Lorene::Isol_hor Class Reference
[Time evolution (under development)]

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:
Lorene::Time_slice_conf Lorene::Time_slice

List of all members.

Public Member Functions

 Isol_hor (Map_af &mpi, int depth_in=3)
 Standard constructor.
 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.
 Isol_hor (const Isol_hor &)
 Copy constructor.
 Isol_hor (Map_af &mp, FILE *fich, bool partial_read, int depth_in=3)
 Constructor from a binary file.
virtual ~Isol_hor ()
 Destructor.
void operator= (const Isol_hor &)
 Assignment to another Isol_hor.
const Map_afget_mp () const
 Returns the mapping (readonly).
Map_afset_mp ()
 Read/write of the mapping.
double get_radius () const
 Returns the radius of the horizon.
void set_radius (double rad)
 Sets the radius of the horizon to rad .
double get_omega () const
 Returns the angular velocity.
void set_omega (double ome)
 Sets the angular velocity to ome .
double get_boost_x () const
 Returns the boost velocity in x-direction.
void set_boost_x (double bo)
 Sets the boost velocity in x-direction to bo .
double get_boost_z () const
 Returns the boost velocity in z-direction.
void set_boost_z (double bo)
 Sets the boost velocity in z-direction to bo .
virtual const Scalarn_auto () const
 Lapse function $ N_{auto} $ at the current time step jtime.
virtual const Scalarn_comp () const
 Lapse function $ N_{comp} $ at the current time step jtime.
virtual const Scalarpsi_auto () const
 Conformal factor $ \Psi_{auto} $ at the current time step jtime.
virtual const Scalarpsi_comp () const
 Conformal factor $ \Psi_{comp} $ at the current time step jtime.
virtual const Vectordnn () const
 Covariant derivative of the lapse function $ \overline\nabla_i N $ at the current time step jtime.
virtual const Vectordpsi () const
 Covariant derivative with respect to the flat metric of the conformal factor $ \overline\nabla_i \Psi $ at the current time step jtime.
virtual const Vectorbeta_auto () const
 Shift function $ \beta^i_{auto} $ at the current time step jtime.
virtual const Vectorbeta_comp () const
 Shift function $ \beta^i_{comp} $ at the current time step jtime.
virtual const Sym_tensoraa_auto () const
 Conformal representation $ A^{ij}_{auto} $ of the traceless part of the extrinsic curvature: Returns the value at the current time step jtime.
virtual const Sym_tensoraa_comp () const
 Conformal representation $ A^{ij}_{comp} $ of the traceless part of the extrinsic curvature: Returns the value at the current time step jtime.
virtual const Scalaraa_quad () const
 Conformal representation $ A^{ij}A_{ij} $.
virtual const Metrictgam () const
 Conformal metric $ \tilde\gamma_{ij} = \Psi^{-4} \gamma_{ij} $ Returns the value at the current time step (jtime ).
const Scalar get_decouple () const
 Returns the function used to construct tkij_auto from tkij_tot .
void n_comp (const Isol_hor &comp)
 Imports the part of N due to the companion hole comp .
void psi_comp (const Isol_hor &comp)
 Imports the part of $\Psi$ due to the companion hole comp .
void beta_comp (const Isol_hor &comp)
 Imports the part of $\beta^i$ due to the companion hole comp.
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 .
void init_bhole ()
 Sets the values of the fields to :.
void init_met_trK ()
 Sets the 3-metric tilde to the flat metric and gamt_point, trK and trK_point to zero.
void init_bhole_seul ()
 Initiates for a single black hole.
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} $.
void set_nn (const Scalar &nn_in)
 Sets the lapse.
void set_gamt (const Metric &gam_tilde)
 Sets the conformal metric to gam_tilde.
const Vector radial_vect_hor () const
 Vector radial normal.
const Vector tradial_vect_hor () const
 Vector radial normal tilde.
const Scalar b_tilde () const
 Radial component of the shift with respect to the conformal metric.
const Scalar darea_hor () const
 Element of area of the horizon.
double area_hor () const
 Area of the horizon.
double radius_hor () const
 Radius of the horizon.
double ang_mom_hor () const
 Angular momentum (modulo).
double mass_hor () const
 Mass computed at the horizon.
double kappa_hor () const
 Surface gravity.
double omega_hor () const
 Orbital velocity.
double ang_mom_adm () const
 ADM angular Momentum.
Scalar expansion () const
 Expansion of the outgoing null normal ($ \bf n + \bf s $).
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 $.
const Scalar source_nn () const
 Source for N.
const Vector source_beta () const
 Source for $ \beta $.
const Scalar source_b_tilde () const
 Source for b_tilde.
const Vector source_vector_b () const
 Source for vector_b.
const Valeur boundary_psi_Dir_evol () const
 Dirichlet boundary condition for $ \Psi $ (evolution).
const Valeur boundary_psi_Neu_evol () const
 Neumann boundary condition for $ \Psi $ (evolution).
const Valeur boundary_psi_Dir_spat () const
 Dirichlet boundary condition for $ \Psi $ (spatial).
const Valeur boundary_psi_Neu_spat () const
 Neumann boundary condition for $ \Psi $ (spatial).
const Valeur boundary_psi_app_hor () const
 Neumann boundary condition for $ \Psi $ (spatial).
const Valeur boundary_psi_Dir () const
 Dirichlet boundary condition for $ \Psi $ (spatial).
const Valeur boundary_nn_Dir_kk () const
 Dirichlet boundary condition for N using the extrinsic curvature.
const Valeur boundary_nn_Neu_kk (int nn=1) const
 Neumann boundary condition for N using the extrinsic curvature.
const Valeur boundary_nn_Neu_Cook () const
 Neumann boundary condition for N using Cook's boundary condition.
const Valeur boundary_nn_Dir_eff (double aa) const
 Dirichlet boundary condition for N (effectif) $ \partial_r N + a N = 0 $.
const Valeur boundary_nn_Dir_lapl (int mer=1) const
 Dirichlet boundary condition for N fixing the divergence of the connection form $ \omega $.
const Valeur boundary_nn_Neu_eff (double aa) const
 Neumann boundary condition on nn (effectif) $ \partial_r N + a N = 0 $.
const Valeur boundary_nn_Dir (double aa) const
 Dirichlet boundary condition $ N = a $.
const Valeur boundary_beta_r () const
 Component r of boundary value of $ \beta $.
const Valeur boundary_beta_theta () const
 Component theta of boundary value of $ \beta $.
const Valeur boundary_beta_phi (double om) const
 Component phi of boundary value of $ \beta $.
const Valeur boundary_beta_x (double om) const
 Component x of boundary value of $ \beta $.
const Valeur boundary_beta_y (double om) const
 Component y of boundary value of $ \beta $.
const Valeur boundary_beta_z () const
 Component z of boundary value of $ \beta $.
const Valeur beta_boost_x () const
 Boundary value for a boost in x-direction.
const Valeur beta_boost_z () const
 Boundary value for a boost in z-direction.
const Vector vv_bound_cart (double om) const
 Vector $ V^i $ for boundary conditions in cartesian.
const Vector vv_bound_cart_bin (double om, int hole=0) const
 Vector $ V^i $ for boundary conditions in cartesian for binary systems.
const Valeur boundary_vv_x (double om) const
 Component x of boundary value of $ V^i $.
const Valeur boundary_vv_y (double om) const
 Component y of boundary value of $ V^i $.
const Valeur boundary_vv_z (double om) const
 Component z of boundary value of $ V^i $.
const Valeur boundary_vv_x_bin (double om, int hole=0) const
 Component x of boundary value of $ V^i $.
const Valeur boundary_vv_y_bin (double om, int hole=0) const
 Component y of boundary value of $ V^i $.
const Valeur boundary_vv_z_bin (double om, int hole=0) const
 Component z of boundary value of $ V^i $.
const Valeur boundary_b_tilde_Neu () const
 Neumann boundary condition for b_tilde.
const Valeur boundary_b_tilde_Dir () const
 Dirichlet boundary condition for b_tilde.
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) $.
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 $K^{ij}$.
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.
void met_kerr_perturb ()
 Initialisation of the metric tilde from equation (15) of Dain (2002).
void aa_kerr_ww (double mm, double aa)
double axi_break () const
 Breaking of the axial symmetry on the horizon.
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.
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} $.
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} $.
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 $\Psi$.
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.
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} $.
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) $.
virtual void set_hata_TT (const Sym_tensor_tt &hata_tt)
 Sets the TT part of $ \hat{A}^{ij} $ (see member hata_evol ).
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 $ X^i $.
virtual const Scalarnn () const
 Lapse function N at the current time step (jtime ).
virtual const Sym_tensorgam_dd () const
 Induced metric (covariant components $ \gamma_{ij} $) at the current time step (jtime ).
virtual const Sym_tensorgam_uu () const
 Induced metric (contravariant components $ \gamma^{ij} $) at the current time step (jtime ).
virtual const Sym_tensork_dd () const
 Extrinsic curvature tensor (covariant components $ K_{ij} $) at the current time step (jtime ).
virtual const Sym_tensork_uu () const
 Extrinsic curvature tensor (contravariant components $ K^{ij} $) at the current time step (jtime ).
virtual const ScalarA_hata () const
 Returns the potential A of $ \hat{A}^{ij} $.
virtual const ScalarB_hata () const
 Returns the potential $\tilde{B}$ of $ \hat{A}^{ij} $.
virtual const Scalarpsi () const
 Conformal factor $ \Psi $ relating the physical metric $ \gamma_{ij} $ to the conformal one: $ \gamma_{ij} = \Psi^4 \tilde\gamma_{ij} $.
const Scalarpsi4 () const
 Factor $ \Psi^4 $ at the current time step (jtime ).
const Scalarln_psi () const
 Logarithm of $ \Psi $ at the current time step (jtime ).
virtual const Scalarnpsi () const
 Factor $ N\Psi $ at the current time step (jtime ).
virtual const Sym_tensorhh (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} $.
virtual const Sym_tensorhata () 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) $.
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) $.
virtual const Scalartrk () const
 Trace K of the extrinsic curvature at the current time step (jtime ).
virtual const Vectorhdirac () const
 Vector $ H^i = {\cal D}_j \tilde\gamma^{ij} $ which vanishes in Dirac gauge.
virtual const Vectorvec_X (int method_poisson=6) const
 Vector $ X^i $ representing the longitudinal part of $ \hat{A}^{ij} $.
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 $ X^i $ from the conformally-rescaled momentum $ \hat{S}^i = \Psi^6 S^i $, using the momentum constraint.
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).
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.
virtual double adm_mass () const
 Returns the ADM mass (geometrical units) at the current step.
void check_psi_dot (Tbl &tlnpsi_dot, Tbl &tdiff, Tbl &tdiff_rel) const
 Checks the $\frac{\partial}{\partial t} \ln\Psi $ relation.
void set_scheme_order (int ord)
 Sets the order of the finite-differences scheme.
int get_scheme_order () const
 Gets the order of the finite-differences scheme.
int get_latest_j () const
 Gets the latest value of time step index.
const Evolution_std< double > & get_time () const
 Gets the time coordinate t at successive time steps.
virtual const Vectorbeta () const
 shift vector $ \beta^i $ at the current time step (jtime )
const Metricgam () const
 Induced metric $ \mathbf{\gamma} $ at the current time step (jtime ).
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.
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.
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.
void save (const char *rootname) const
 Saves in a binary file.

Protected Member Functions

virtual ostream & operator>> (ostream &) const
 Operator >> (virtual function called by the operator<<).
virtual void del_deriv () const
 Deletes all the derived quantities.
void set_der_0x0 () const
 Sets to 0x0 all the pointers on derived quantities.

Protected Attributes

Map_afmp
 Affine mapping.
int nz
 Number of zones.
double radius
 Radius of the horizon in LORENE's units.
double omega
 Angular velocity in LORENE's units.
double boost_x
 Boost velocity in x-direction.
double boost_z
 Boost velocity in z-direction.
double regul
 Intensity of the correction on the shift vector.
Evolution_std< Scalarn_auto_evol
 Values at successive time steps of the lapse function $ N_{auto} $.
Evolution_std< Scalarn_comp_evol
 Values at successive time steps of the lapse function $ N_{comp} $.
Evolution_std< Scalarpsi_auto_evol
 Values at successive time steps of the conformal factor $ \Psi_{auto} $.
Evolution_std< Scalarpsi_comp_evol
 Values at successive time steps of the lapse function $ \Psi_{comp} $.
Evolution_std< Vectordn_evol
 Values at successive time steps of the covariant derivative of the lapse with respect to the flat metric $ \overline\nabla_i N $.
Evolution_std< Vectordpsi_evol
 Values at successive time steps of the covariant derivative of the conformal factor $ \overline\nabla_i \Psi $.
Evolution_std< Vectorbeta_auto_evol
 Values at successive time steps of the shift function $ \beta^i_{auto} $.
Evolution_std< Vectorbeta_comp_evol
 Values at successive time steps of the shift function $ \beta^i_{comp} $.
Evolution_std< Sym_tensoraa_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:.
Evolution_std< Sym_tensoraa_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:.
Evolution_std< Sym_tensoraa_nn
 Values at successive time steps of the components $ A^{ij}*2N $.
Evolution_std< Scalaraa_quad_evol
 Values at successive time steps of the components $ A^{ij}A_{ij} $.
Metric met_gamt
 3 metric tilde
Sym_tensor gamt_point
 Time derivative of the 3-metric tilde.
Scalar trK
 Trace of the extrinsic curvature.
Scalar trK_point
 Time derivative of the trace of the extrinsic curvature.
Scalar decouple
 Function used to construct $ A^{ij}_{auto} $ from the total $A^{ij}$.
const Metric_flatff
 Pointer on the flat metric $ f_{ij} $ with respect to which the conformal decomposition is performed.
Evolution_std< Scalarpsi_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} $.
Evolution_std< Scalarnpsi_evol
 Values at successive time steps of the factor $ N\Psi $.
Evolution_std< Sym_tensorhh_evol
 Values at successive time steps of the components $ h^{ij} $.
Evolution_std< Sym_tensorhata_evol
 Values at successive time steps of the components $ \hat{A}^{ij} $.
Evolution_std< ScalarA_hata_evol
 Potential A associated with the symmetric tensor $ \hat{A}^{ij}_{TT} $.
Evolution_std< ScalarB_hata_evol
 Potential $ \tilde{B} $ associated with the symmetric tensor $ \hat{A}^{ij}_{TT} $.
Metricp_tgamma
 Pointer on the conformal metric $ \tilde\gamma_{ij} $ at the current time step (jtime).
Scalarp_psi4
 Pointer on the factor $ \Psi^4 $ at the current time step (jtime).
Scalarp_ln_psi
 Pointer on the logarithm of $ \Psi $ at the current time step (jtime).
Vectorp_hdirac
 Pointer on the vector $ H^i = {\cal D}_j \tilde\gamma^{ij} $ (which vanishes in Dirac gauge), at the current time step (jtime).
Vectorp_vec_X
 Pointer on the vector $ X^i $ representing the longitudinal part of $ \hat{A}^{ij} $.
int depth
 Number of stored time slices.
int scheme_order
 Order of the finite-differences scheme for the computation of time derivatives.
