LORENE
Lorene::Black_hole Class Reference

Base class for black holes. More...

#include <blackhole.h>

Inheritance diagram for Lorene::Black_hole:
Lorene::Hole_bhns

Public Member Functions

 Black_hole (Map &mp_i, bool Kerr_schild, double massbh)
 Standard constructor.
 
 Black_hole (const Black_hole &)
 Copy constructor.
 
 Black_hole (Map &mp_i, FILE *fich)
 Constructor from a file (see sauve(FILE*) )
 
virtual ~Black_hole ()
 Destructor.
 
void operator= (const Black_hole &)
 Assignment to another Black_hole.
 
Mapset_mp ()
 Read/write of the mapping.
 
doubleset_mass_bh ()
 Read/write of the gravitational mass of BH [{\tt m_unit}].
 
const Mapget_mp () const
 Returns the mapping.
 
bool is_kerrschild () const
 Returns true for a Kerr-Schild background, false for a Conformally flat one.
 
double get_mass_bh () const
 Returns the gravitational mass of BH [{\tt m_unit}].
 
const Scalarget_lapconf () const
 Returns lapconf generated by the black hole.
 
const Scalarget_lapconf_rs () const
 Returns the part of lapconf from the numerical computation.
 
const Scalarget_lapse () const
 Returns the lapse function generated by the black hole.
 
const Vectorget_shift () const
 Returns the shift vector generated by the black hole.
 
const Vectorget_shift_rs () const
 Returns the part of the shift vector from the numerical computation.
 
const Scalarget_confo () const
 Returns the conformal factor generated by the black hole.
 
virtual void sauve (FILE *) const
 Save in a file.
 
virtual double mass_irr () const
 Irreducible mass of the black hole.
 
virtual double mass_adm () const
 ADM mass.
 
virtual double mass_kom () const
 Komar mass.
 
virtual double rad_ah () const
 Radius of the apparent horizon.
 
double spin_am_bh (bool bclapconf_nd, bool bclapconf_fs, const Tbl &xi_i, const double &phi_i, const double &theta_i, const int &nrk_phi, const int &nrk_theta) const
 Spin angular momentum.
 
const Tblangu_mom_bh () const
 Total angular momentum.
 
const Valeur bc_lapconf (bool neumann, bool first) const
 Boundary condition on the apparent horizon of the black hole for the lapse function: 2-D Valeur.
 
const Valeur bc_shift_x (double omega_r) const
 Boundary condition on the apparent horizon of the black hole for the shift vector of the \fx\f direction: 2-D Valeur.
 
const Valeur bc_shift_y (double omega_r) const
 Boundary condition on the apparent horizon of the black hole for the shift vector of the \fy\f direction: 2-D Valeur.
 
const Valeur bc_shift_z () const
 Boundary condition on the apparent horizon of the black hole for the shift vector of the \fz\f direction: 2-D Valeur.
 
const Valeur bc_confo () const
 Boundary condition on the apparent horizon of the black hole for the conformal factor: 2-D Valeur.
 
void extr_curv_bh ()
 Computes taij , taij_quad from shift , lapse , confo .
 
void equilibrium_spher (bool neumann, bool first, double spin_omega, double precis=1.e-14, double precis_shift=1.e-8)
 Computes a spherical, static black-hole by giving boundary conditions on the apparent horizon.
 
void static_bh (bool neumann, bool first)
 Sets the metric quantities to a spherical, static blach-hole analytic solution.
 
double rah_iso (bool neumann, bool first) const
 Computes a radius of apparent horizon (excised surface) in isotropic coordinates.
 
const Scalar r_coord (bool neumann, bool first) const
 Expresses the areal radial coordinate by that in spatially isotropic coordinates.
 
Tbl runge_kutta_phi_bh (const Tbl &xi_i, const double &phi_i, const int &nrk) const
 Compute a forth-order Runge-Kutta integration to the phi direction for the solution of the Killing vectors on the equator.
 
