Spacelike time slice of a 3+1 spacetime with conformal decomposition. More...

#include <time_slice.h>

Inheritance diagram for Lorene::Time_slice_conf:

Public Member Functions
	Time_slice_conf (const Scalar &lapse_in, const Vector &shift_in, const Metric_flat &ff_in, const Scalar &psi_in, const Sym_tensor &hh_in, const Sym_tensor &hata_in, const Scalar &trk_in, int depth_in=3)
	Constructor from conformal decomposition. More...

	Time_slice_conf (const Scalar &lapse_in, const Vector &shift_in, const Sym_tensor &gamma_in, const Sym_tensor &kk_in, const Metric_flat &ff_in, int depth_in=3)
	Constructor from physical metric. More...

	Time_slice_conf (const Map &mp, const Base_vect &triad, const Metric_flat &ff_in, int depth_in=3)
	Constructor as standard time slice of flat spacetime (Minkowski). More...

	Time_slice_conf (const Map &mp, const Base_vect &triad, const Metric_flat &ff_in, FILE *fich, bool partial_read, int depth_in=3)
	Constructor from binary file. More...

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

virtual	~Time_slice_conf ()
	Destructor. More...

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

void	operator= (const Time_slice &)
	Assignment to a `Time_slice`. 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 Metric &	tgam () const
	Conformal metric $\tilde\gamma_{ij} = \Psi^{-4} \gamma_{ij}$ Returns the value 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 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...

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

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

Protected Attributes
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...

Detailed Description

Spacelike time slice of a 3+1 spacetime with conformal decomposition.

()

Definition at line 501 of file time_slice.h.

Constructor & Destructor Documentation

◆ Time_slice_conf() [1/5]

Lorene::Time_slice_conf::Time_slice_conf	(	const Scalar &	lapse_in,
		const Vector &	shift_in,
		const Metric_flat &	ff_in,
		const Scalar &	psi_in,
		const Sym_tensor &	hh_in,
		const Sym_tensor &	hata_in,
		const Scalar &	trk_in,
		int	depth_in = `3`
	)

Constructor from conformal decomposition.

Parameters

lapse_in	lapse function N
shift_in	shift vector
ff_in	reference flat metric with respect to which the conformal decomposition is performed
psi_in	conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$
hh_in	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 $\det\tilde\gamma^{ij} = f^{-1}$ .
hata_in	conformal representation $A^{ij}$ of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$
trk_in	trace K of the extrinsic curvature
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 121 of file time_slice_conf.C.

References A_hata(), B_hata(), Lorene::Time_slice::beta_evol, Lorene::Metric_flat::con(), Lorene::Metric_flat::determinant(), ff, Lorene::Tensor::get_index_type(), Lorene::Time_slice::jtime, Lorene::max(), Lorene::maxabs(), Lorene::Time_slice::n_evol, set_der_0x0(), Lorene::Time_slice::the_time, and Lorene::Time_slice::trk_evol.

◆ Time_slice_conf() [2/5]

Lorene::Time_slice_conf::Time_slice_conf	(	const Scalar &	lapse_in,
		const Vector &	shift_in,
		const Sym_tensor &	gamma_in,
		const Sym_tensor &	kk_in,
		const Metric_flat &	ff_in,
		int	depth_in = `3`
	)

Constructor from physical metric.

The conformal decomposition is performed by the constructor.

Parameters

lapse_in	lapse function N
shift_in	shift vector
gamma_in	induced metric (covariant or contravariant components)
kk_in	extrinsic curvature (covariant or contravariant components)
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 175 of file time_slice_conf.C.

References A_hata(), B_hata(), Lorene::Metric::con(), Lorene::Metric_flat::con(), Lorene::Metric::determinant(), Lorene::Metric_flat::determinant(), ff, hata_evol, hh_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::k_uu(), Lorene::Time_slice::p_gamma, p_psi4, Lorene::pow(), psi_evol, set_der_0x0(), Lorene::Scalar::std_spectral_base(), Lorene::Time_slice::the_time, and Lorene::Time_slice::trk_evol.

◆ Time_slice_conf() [3/5]

Lorene::Time_slice_conf::Time_slice_conf	(	const Map &	mp,
		const Base_vect &	triad,
		const Metric_flat &	ff_in,
		int	depth_in = `3`
	)

Constructor as standard time slice of flat spacetime (Minkowski).