int jtime
 Time step index of the latest slice.
Evolution_std< double > the_time
 Time label of each slice.
Evolution_std< Sym_tensorgam_dd_evol
 Values at successive time steps of the covariant components of the induced metric $ \gamma_{ij} $.
Evolution_std< Sym_tensorgam_uu_evol
 Values at successive time steps of the contravariant components of the induced metric $ \gamma^{ij} $.
Evolution_std< Sym_tensork_dd_evol
 Values at successive time steps of the covariant components of the extrinsic curvature tensor $ K_{ij} $.
Evolution_std< Sym_tensork_uu_evol
 Values at successive time steps of the contravariant components of the extrinsic curvature tensor $ K^{ij} $.
Evolution_std< Scalarn_evol
 Values at successive time steps of the lapse function N.
Evolution_std< Vectorbeta_evol
 Values at successive time steps of the shift vector $ \beta^i $.
Evolution_std< Scalartrk_evol
 Values at successive time steps of the trace K of the extrinsic curvature.
Evolution_full< Tbladm_mass_evol
 ADM mass at each time step, since the creation of the slice.
Metricp_gamma
 Pointer on the induced metric at the current time step (jtime).

Friends

class Bin_hor
ostream & operator<< (ostream &, const Time_slice &)
 Display.

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

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.

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_flat::con(), Lorene::Metric::con(), Lorene::Time_slice_conf::ff, Lorene::Time_slice_conf::hh_evol, Lorene::Time_slice::jtime, met_gamt, Lorene::Time_slice::the_time, trK, Lorene::Time_slice::trk_evol, and Lorene::Evolution_std< TyT >::update().

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

Copy constructor.

Definition at line 225 of file isol_hor.C.

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_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, trK_point, and Lorene::Evolution_std< TyT >::update().

Lorene::Isol_hor::~Isol_hor (  )  [virtual]

Destructor.

Definition at line 339 of file isol_hor.C.


Member Function Documentation

const Scalar & Lorene::Time_slice_conf::A_hata (  )  const [virtual, inherited]

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::Evolution< TyT >::is_known(), Lorene::Time_slice::jtime, Lorene::Time_slice::the_time, and Lorene::Evolution_std< TyT >::update().

Sym_tensor Lorene::Time_slice_conf::aa (  )  const [virtual, inherited]

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().

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, Lorene::Evolution< TyT >::is_known(), and Lorene::Time_slice::jtime.

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, Lorene::Evolution< TyT >::is_known(), and Lorene::Time_slice::jtime.

const Scalar & Lorene::Isol_hor::aa_quad (  )  const [virtual]
double Lorene::Time_slice_conf::adm_mass (  )  const [virtual, inherited]
double Lorene::Isol_hor::ang_mom_adm (  )  const
double Lorene::Isol_hor::ang_mom_hor (  )  const
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.

double Lorene::Isol_hor::axi_break (  )  const
const Scalar & Lorene::Time_slice_conf::B_hata (  )  const [virtual, inherited]

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::Evolution< TyT >::is_known(), Lorene::Time_slice::jtime, Lorene::Time_slice::the_time, and Lorene::Evolution_std< TyT >::update().

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().

const Vector & Lorene::Time_slice::beta (  )  const [virtual, inherited]

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, Lorene::Evolution< TyT >::is_known(), and Lorene::Time_slice::jtime.