Tbl runge_kutta_theta_bh (const Tbl &xi_i, const double &theta_i, const double &phi, const int &nrk) const
 Compute a forth-order Runge-Kutta integration to the theta direction for the solution of the Killing vectors.
 
Vector killing_vect_bh (const Tbl &xi_i, const double &phi_i, const double &theta_i, const int &nrk_phi, const int &nrk_theta) const
 Compute the Killing vector of a black hole normalized so that its affine length is 2 M_PI.
 

Protected Member Functions

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

Protected Attributes

Mapmp
 Mapping associated with the black hole.
 
bool kerrschild
 true for a Kerr-Schild background, false for a conformally flat background
 
double mass_bh
 Gravitational mass of BH.
 
Scalar lapconf
 A function (lapse function * conformal factor) lapconf generated by the black hole.
 
Scalar lapconf_rs
 Part of lapconf from the numerical computation.
 
Scalar lapconf_bh
 Part of lapconf from the analytic background.
 
Scalar lapse
 Lapse function generated by the black hole.
 
Vector shift
 Shift vector generated by the black hole.
 
Vector shift_rs
 Part of the shift vector from the numerical computation.
 
Vector shift_bh
 Part of the shift vector from the analytic background.
 
Scalar confo
 Conformal factor generated by the black hole.
 
Sym_tensor taij
 Trace of the extrinsic curvature.
 
Sym_tensor taij_rs
 Part of the extrinsic curvature tensor.
 
Scalar taij_quad
 Part of the scalar $\eta_{ik} \eta_{jl} A^{ij} A^{kl}$ generated by $A_{ij}$.
 
Scalar taij_quad_rs
 Part of the scalar.
 
Metric_flat flat
 Flat metric defined on the mapping (Spherical components with respect to the mapping of the black hole ).
 
doublep_mass_irr
 Conformal metric $\tilde \gamma_{ij}$.
 
doublep_mass_adm
 Irreducible mass of the black hole.
 
doublep_mass_kom
 ADM mass.
 
doublep_rad_ah
 Komar mass.
 
doublep_spin_am_bh
 Radius of the apparent horizon.
 
Tblp_angu_mom_bh
 Spin angular momentum.
 

Friends

ostreamoperator<< (ostream &, const Black_hole &)
 Display.
 

Detailed Description

Base class for black holes.

()

According to the 3+1 formalism, the spacetime metric is written

\[
  ds^2 = - \alpha^2 dt^2 + \gamma_{ij} ( dx^i + \beta^i dt )
                                       ( dx^j + \beta^j dt )
\]

where $\gamma_{ij}$ is the spatial metric.

Definition at line 74 of file blackhole.h.

Constructor & Destructor Documentation

◆ Black_hole() [1/3]

Lorene::Black_hole::Black_hole ( Map mp_i,
bool  Kerr_schild,
double  massbh 
)

Standard constructor.

Parameters
mp_iMapping on which the black hole will be defined

Definition at line 71 of file blackhole.C.

References confo, lapconf, lapconf_bh, lapconf_rs, lapse, set_der_0x0(), Lorene::Tensor::set_etat_zero(), shift, shift_bh, shift_rs, Lorene::Scalar::std_spectral_base(), taij, taij_quad, taij_quad_rs, and taij_rs.

◆ Black_hole() [2/3]

Lorene::Black_hole::Black_hole ( const Black_hole bh)

Copy constructor.

Definition at line 118 of file blackhole.C.

References set_der_0x0().

◆ Black_hole() [3/3]

Lorene::Black_hole::Black_hole ( Map mp_i,
FILE fich 
)

Constructor from a file (see sauve(FILE*) )

Parameters
mp_iMapping on which the black hole will be defined
fichinput file (must have been created by the function sauve )

Definition at line 142 of file blackhole.C.

References confo, kerrschild, lapconf, lapconf_bh, lapconf_rs, lapse, mass_bh, set_der_0x0(), Lorene::Tensor::set_etat_zero(), shift, shift_bh, shift_rs, Lorene::Scalar::std_spectral_base(), