Lorene::Time_slice_conf::p_psi4, Lorene::Time_slice_conf::p_tgamma, and Lorene::Time_slice_conf::p_vec_X.

◆ set_gamt()

void Lorene::Isol_hor::set_gamt ( const Metric & gam_tilde )

Sets the conformal metric to gam_tilde.

Definition at line 553 of file isol_hor.C.

References Lorene::Metric::con(), Lorene::Metric_flat::con(), Lorene::Time_slice_conf::ff, Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::gam_uu_evol, Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu_evol, met_gamt, Lorene::Time_slice::p_gamma, Lorene::Time_slice_conf::p_tgamma, and Lorene::Time_slice::the_time.

◆ set_hata()

void Lorene::Time_slice_conf::set_hata ( const Sym_tensor & hata_in )

virtualinherited

Sets the conformal representation $\hat{A}{ij}$ of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .

Sets the value at the current time step (jtime ), and updates the potentials A_hata_evol, B_hata_evol and p_vec_X accordingly.

Definition at line 537 of file time_slice_conf.C.

References Lorene::Time_slice_conf::A_hata_evol, Lorene::Time_slice_conf::B_hata_evol, Lorene::Time_slice_conf::hata_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu_evol, and Lorene::Time_slice::the_time.

◆ set_hata_from_XAB()

void Lorene::Time_slice_conf::set_hata_from_XAB	(	Param *	par_bc = `0x0`,
		Param *	par_mat = `0x0`
	)

virtualinherited

Sets the conformal representation $\hat{A}{ij}$ of the traceless part of the extrinsic curvature from its potentials A, $\tilde{B}$ and $ X^i $ .

These potentials must be up-to-date. It sets the value at the current time step (jtime ).

Definition at line 569 of file time_slice_conf.C.

References Lorene::Time_slice_conf::A_hata_evol, Lorene::Time_slice_conf::B_hata_evol, Lorene::Time_slice_conf::ff, Lorene::Tensor::get_mp(), Lorene::Time_slice_conf::hata_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu_evol, Lorene::Vector::ope_killing_conf(), Lorene::Time_slice_conf::p_vec_X, Lorene::Sym_tensor_tt::set_A_tildeB(), and Lorene::Time_slice::the_time.

◆ set_hata_TT()

void Lorene::Time_slice_conf::set_hata_TT ( const Sym_tensor_tt & hata_tt )

virtualinherited

Sets the TT part of $\hat{A}^{ij}$ (see member hata_evol ).

Sets the value at current time-step (jtime ) and updates the potentials A and $\tilde{B}$ .

Definition at line 549 of file time_slice_conf.C.

References Lorene::Time_slice_conf::A_hata_evol, Lorene::Time_slice_conf::B_hata_evol, Lorene::Sym_tensor::compute_A(), Lorene::Sym_tensor::compute_tilde_B_tt(), Lorene::Scalar::dec_dzpuis(), Lorene::Scalar::get_dzpuis(), Lorene::Time_slice_conf::hata_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu_evol, and Lorene::Time_slice::the_time.

◆ set_hh()

void Lorene::Time_slice_conf::set_hh ( const Sym_tensor & hh_in )

virtualinherited

Sets the deviation $h^{ij}$ of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ .

$h^{ij}$ must be such that $\det\tilde\gamma^{ij} = f^{-1}$ . Sets the value at the current time step (jtime ).

Reimplemented in Lorene::Tslice_dirac_max.

Definition at line 492 of file time_slice_conf.C.

References Lorene::Time_slice::adm_mass_evol, Lorene::Metric_flat::con(), Lorene::Metric_flat::determinant(), Lorene::Time_slice_conf::ff, Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::gam_uu_evol, Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice::jtime, Lorene::max(), Lorene::maxabs(), Lorene::Time_slice::p_gamma, Lorene::Time_slice_conf::p_hdirac, Lorene::Time_slice_conf::p_tgamma, and Lorene::Time_slice::the_time.

◆ set_mp()

Map_af& Lorene::Isol_hor::set_mp ( )

inline

Read/write of the mapping.

Definition at line 421 of file isol_hor.h.

References mp.

◆ set_nn()

void Lorene::Isol_hor::set_nn ( const Scalar & nn_in )

Sets the lapse.