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, Lorene::Evolution< TyT >::is_known(), and Lorene::Time_slice::jtime.

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().

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().

void Lorene::Isol_hor::beta_comp ( const Isol_hor comp  ) 
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, Lorene::Evolution< TyT >::is_known(), and Lorene::Time_slice::jtime.

const Valeur Lorene::Isol_hor::boundary_b_tilde_Dir (  )  const
const Valeur Lorene::Isol_hor::boundary_b_tilde_Neu (  )  const
const Valeur Lorene::Isol_hor::boundary_beta_phi ( double  om  )  const
const Valeur Lorene::Isol_hor::boundary_beta_r (  )  const
const Valeur Lorene::Isol_hor::boundary_beta_theta (  )  const
const Valeur Lorene::Isol_hor::boundary_beta_x ( double  om  )  const
const Valeur Lorene::Isol_hor::boundary_beta_y ( double  om  )  const
const Valeur Lorene::Isol_hor::boundary_beta_z (  )  const
const Valeur Lorene::Isol_hor::boundary_nn_Dir ( double  aa  )  const
const Valeur Lorene::Isol_hor::boundary_nn_Dir_eff ( double  aa  )  const
const Valeur Lorene::Isol_hor::boundary_nn_Dir_kk (  )  const
const Valeur Lorene::Isol_hor::boundary_nn_Dir_lapl ( int  mer = 1  )  const
const Valeur Lorene::Isol_hor::boundary_nn_Neu_Cook (  )  const
const Valeur Lorene::Isol_hor::boundary_nn_Neu_eff ( double  aa  )  const
const Valeur Lorene::Isol_hor::boundary_nn_Neu_kk ( int  nn = 1  )  const
const Valeur Lorene::Isol_hor::boundary_psi_app_hor (  )  const
const Valeur Lorene::Isol_hor::boundary_psi_Dir (  )  const
const Valeur Lorene::Isol_hor::boundary_psi_Dir_evol (  )  const
const Valeur Lorene::Isol_hor::boundary_psi_Dir_spat (  )  const
const Valeur Lorene::Isol_hor::boundary_psi_Neu_evol (  )  const
const Valeur Lorene::Isol_hor::boundary_psi_Neu_spat (  )  const
const Valeur Lorene::Isol_hor::boundary_vv_x ( double  om  )  const
const Valeur Lorene::Isol_hor::boundary_vv_x_bin ( double  om,
int  hole = 0 
) const
const Valeur Lorene::Isol_hor::boundary_vv_y ( double  om  )  const
const Valeur Lorene::Isol_hor::boundary_vv_y_bin ( double  om,
int  hole = 0 
) const
const Valeur Lorene::Isol_hor::boundary_vv_z ( double  om  )  const
const Valeur Lorene::Isol_hor::boundary_vv_z_bin ( double  om,
int  hole = 0 
) const
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 $ J_i $ = 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::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::Evolution< TyT >::time_derive(), Lorene::Tensor::trace(), Lorene::Time_slice::trk(), and Lorene::Tensor::up_down().

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().

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 $ J_i $ measured by the Eulerian observer of 4-velocity $\mbox{\boldmath{$n $}}$ ; if this is the null pointer, it is assumed that$ J_i $ = 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 $ J_i $ = 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().

void Lorene::Time_slice_conf::check_psi_dot ( Tbl tlnpsi_dot,
Tbl tdiff,
Tbl tdiff_rel 
) const [inherited]
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().

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().

void Lorene::Time_slice_conf::del_deriv (  )  const [protected, virtual, inherited]
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, Lorene::Evolution< TyT >::is_known(), and Lorene::Time_slice::jtime.

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, Lorene::Evolution< TyT >::is_known(), and Lorene::Time_slice::jtime.

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().

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.

const Sym_tensor & Lorene::Time_slice_conf::gam_dd (  )  const [virtual, inherited]
const Sym_tensor & Lorene::Time_slice_conf::gam_uu (  )  const [virtual, inherited]
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.

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.

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.

int Lorene::Time_slice::get_latest_j (  )  const [inline, inherited]

Gets the latest value of time step index.

Definition at line 346 of file time_slice.h.

References Lorene::Time_slice::jtime.

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.

double Lorene::Isol_hor::get_omega (  )  const [inline]

Returns the angular velocity.

Definition at line 436 of file isol_hor.h.

References omega.

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.

int Lorene::Time_slice::get_scheme_order (  )  const [inline, inherited]

Gets the order of the finite-differences scheme.

Definition at line 343 of file time_slice.h.

References Lorene::Time_slice::scheme_order.

const Evolution_std<double>& Lorene::Time_slice::get_time (  )  const [inline, inherited]

Gets the time coordinate t at successive time steps.