Parameters

mp	Mapping on which the various Lorene fields will be constructed
triad	vector basis with respect to which the various tensor components will be defined
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 212 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, hata_evol, hh_evol, Lorene::Time_slice::jtime, npsi_evol, psi_evol, set_der_0x0(), Lorene::Scalar::set_etat_one(), Lorene::Scalar::set_etat_zero(), Lorene::Tensor::set_etat_zero(), Lorene::Scalar::std_spectral_base(), and Lorene::Time_slice::the_time.

◆ Time_slice_conf() [4/5]

Lorene::Time_slice_conf::Time_slice_conf	(	const Map &	mp,
		const Base_vect &	triad,
		const Metric_flat &	ff_in,
		FILE *	fich,
		bool	partial_read,
		int	depth_in = `3`
	)

Constructor from binary file.

The binary file must have been created by method save.

Parameters

mp	Mapping on which the various Lorene fields will be constructed
triad	vector basis with respect to which the various tensor components will be defined
ff_in	reference flat metric with respect to which the conformal decomposition is performed
fich	file containing the saved `Time_slice_conf`
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; the given must coincide with that stored in the file.

Definition at line 253 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, Lorene::Time_slice::depth, Lorene::fread_be(), Lorene::Map::get_mg(), hata_evol, Lorene::Time_slice::jtime, psi_evol, set_der_0x0(), and Lorene::Time_slice::the_time.

◆ Time_slice_conf() [5/5]

Lorene::Time_slice_conf::Time_slice_conf ( const Time_slice_conf & tin )

Copy constructor.

Definition at line 323 of file time_slice_conf.C.

References set_der_0x0().

◆ ~Time_slice_conf()

Lorene::Time_slice_conf::~Time_slice_conf ( )

virtual

Destructor.

Definition at line 340 of file time_slice_conf.C.

References del_deriv().

Member Function Documentation

◆ A_hata()

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

virtual

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

◆ aa()

Sym_tensor Lorene::Time_slice_conf::aa ( ) const

virtual

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 hata(), psi(), and psi4().

◆ adm_mass()

double Lorene::Time_slice_conf::adm_mass ( ) const

virtual

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

◆ B_hata()

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

virtual

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

◆ 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.

◆ 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

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.

References Lorene::abs(), Lorene::Time_slice::beta(), Lorene::contract(), Lorene::Scalar::dec_dzpuis(), Lorene::Vector::divergence(), ff, Lorene::Time_slice::jtime, ln_psi(), Lorene::max(), Lorene::Time_slice::n_evol, nn(), npsi(), npsi_evol, psi(), psi_evol, Lorene::Time_slice::scheme_order, and trk().

◆ 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`
	)

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().

◆ del_deriv()

void Lorene::Time_slice_conf::del_deriv ( ) const

protectedvirtual

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(), p_hdirac, p_ln_psi, p_psi4, p_tgamma, p_vec_X, and set_der_0x0().

◆ 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

virtual

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, psi4(), tgam(), and Lorene::Time_slice::the_time.

◆ gam_uu()

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

virtual

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, psi4(), tgam(), and Lorene::Time_slice::the_time.

◆ 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_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

virtual

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(), ff, hata_evol, hh(), hh_evol, Lorene::Time_slice::jtime, nn(), Lorene::Vector::ope_killing_conf(), psi(), psi4(), Lorene::Time_slice::scheme_order, and Lorene::Time_slice::the_time.

◆ hdirac()

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

virtual

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 ff, hh(), and p_hdirac.

◆ hh()

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

virtual

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 hh_evol, and Lorene::Time_slice::jtime.

◆ 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`
	)

virtual

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.