Definition at line 543 of file isol_hor.C.

References aa_quad_evol, Lorene::Time_slice_conf::hata_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu_evol, Lorene::Time_slice::n_evol, and Lorene::Time_slice::the_time.

◆ set_npsi_del_n()

void Lorene::Time_slice_conf::set_npsi_del_n ( const Scalar & npsi_in )

virtualinherited

Sets the factor $N\Psi$ at the current time step (jtime ) and deletes the value of N.

Definition at line 481 of file time_slice_conf.C.

References Lorene::Time_slice::adm_mass_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::n_evol, Lorene::Time_slice_conf::npsi_evol, and Lorene::Time_slice::the_time.

◆ set_npsi_del_psi()

void Lorene::Time_slice_conf::set_npsi_del_psi ( const Scalar & npsi_in )

virtualinherited

Sets the factor $N\Psi$ at the current time step (jtime ) and deletes the value of $\Psi$ .

Definition at line 456 of file time_slice_conf.C.

References Lorene::Time_slice::adm_mass_evol, Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::gam_uu_evol, Lorene::Time_slice::jtime, Lorene::Time_slice_conf::npsi_evol, Lorene::Time_slice::p_gamma, Lorene::Time_slice_conf::p_ln_psi, Lorene::Time_slice_conf::p_psi4, Lorene::Time_slice_conf::psi_evol, and Lorene::Time_slice::the_time.

◆ set_omega()

void Lorene::Isol_hor::set_omega ( double ome )

inline

Sets the angular velocity to ome .

Definition at line 440 of file isol_hor.h.

References omega.

◆ set_psi()

void Lorene::Isol_hor::set_psi ( const Scalar & psi_in )

Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .

$\Psi$ is defined by

$\Psi := \left( \frac{\det\gamma_{ij}}{\det f_{ij}} \right) ^{1/12}$

Sets the value at the current time step (jtime ) and delete all quantities which depend on $\Psi$ .

Definition at line 518 of file isol_hor.C.

References Lorene::Time_slice::adm_mass_evol, Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::gam_uu_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu_evol, Lorene::Time_slice::p_gamma, Lorene::Time_slice_conf::p_ln_psi, Lorene::Time_slice_conf::p_psi4, Lorene::Time_slice_conf::psi_evol, and Lorene::Time_slice::the_time.

◆ set_psi_del_n()

void Lorene::Time_slice_conf::set_psi_del_n ( const Scalar & psi_in )

virtualinherited

Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .

$\Psi$ is defined by

$\Psi := \left( \frac{\det\gamma_{ij}}{\det f_{ij}} \right) ^{1/12}$

Sets the value at the current time step (jtime ) and deletes the value of N.

Definition at line 431 of file time_slice_conf.C.

References Lorene::Time_slice::adm_mass_evol, Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::gam_uu_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::n_evol, Lorene::Time_slice::p_gamma, Lorene::Time_slice_conf::p_ln_psi, Lorene::Time_slice_conf::p_psi4, Lorene::Time_slice_conf::psi_evol, and Lorene::Time_slice::the_time.

◆ set_psi_del_npsi()

void Lorene::Time_slice_conf::set_psi_del_npsi ( const Scalar & psi_in )

virtualinherited

Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .

$\Psi$ is defined by

$\Psi := \left( \frac{\det\gamma_{ij}}{\det f_{ij}} \right) ^{1/12}$

Sets the value at the current time step (jtime ) and deletes the value of $N\Psi$ .

Definition at line 407 of file time_slice_conf.C.

References Lorene::Time_slice::adm_mass_evol, Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::gam_uu_evol, Lorene::Time_slice::jtime, Lorene::Time_slice_conf::npsi_evol, Lorene::Time_slice::p_gamma, Lorene::Time_slice_conf::p_ln_psi, Lorene::Time_slice_conf::p_psi4, Lorene::Time_slice_conf::psi_evol, and Lorene::Time_slice::the_time.

◆ set_radius()

void Lorene::Isol_hor::set_radius ( double rad )

inline

Sets the radius of the horizon to rad .

Definition at line 431 of file isol_hor.h.

References radius.