Definition at line 349 of file time_slice.h.

References Lorene::Time_slice::the_time.

const Sym_tensor & Lorene::Time_slice_conf::hata (  )  const [virtual, inherited]
const Vector & Lorene::Time_slice_conf::hdirac (  )  const [virtual, inherited]

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.

const Sym_tensor & Lorene::Time_slice_conf::hh ( Param = 0x0,
Param = 0x0 
) const [virtual, inherited]

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, Lorene::Evolution< TyT >::is_known(), and Lorene::Time_slice::jtime.

void Lorene::Isol_hor::init_bhole (  ) 
void Lorene::Isol_hor::init_bhole_seul (  ) 
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.

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, inherited]

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 Lorene::Time_slice_conf::A_hata(), Lorene::Time_slice_conf::A_hata_evol, Lorene::Time_slice_conf::aa(), Lorene::Time_slice_conf::B_hata(), Lorene::Time_slice_conf::B_hata_evol, Lorene::Time_slice::beta(), Lorene::Time_slice::beta_evol, Lorene::Scalar::check_dzpuis(), Lorene::contract(), Lorene::Tensor::dec_dzpuis(), Lorene::Time_slice_conf::del_deriv(), Lorene::Time_slice::depth, Lorene::Tensor::derive_con(), Lorene::Scalar::derive_con(), Lorene::Tensor::derive_cov(), Lorene::Scalar::derive_cov(), Lorene::Vector::derive_lie(), des_meridian(), Lorene::diffrel(), Lorene::Vector::divergence(), Lorene::Sym_tensor::divergence(), Lorene::Evolution< TyT >::downdate(), Lorene::Time_slice_conf::ff, Lorene::Scalar::get_etat(), Lorene::Map::get_mg(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_nzone(), Lorene::Tensor::get_triad(), Lorene::Time_slice_conf::hata_evol, Lorene::Time_slice_conf::hdirac(), Lorene::Time_slice_conf::hh(), Lorene::Time_slice_conf::hh_evol, Lorene::Tensor::inc_dzpuis(), Lorene::Scalar::inc_dzpuis(), Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice::k_uu_evol, Lorene::Scalar::laplacian(), Lorene::Time_slice_conf::ln_psi(), Lorene::max(), Lorene::maxabs(), Lorene::Time_slice::n_evol, Lorene::Time_slice_conf::nn(), Lorene::Time_slice_conf::npsi_evol, Lorene::Vector::ope_killing_conf(), Lorene::Vector::poisson(), Lorene::Scalar::poisson(), Lorene::Time_slice_conf::psi(), Lorene::Time_slice_conf::psi4(), Lorene::Time_slice_conf::psi_evol, Lorene::Metric::ricci_scal(), Lorene::Tensor::set_etat_zero(), Lorene::Scalar::set_etat_zero(), Lorene::Time_slice_conf::set_hata(), Lorene::Time_slice_conf::set_psi_del_npsi(), Lorene::Scalar::std_spectral_base(), Lorene::Time_slice_conf::tgam(), Lorene::Time_slice::the_time, Lorene::Tensor::trace(), Lorene::Time_slice_conf::trk(), Lorene::Time_slice::trk_evol, Lorene::Tensor::up_down(), Lorene::Evolution_std< TyT >::update(), and Lorene::Map::val_r().

const Sym_tensor & Lorene::Time_slice_conf::k_dd (  )  const [virtual, inherited]

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::Evolution< TyT >::is_known(), Lorene::Time_slice::jtime, Lorene::Time_slice::k_dd_evol, Lorene::Time_slice_conf::k_uu(), Lorene::Time_slice::the_time, and Lorene::Evolution_std< TyT >::update().

const Sym_tensor & Lorene::Time_slice_conf::k_uu (  )  const [virtual, inherited]
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().

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().

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().

void Lorene::Isol_hor::met_kerr_perturb (  ) 
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::Evolution< TyT >::is_known(), Lorene::Time_slice::jtime, and n_auto_evol.

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::Scalar::derive_cov(), dn_evol, Lorene::Time_slice_conf::ff, Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Scalar::import(), Lorene::Time_slice::jtime, mp, n_auto(), n_comp_evol, Lorene::Time_slice::n_evol, Lorene::Scalar::std_spectral_base(), Lorene::Time_slice::the_time, and Lorene::Evolution_std< TyT >::update().