References aa(), Lorene::Time_slice::beta(), Lorene::Scalar::check_dzpuis(), Lorene::contract(), Lorene::Scalar::derive_con(), Lorene::Tensor::derive_cov(), Lorene::Scalar::derive_cov(), Lorene::Vector::derive_lie(), Lorene::Sym_tensor::divergence(), Lorene::Vector::divergence(), ff, Lorene::Scalar::get_etat(), Lorene::Map::get_mg(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_nzone(), Lorene::Tensor::get_triad(), hdirac(), hh(), Lorene::Tensor::inc_dzpuis(), Lorene::Scalar::inc_dzpuis(), Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu_evol, ln_psi(), Lorene::max(), Lorene::maxabs(), nn(), Lorene::Scalar::poisson(), psi(), psi4(), Lorene::Metric::ricci_scal(), Lorene::Scalar::set_etat_zero(), Lorene::Tensor::set_etat_zero(), set_hata(), tgam(), Lorene::Time_slice::the_time, Lorene::Tensor::trace(), trk(), Lorene::Time_slice::trk_evol, Lorene::Tensor::up_down(), and Lorene::Map::val_r().

◆ k_dd()

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

virtual

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, k_uu(), and Lorene::Time_slice::the_time.

◆ k_uu()

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

virtual

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

◆ ln_psi()

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

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

Definition at line 722 of file time_slice_conf.C.

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

◆ nn()

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

virtual

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, npsi_evol, psi_evol, and Lorene::Time_slice::the_time.

◆ npsi()

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

virtual

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, npsi_evol, psi_evol, and Lorene::Time_slice::the_time.

◆ operator=() [1/2]

void Lorene::Time_slice_conf::operator= ( const Time_slice_conf & tin )

Assignment to another Time_slice_conf.

Definition at line 379 of file time_slice_conf.C.

References A_hata_evol, B_hata_evol, del_deriv(), hata_evol, hh_evol, npsi_evol, Lorene::Time_slice::operator=(), and psi_evol.

◆ operator=() [2/2]

void Lorene::Time_slice_conf::operator= ( const Time_slice & tin )

Assignment to a Time_slice.

Definition at line 394 of file time_slice_conf.C.

References del_deriv(), and Lorene::Time_slice::operator=().

◆ operator>>()

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

protectedvirtual

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

Reimplemented from Lorene::Time_slice.

Reimplemented in Lorene::Tslice_dirac_max, and Lorene::Isol_hor.

Definition at line 944 of file time_slice_conf.C.

References ff, Lorene::Metric_flat::get_triad(), hata_evol, hh_evol, Lorene::Time_slice::jtime, Lorene::maxabs(), npsi_evol, Lorene::Time_slice::operator>>(), p_hdirac, p_ln_psi, p_psi4, p_tgamma, p_vec_X, and psi_evol.

◆ psi()

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

virtual

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, npsi_evol, psi_evol, and Lorene::Time_slice::the_time.

◆ psi4()

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

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

Definition at line 710 of file time_slice_conf.C.

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

◆ sauve()

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

protectedvirtual

Total or partial saves in a binary file.

This protected method is to be called either from public method save or from method sauve of a derived class.

Parameters

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

Reimplemented from Lorene::Time_slice.

Reimplemented in Lorene::Tslice_dirac_max, and Lorene::Isol_hor.

Definition at line 977 of file time_slice_conf.C.

References A_hata(), A_hata_evol, B_hata(), B_hata_evol, Lorene::Time_slice::depth, Lorene::fwrite_be(), hata(), hata_evol, Lorene::Time_slice::jtime, psi(), psi_evol, and Lorene::Time_slice::sauve().

◆ 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
	)

virtual

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 A_hata_evol, B_hata_evol, 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_der_0x0()

void Lorene::Time_slice_conf::set_der_0x0 ( ) const

protected

Sets to 0x0 all the pointers on derived quantities.

Definition at line 364 of file time_slice_conf.C.

References p_hdirac, p_ln_psi, p_psi4, p_tgamma, and p_vec_X.

◆ set_hata()

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

virtual

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 A_hata_evol, B_hata_evol, 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`
	)

virtual

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 A_hata_evol, B_hata_evol, ff, Lorene::Tensor::get_mp(), hata_evol, Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu_evol, Lorene::Vector::ope_killing_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 )

virtual

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 A_hata_evol, B_hata_evol, Lorene::Sym_tensor::compute_A(), Lorene::Sym_tensor::compute_tilde_B_tt(), Lorene::Scalar::dec_dzpuis(), Lorene::Scalar::get_dzpuis(), 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 )

virtual

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(), ff, Lorene::Time_slice::gam_dd_evol, Lorene::Time_slice::gam_uu_evol, hh_evol, Lorene::Time_slice::jtime, Lorene::max(), Lorene::maxabs(), Lorene::Time_slice::p_gamma, p_hdirac, p_tgamma, and Lorene::Time_slice::the_time.