◆ set_scheme_order()

void Lorene::Time_slice::set_scheme_order ( int ord )

inlineinherited

Sets the order of the finite-differences scheme.

Definition at line 334 of file time_slice.h.

References Lorene::Time_slice::scheme_order.

◆ source_b_tilde()

const Scalar Lorene::Isol_hor::source_b_tilde ( ) const

Source for b_tilde.

◆ source_beta()

const Vector Lorene::Isol_hor::source_beta ( ) const

◆ source_nn()

const Scalar Lorene::Isol_hor::source_nn ( ) const

◆ source_psi()

const Scalar Lorene::Isol_hor::source_psi ( ) const

Source for $\Psi$ .

Definition at line 111 of file sources_hor.C.

References aa_quad(), Lorene::Tensor::annule_domain(), Lorene::contract(), Lorene::Tensor::derive_cov(), Lorene::Scalar::derive_cov(), Lorene::Time_slice_conf::ff, Lorene::Metric_flat::get_triad(), Lorene::Time_slice_conf::hdirac(), Lorene::Time_slice_conf::hh(), Lorene::Scalar::inc_dzpuis(), met_gamt, mp, Lorene::Time_slice_conf::psi(), Lorene::Time_slice_conf::psi4(), Lorene::Metric::ricci_scal(), and trK.

◆ source_vector_b()

const Vector Lorene::Isol_hor::source_vector_b ( ) const

Source for vector_b.

◆ tgam()

virtual const Metric& Lorene::Isol_hor::tgam ( ) const

inlinevirtual

Conformal metric $\tilde\gamma_{ij} = \Psi^{-4} \gamma_{ij}$ Returns the value at the current time step (jtime ).

Reimplemented from Lorene::Time_slice_conf.

Definition at line 514 of file isol_hor.h.

References met_gamt.

◆ tradial_vect_hor()

const Vector Lorene::Isol_hor::tradial_vect_hor ( ) const

Vector radial normal tilde.

Definition at line 119 of file phys_param.C.

References Lorene::Metric::con(), Lorene::Time_slice_conf::ff, Lorene::Metric::get_mp(), Lorene::Metric_flat::get_triad(), met_gamt, Lorene::Vector::set(), Lorene::sqrt(), and Lorene::Vector::std_spectral_base().

◆ trk()

const Scalar & Lorene::Time_slice_conf::trk ( ) const

virtualinherited

Trace K of the extrinsic curvature at the current time step (jtime )

Reimplemented from Lorene::Time_slice.

Reimplemented in Lorene::Tslice_dirac_max.

Definition at line 799 of file time_slice_conf.C.

References Lorene::Time_slice::beta(), Lorene::contract(), Lorene::Vector::divergence(), Lorene::Time_slice_conf::ff, Lorene::Scalar::inc_dzpuis(), Lorene::Time_slice::jtime, Lorene::Time_slice_conf::ln_psi(), Lorene::Time_slice_conf::nn(), Lorene::Time_slice_conf::psi(), Lorene::Time_slice_conf::psi_evol, Lorene::Time_slice::scheme_order, Lorene::Time_slice::the_time, and Lorene::Time_slice::trk_evol.

◆ update_aa()

void Lorene::Isol_hor::update_aa ( )

Conformal representation $A^{ij}$ of the traceless part of the extrinsic curvature: $A^{ij} = \Psi^4 \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .

Definition at line 845 of file isol_hor.C.

References aa_quad_evol, Lorene::Time_slice::beta(), Lorene::contract(), gamt_point, Lorene::Map::get_bvect_spher(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Time_slice::jtime, met_gamt, mp, Lorene::Time_slice_conf::nn(), Lorene::Vector::ope_killing_conf(), Lorene::Time_slice_conf::psi(), Lorene::Time_slice_conf::psi4(), regul, regularise_one(), Lorene::Time_slice_conf::set_hata(), and Lorene::Time_slice::the_time.

◆ vec_X()

const Vector & Lorene::Time_slice_conf::vec_X ( int method_poisson = 6 ) const

virtualinherited

Vector $ X^i $ representing the longitudinal part of $\hat{A}^{ij}$ .

(see the documentation of hata_evol)

Definition at line 828 of file time_slice_conf.C.