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::Evolution< TyT >::is_known(), Lorene::Time_slice::jtime, and n_comp_evol.

const Scalar & Lorene::Time_slice_conf::nn (  )  const [virtual, inherited]
const Scalar & Lorene::Time_slice_conf::npsi (  )  const [virtual, inherited]
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().

void Lorene::Isol_hor::operator= ( const Isol_hor isolhor_in  ) 
ostream & Lorene::Isol_hor::operator>> ( ostream &  flux  )  const [protected, virtual]

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(), and radius.

const Scalar & Lorene::Time_slice_conf::psi (  )  const [virtual, inherited]

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::Evolution< TyT >::is_known(), Lorene::Time_slice::jtime, Lorene::Time_slice::n_evol, Lorene::Time_slice_conf::npsi_evol, Lorene::Time_slice_conf::psi_evol, Lorene::Time_slice::the_time, and Lorene::Evolution_std< TyT >::update().

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().

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::Evolution< TyT >::is_known(), Lorene::Time_slice::jtime, and psi_auto_evol.

void Lorene::Isol_hor::psi_comp ( const Isol_hor comp  ) 
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::Evolution< TyT >::is_known(), Lorene::Time_slice::jtime, and psi_comp_evol.

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

double Lorene::Isol_hor::regularisation ( const Vector shift_auto,
const Vector shift_comp,
double  ang_vel 
)
double Lorene::Isol_hor::regularise_one (  ) 
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::Evolution< TyT >::is_known(), Lorene::Time_slice::jtime, met_gamt, n_auto_evol, omega, psi_auto_evol, Lorene::Time_slice_conf::psi_evol, Lorene::Scalar::sauve(), Lorene::Tensor_sym::sauve(), trK, and trK_point.

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::Time_slice::sauve(), Lorene::Base_vect::sauve(), Lorene::Map::sauve(), and Lorene::Mg3d::sauve().

void Lorene::Time_slice_conf::set_AB_hata ( const Scalar A_in,
const Scalar B_in 
) [virtual, inherited]
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.

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.

void Lorene::Time_slice_conf::set_der_0x0 (  )  const [protected, inherited]
void Lorene::Isol_hor::set_gamt ( const Metric gam_tilde  ) 
void Lorene::Time_slice_conf::set_hata ( const Sym_tensor hata_in  )  [virtual, inherited]

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::Evolution< TyT >::downdate(), 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::the_time, and Lorene::Evolution_std< TyT >::update().

void Lorene::Time_slice_conf::set_hata_from_XAB ( Param par_bc = 0x0,
Param par_mat = 0x0 
) [virtual, inherited]
void Lorene::Time_slice_conf::set_hata_TT ( const Sym_tensor_tt hata_tt  )  [virtual, inherited]
void Lorene::Time_slice_conf::set_hh ( const Sym_tensor hh_in  )  [virtual, inherited]
Map_af& Lorene::Isol_hor::set_mp (  )  [inline]

Read/write of the mapping.

Definition at line 421 of file isol_hor.h.

References mp.

void Lorene::Isol_hor::set_nn ( const Scalar nn_in  ) 
void Lorene::Time_slice_conf::set_npsi_del_n ( const Scalar npsi_in  )  [virtual, inherited]
void Lorene::Time_slice_conf::set_npsi_del_psi ( const Scalar npsi_in  )  [virtual, inherited]
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.

void Lorene::Isol_hor::set_psi ( const Scalar psi_in  ) 
void Lorene::Time_slice_conf::set_psi_del_n ( const Scalar psi_in  )  [virtual, inherited]
void Lorene::Time_slice_conf::set_psi_del_npsi ( const Scalar psi_in  )  [virtual, inherited]
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.

void Lorene::Time_slice::set_scheme_order ( int  ord  )  [inline, inherited]

Sets the order of the finite-differences scheme.

Definition at line 334 of file time_slice.h.

References Lorene::Time_slice::scheme_order.

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

Source for b_tilde.

const Vector Lorene::Isol_hor::source_beta (  )  const
const Scalar Lorene::Isol_hor::source_nn (  )  const
const Scalar Lorene::Isol_hor::source_psi (  )  const
const Vector Lorene::Isol_hor::source_vector_b (  )  const

Source for vector_b.

virtual const Metric& Lorene::Isol_hor::tgam (  )  const [inline, virtual]

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.

const Vector Lorene::Isol_hor::tradial_vect_hor (  )  const
const Scalar & Lorene::Time_slice_conf::trk (  )  const [virtual, inherited]
void Lorene::Isol_hor::update_aa (  ) 
const Vector & Lorene::Time_slice_conf::vec_X ( int  method_poisson = 6  )  const [virtual, inherited]

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::Evolution< TyT >::is_known(), Lorene::Time_slice::jtime, and Lorene::Time_slice_conf::p_vec_X.

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.

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


Friends And Related Function Documentation

ostream& operator<< ( ostream &  ,
const Time_slice  
) [friend, inherited]

Display.


Member Data Documentation

Evolution_std<Scalar> Lorene::Time_slice_conf::A_hata_evol [mutable, protected, inherited]

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.