◆ set_npsi_del_n()

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

virtual

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, 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 )

virtual

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, npsi_evol, Lorene::Time_slice::p_gamma, p_ln_psi, p_psi4, 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 )

virtual

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, p_ln_psi, p_psi4, 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 )

virtual

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, npsi_evol, Lorene::Time_slice::p_gamma, p_ln_psi, p_psi4, psi_evol, and Lorene::Time_slice::the_time.

◆ 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.

◆ tgam()

const Metric & Lorene::Time_slice_conf::tgam ( ) const

virtual

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

Reimplemented in Lorene::Isol_hor.

Definition at line 750 of file time_slice_conf.C.

References Lorene::Metric_flat::con(), ff, hh(), and p_tgamma.

◆ trk()

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

virtual

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(), ff, Lorene::Scalar::inc_dzpuis(), Lorene::Time_slice::jtime, ln_psi(), nn(), psi(), psi_evol, Lorene::Time_slice::scheme_order, Lorene::Time_slice::the_time, and Lorene::Time_slice::trk_evol.

◆ vec_X()

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

virtual

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

Member Data Documentation

◆ A_hata_evol

Evolution_std<Scalar> Lorene::Time_slice_conf::A_hata_evol

mutableprotected

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.

◆ 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

mutableprotected

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_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.

◆ depth

int Lorene::Time_slice::depth

protectedinherited

Number of stored time slices.

Definition at line 182 of file time_slice.h.

◆ ff

const Metric_flat& Lorene::Time_slice_conf::ff

protected

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.

◆ hata_evol

Evolution_std<Sym_tensor> Lorene::Time_slice_conf::hata_evol

mutableprotected

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

mutableprotected

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.

◆ 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

mutableprotected

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

Definition at line 525 of file time_slice.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

mutableprotected

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

mutableprotected

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

mutableprotected

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

mutableprotected

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

mutableprotected

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_evol

Evolution_std<Scalar> Lorene::Time_slice_conf::psi_evol

mutableprotected

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.

◆ 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_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.

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

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Time_slice_conf() [1/5]

◆ Time_slice_conf() [2/5]

◆ Time_slice_conf() [3/5]

◆ Time_slice_conf() [4/5]

◆ Time_slice_conf() [5/5]

◆ ~Time_slice_conf()

Member Function Documentation

◆ A_hata()

◆ aa()

◆ adm_mass()

◆ B_hata()

◆ beta()

◆ check_dynamical_equations()

◆ check_hamiltonian_constraint()

◆ check_momentum_constraint()

◆ check_psi_dot()

◆ compute_X_from_momentum_constraint()

◆ del_deriv()

◆ gam()

◆ gam_dd()

◆ gam_uu()

◆ get_latest_j()

◆ get_scheme_order()

◆ get_time()

◆ hata()

◆ hdirac()

◆ hh()

◆ initial_data_cts()

◆ k_dd()

◆ k_uu()

◆ ln_psi()

◆ nn()

◆ npsi()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator>>()

◆ psi()

◆ psi4()

◆ sauve()

◆ save()

◆ set_AB_hata()

◆ set_der_0x0()

◆ set_hata()

◆ set_hata_from_XAB()

◆ set_hata_TT()

◆ set_hh()

◆ set_npsi_del_n()

◆ set_npsi_del_psi()

◆ set_psi_del_n()

◆ set_psi_del_npsi()

◆ set_scheme_order()

◆ tgam()

◆ trk()

◆ vec_X()

Member Data Documentation

◆ A_hata_evol

◆ adm_mass_evol

◆ B_hata_evol

◆ beta_evol

◆ depth

◆ ff

◆ gam_dd_evol

◆ gam_uu_evol

◆ hata_evol

◆ hh_evol

◆ jtime

◆ k_dd_evol

◆ k_uu_evol

◆ n_evol

◆ npsi_evol

◆ p_gamma

◆ p_hdirac

◆ p_ln_psi

◆ p_psi4

◆ p_tgamma