References Lorene::Time_slice_conf::ff, Lorene::Time_slice_conf::hata_evol, Lorene::Time_slice::jtime, and Lorene::Time_slice_conf::p_vec_X.

◆ viriel_seul()

double Lorene::Isol_hor::viriel_seul ( ) const

Computes the viriel error, that is the difference between the ADM and the Komar masses, calculated by the asymptotic behaviours of respectively $\Psi$ and N .

WARNING this should only be used for an isolated black hole.

◆ vv_bound_cart()

const Vector Lorene::Isol_hor::vv_bound_cart ( double om ) const

Vector $ V^i $ for boundary conditions in cartesian.

Definition at line 1254 of file bound_hor.C.

References Lorene::Scalar::annule_hard(), b_tilde(), Lorene::Time_slice::beta(), Lorene::Vector::change_triad(), Lorene::Metric::con(), Lorene::contract(), Lorene::Map::cosp, Lorene::Map::cost, Lorene::Scalar::dec_dzpuis(), Lorene::Tensor::derive_cov(), Lorene::Tensor::down(), Lorene::Time_slice_conf::ff, Lorene::Time_slice::gam(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Map::get_mg(), Lorene::Map::get_rot_phi(), Lorene::Scalar::inc_dzpuis(), kappa_hor(), met_gamt, mp, Lorene::Time_slice_conf::nn(), Lorene::Metric::radial_vect(), Lorene::Coord::set(), Lorene::Vector::set(), Lorene::Tensor::set(), Lorene::Scalar::set_dzpuis(), Lorene::Map::sinp, Lorene::Map::sint, Lorene::Mg3d::std_base_vect_cart(), Lorene::Time_slice_conf::trk(), Lorene::Map::xa, and Lorene::Map::ya.

◆ vv_bound_cart_bin()

const Vector Lorene::Isol_hor::vv_bound_cart_bin	(	double	om,
		int	hole = `0`
	)		const

Vector $ V^i $ for boundary conditions in cartesian for binary systems.

Definition at line 1382 of file bound_hor.C.

References Lorene::Map::get_bvect_cart(), and mp.

Member Data Documentation

◆ A_hata_evol

Evolution_std<Scalar> Lorene::Time_slice_conf::A_hata_evol

mutableprotectedinherited

Potential A associated with the symmetric tensor $\hat{A}^{ij}_{TT}$ .

(see documentation of Sym_tensor::p_aaa).

Definition at line 550 of file time_slice.h.

◆ aa_auto_evol

Evolution_std<Sym_tensor> Lorene::Isol_hor::aa_auto_evol

mutableprotected

Values at successive time steps of the components $A^{ij}_{auto}$ of the conformal representation of the traceless part of the extrinsic curvature:

Definition at line 310 of file isol_hor.h.

◆ aa_comp_evol

Evolution_std<Sym_tensor> Lorene::Isol_hor::aa_comp_evol

mutableprotected

Values at successive time steps of the components $A^{ij}_{comp}$ of the conformal representation of the traceless part of the extrinsic curvature:

Definition at line 316 of file isol_hor.h.

◆ aa_nn

Evolution_std<Sym_tensor> Lorene::Isol_hor::aa_nn

mutableprotected

Values at successive time steps of the components $A^{ij}*2N$ .

Definition at line 320 of file isol_hor.h.

◆ aa_quad_evol

Evolution_std<Scalar> Lorene::Isol_hor::aa_quad_evol

mutableprotected

Values at successive time steps of the components $A^{ij}A_{ij}$ .

Definition at line 323 of file isol_hor.h.

◆ adm_mass_evol

Evolution_full<Tbl> Lorene::Time_slice::adm_mass_evol

mutableprotectedinherited

ADM mass at each time step, since the creation of the slice.

At a given time step j, adm_mass_evol[j] is a 1-D Tbl of size the number nz of domains, containing the "ADM mass" evaluated at the outer boundary of each domain. The true ADM mass is thus the last value, i.e. adm_mass_evol[j](nz-1).

Definition at line 236 of file time_slice.h.