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.

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.

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

Definition at line 320 of file isol_hor.h.

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

Definition at line 323 of file isol_hor.h.

Evolution_full<Tbl> Lorene::Time_slice::adm_mass_evol [mutable, protected, inherited]

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.

Evolution_std<Scalar> Lorene::Time_slice_conf::B_hata_evol [mutable, protected, inherited]

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.

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

Definition at line 301 of file isol_hor.h.

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

Definition at line 304 of file isol_hor.h.

Evolution_std<Vector> Lorene::Time_slice::beta_evol [mutable, protected, inherited]

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

Definition at line 222 of file time_slice.h.

double Lorene::Isol_hor::boost_x [protected]

Boost velocity in x-direction.

Definition at line 272 of file isol_hor.h.

double Lorene::Isol_hor::boost_z [protected]

Boost velocity in z-direction.

Definition at line 275 of file isol_hor.h.

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.

int Lorene::Time_slice::depth [protected, inherited]

Number of stored time slices.

Definition at line 182 of file time_slice.h.

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.

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.

const Metric_flat& Lorene::Time_slice_conf::ff [protected, inherited]

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.

Evolution_std<Sym_tensor> Lorene::Time_slice::gam_dd_evol [mutable, protected, inherited]

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

Definition at line 201 of file time_slice.h.

Evolution_std<Sym_tensor> Lorene::Time_slice::gam_uu_evol [mutable, protected, inherited]

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

Definition at line 206 of file time_slice.h.

Time derivative of the 3-metric tilde.

Definition at line 329 of file isol_hor.h.

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.

Evolution_std<Sym_tensor> Lorene::Time_slice_conf::hh_evol [mutable, protected, inherited]

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.

int Lorene::Time_slice::jtime [protected, inherited]

Time step index of the latest slice.

Definition at line 193 of file time_slice.h.

Evolution_std<Sym_tensor> Lorene::Time_slice::k_dd_evol [mutable, protected, inherited]

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.

Evolution_std<Sym_tensor> Lorene::Time_slice::k_uu_evol [mutable, protected, inherited]

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.

3 metric tilde

Definition at line 326 of file isol_hor.h.

Affine mapping.

Definition at line 260 of file isol_hor.h.

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

Definition at line 281 of file isol_hor.h.

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

Definition at line 284 of file isol_hor.h.

Evolution_std<Scalar> Lorene::Time_slice::n_evol [mutable, protected, inherited]

Values at successive time steps of the lapse function N.

Definition at line 219 of file time_slice.h.

Evolution_std<Scalar> Lorene::Time_slice_conf::npsi_evol [mutable, protected, inherited]

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

Definition at line 525 of file time_slice.h.

int Lorene::Isol_hor::nz [protected]

Number of zones.

Definition at line 263 of file isol_hor.h.

double Lorene::Isol_hor::omega [protected]

Angular velocity in LORENE's units.

Definition at line 269 of file isol_hor.h.

Metric* Lorene::Time_slice::p_gamma [mutable, protected, inherited]

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

Definition at line 242 of file time_slice.h.

Vector* Lorene::Time_slice_conf::p_hdirac [mutable, protected, inherited]

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.

Scalar* Lorene::Time_slice_conf::p_ln_psi [mutable, protected, inherited]

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

Definition at line 569 of file time_slice.h.

Scalar* Lorene::Time_slice_conf::p_psi4 [mutable, protected, inherited]

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

Definition at line 566 of file time_slice.h.

Metric* Lorene::Time_slice_conf::p_tgamma [mutable, protected, inherited]

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

Definition at line 563 of file time_slice.h.

Vector* Lorene::Time_slice_conf::p_vec_X [mutable, protected, inherited]

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.

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

Definition at line 287 of file isol_hor.h.

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

Definition at line 290 of file isol_hor.h.

Evolution_std<Scalar> Lorene::Time_slice_conf::psi_evol [mutable, protected, inherited]

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.

double Lorene::Isol_hor::radius [protected]

Radius of the horizon in LORENE's units.

Definition at line 266 of file isol_hor.h.

double Lorene::Isol_hor::regul [protected]

Intensity of the correction on the shift vector.

Definition at line 278 of file isol_hor.h.

int Lorene::Time_slice::scheme_order [protected, inherited]

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.

Evolution_std<double> Lorene::Time_slice::the_time [protected, inherited]

Time label of each slice.

Definition at line 196 of file time_slice.h.

Trace of the extrinsic curvature.

Definition at line 332 of file isol_hor.h.

Evolution_std<Scalar> Lorene::Time_slice::trk_evol [mutable, protected, inherited]

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

Definition at line 227 of file time_slice.h.

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:

Generated on 7 Dec 2019 for LORENE by  doxygen 1.6.1