◆ B_hata_evol

Evolution_std<Scalar> Lorene::Time_slice_conf::B_hata_evol

mutableprotectedinherited

Potential $\tilde{B}$ associated with the symmetric tensor $\hat{A}^{ij}_{TT}$ .

(see documentation of Sym_tensor::p_tilde_b).

Definition at line 555 of file time_slice.h.

◆ beta_auto_evol

Evolution_std<Vector> Lorene::Isol_hor::beta_auto_evol

mutableprotected

Values at successive time steps of the shift function $\beta^i_{auto}$ .

Definition at line 301 of file isol_hor.h.

◆ beta_comp_evol

Evolution_std<Vector> Lorene::Isol_hor::beta_comp_evol

mutableprotected

Values at successive time steps of the shift function $\beta^i_{comp}$ .

Definition at line 304 of file isol_hor.h.

◆ beta_evol

Evolution_std<Vector> Lorene::Time_slice::beta_evol

mutableprotectedinherited

Values at successive time steps of the shift vector $\beta^i$ .

Definition at line 222 of file time_slice.h.

◆ boost_x

double Lorene::Isol_hor::boost_x

protected

Boost velocity in x-direction.

Definition at line 272 of file isol_hor.h.

◆ boost_z

double Lorene::Isol_hor::boost_z

protected

Boost velocity in z-direction.

Definition at line 275 of file isol_hor.h.

◆ decouple

Scalar Lorene::Isol_hor::decouple

protected

Function used to construct $A^{ij}_{auto}$ from the total $A^{ij}$ .

Only used for a binary system.

Mainly this Scalar is 1 around the hole and 0 around the companion and the sum of decouple for the hole and his companion is 1 everywhere.

Definition at line 345 of file isol_hor.h.

◆ depth

int Lorene::Time_slice::depth

protectedinherited

Number of stored time slices.

Definition at line 182 of file time_slice.h.

◆ dn_evol

Evolution_std<Vector> Lorene::Isol_hor::dn_evol

mutableprotected

Values at successive time steps of the covariant derivative of the lapse with respect to the flat metric $\overline\nabla_i N$ .

Definition at line 294 of file isol_hor.h.

◆ dpsi_evol

Evolution_std<Vector> Lorene::Isol_hor::dpsi_evol

mutableprotected

Values at successive time steps of the covariant derivative of the conformal factor $\overline\nabla_i \Psi$ .

Definition at line 298 of file isol_hor.h.

◆ ff

const Metric_flat& Lorene::Time_slice_conf::ff

protectedinherited

Pointer on the flat metric $f_{ij}$ with respect to which the conformal decomposition is performed.

Definition at line 510 of file time_slice.h.

◆ gam_dd_evol

Evolution_std<Sym_tensor> Lorene::Time_slice::gam_dd_evol

mutableprotectedinherited

Values at successive time steps of the covariant components of the induced metric $\gamma_{ij}$ .

Definition at line 201 of file time_slice.h.

◆ gam_uu_evol

Evolution_std<Sym_tensor> Lorene::Time_slice::gam_uu_evol

mutableprotectedinherited

Values at successive time steps of the contravariant components of the induced metric $\gamma^{ij}$ .

Definition at line 206 of file time_slice.h.

◆ gamt_point

Sym_tensor Lorene::Isol_hor::gamt_point

protected

Time derivative of the 3-metric tilde.

Definition at line 329 of file isol_hor.h.

◆ hata_evol

Evolution_std<Sym_tensor> Lorene::Time_slice_conf::hata_evol

mutableprotectedinherited

Values at successive time steps of the components $\hat{A}^{ij}$ .

It is the conformal representation of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ . One can uniquely (up to the boundary conditions) define the decomposition: $\hat{A}^{ij} = {\cal D}^i X^j + {\cal D}^j X^i - \frac{2}{3} {\cal D}_k X^k f^{ij} + \hat{A}^{ij}_{TT}$ , where $ X^i $ represents the longitudinal part and $\hat{A}^{ij}_{TT}$ is the transverse-traceless part.

Definition at line 545 of file time_slice.h.

◆ hh_evol

Evolution_std<Sym_tensor> Lorene::Time_slice_conf::hh_evol

mutableprotectedinherited

Values at successive time steps of the components $h^{ij}$ .

It is the deviation of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ .

Definition at line 533 of file time_slice.h.

◆ jtime

int Lorene::Time_slice::jtime

protectedinherited

Time step index of the latest slice.

Definition at line 193 of file time_slice.h.

◆ k_dd_evol

Evolution_std<Sym_tensor> Lorene::Time_slice::k_dd_evol

mutableprotectedinherited

Values at successive time steps of the covariant components of the extrinsic curvature tensor $K_{ij}$ .

Definition at line 211 of file time_slice.h.

◆ k_uu_evol

Evolution_std<Sym_tensor> Lorene::Time_slice::k_uu_evol

mutableprotectedinherited

Values at successive time steps of the contravariant components of the extrinsic curvature tensor $K^{ij}$ .

Definition at line 216 of file time_slice.h.

◆ met_gamt

Metric Lorene::Isol_hor::met_gamt

protected

3 metric tilde

Definition at line 326 of file isol_hor.h.

◆ mp

Map_af& Lorene::Isol_hor::mp

protected

Affine mapping.

Definition at line 260 of file isol_hor.h.

◆ n_auto_evol

Evolution_std<Scalar> Lorene::Isol_hor::n_auto_evol

mutableprotected

Values at successive time steps of the lapse function $N_{auto}$ .

Definition at line 281 of file isol_hor.h.

◆ n_comp_evol

Evolution_std<Scalar> Lorene::Isol_hor::n_comp_evol

mutableprotected

Values at successive time steps of the lapse function $N_{comp}$ .

Definition at line 284 of file isol_hor.h.

◆ n_evol

Evolution_std<Scalar> Lorene::Time_slice::n_evol

mutableprotectedinherited

Values at successive time steps of the lapse function N.

Definition at line 219 of file time_slice.h.

◆ npsi_evol

Evolution_std<Scalar> Lorene::Time_slice_conf::npsi_evol

mutableprotectedinherited

Values at successive time steps of the factor $N\Psi$ .

Definition at line 525 of file time_slice.h.

◆ nz

int Lorene::Isol_hor::nz

protected

Number of zones.

Definition at line 263 of file isol_hor.h.

◆ omega

double Lorene::Isol_hor::omega

protected

Angular velocity in LORENE's units.

Definition at line 269 of file isol_hor.h.

◆ p_gamma

Metric* Lorene::Time_slice::p_gamma

mutableprotectedinherited

Pointer on the induced metric at the current time step (jtime)

Definition at line 242 of file time_slice.h.

◆ p_hdirac

Vector* Lorene::Time_slice_conf::p_hdirac

mutableprotectedinherited

Pointer on the vector $H^i = {\cal D}_j \tilde\gamma^{ij}$ (which vanishes in Dirac gauge), at the current time step (jtime).

Definition at line 574 of file time_slice.h.

◆ p_ln_psi

Scalar* Lorene::Time_slice_conf::p_ln_psi

mutableprotectedinherited

Pointer on the logarithm of $\Psi$ at the current time step (jtime)

Definition at line 569 of file time_slice.h.

◆ p_psi4

Scalar* Lorene::Time_slice_conf::p_psi4

mutableprotectedinherited

Pointer on the factor $\Psi^4$ at the current time step (jtime)

Definition at line 566 of file time_slice.h.

◆ p_tgamma

Metric* Lorene::Time_slice_conf::p_tgamma

mutableprotectedinherited

Pointer on the conformal metric $\tilde\gamma_{ij}$ at the current time step (jtime)

Definition at line 563 of file time_slice.h.

◆ p_vec_X

Vector* Lorene::Time_slice_conf::p_vec_X

mutableprotectedinherited

Pointer on the vector $ X^i $ representing the longitudinal part of $\hat{A}^{ij}$ .

(see the documentation of hata_evol)

Definition at line 580 of file time_slice.h.

◆ psi_auto_evol

Evolution_std<Scalar> Lorene::Isol_hor::psi_auto_evol

mutableprotected

Values at successive time steps of the conformal factor $\Psi_{auto}$ .

Definition at line 287 of file isol_hor.h.

◆ psi_comp_evol

Evolution_std<Scalar> Lorene::Isol_hor::psi_comp_evol

mutableprotected

Values at successive time steps of the lapse function $\Psi_{comp}$ .

Definition at line 290 of file isol_hor.h.

◆ psi_evol

Evolution_std<Scalar> Lorene::Time_slice_conf::psi_evol

mutableprotectedinherited

Values at successive time steps of the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .

$\Psi$ is defined by

$\Psi := \left( \frac{\det\gamma_{ij}}{\det f_{ij}} \right) ^{1/12}$

Definition at line 520 of file time_slice.h.

◆ radius

double Lorene::Isol_hor::radius

protected

Radius of the horizon in LORENE's units.

Definition at line 266 of file isol_hor.h.

◆ regul

double Lorene::Isol_hor::regul

protected

Intensity of the correction on the shift vector.

Definition at line 278 of file isol_hor.h.

◆ scheme_order

int Lorene::Time_slice::scheme_order

protectedinherited

Order of the finite-differences scheme for the computation of time derivatives.

This order is not constant and can be adjusted via set_scheme_order() .

Definition at line 190 of file time_slice.h.

◆ the_time

Evolution_std<double> Lorene::Time_slice::the_time

protectedinherited

Time label of each slice.

Definition at line 196 of file time_slice.h.

◆ trK

Scalar Lorene::Isol_hor::trK

protected

Trace of the extrinsic curvature.

Definition at line 332 of file isol_hor.h.

◆ trk_evol

Evolution_std<Scalar> Lorene::Time_slice::trk_evol

mutableprotectedinherited

Values at successive time steps of the trace K of the extrinsic curvature.

Definition at line 227 of file time_slice.h.

◆ trK_point

Scalar Lorene::Isol_hor::trK_point

protected

Time derivative of the trace of the extrinsic curvature.

Definition at line 335 of file isol_hor.h.

The documentation for this class was generated from the following files:

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Isol_hor() [1/4]

◆ Isol_hor() [2/4]

◆ Isol_hor() [3/4]

◆ Isol_hor() [4/4]

◆ ~Isol_hor()

Member Function Documentation

◆ A_hata()

◆ aa()

◆ aa_auto()

◆ aa_comp()

◆ aa_quad()

◆ adm_mass()

◆ ang_mom_adm()

◆ ang_mom_hor()

◆ area_hor()

◆ axi_break()

◆ B_hata()

◆ b_tilde()

◆ beta()

◆ beta_auto()

◆ beta_boost_x()

◆ beta_boost_z()

◆ beta_comp() [1/2]

◆ beta_comp() [2/2]

◆ boundary_b_tilde_Dir()

◆ boundary_b_tilde_Neu()

◆ boundary_beta_phi()

◆ boundary_beta_r()

◆ boundary_beta_theta()

◆ boundary_beta_x()

◆ boundary_beta_y()

◆ boundary_beta_z()

◆ boundary_nn_Dir()

◆ boundary_nn_Dir_eff()

◆ boundary_nn_Dir_kk()

◆ boundary_nn_Dir_lapl()

◆ boundary_nn_Neu_Cook()

◆ boundary_nn_Neu_eff()

◆ boundary_nn_Neu_kk()

◆ boundary_psi_app_hor()

◆ boundary_psi_Dir()

◆ boundary_psi_Dir_evol()

◆ boundary_psi_Dir_spat()

◆ boundary_psi_Neu_evol()

◆ boundary_psi_Neu_spat()

◆ boundary_vv_x()

◆ boundary_vv_x_bin()

◆ boundary_vv_y()

◆ boundary_vv_y_bin()

◆ boundary_vv_z()

◆ boundary_vv_z_bin()

◆ check_dynamical_equations()

◆ check_hamiltonian_constraint()

◆ check_momentum_constraint()

◆ check_psi_dot()

◆ compute_X_from_momentum_constraint()

◆ darea_hor()

◆ del_deriv()

◆ dnn()

◆ dpsi()

◆ expansion()

◆ gam()

◆ gam_dd()

◆ gam_uu()

◆ get_boost_x()

◆ get_boost_z()

◆ get_decouple()

◆ get_latest_j()

◆ get_mp()

◆ get_omega()

◆ get_radius()

◆ get_scheme_order()

◆ get_time()

◆ hata()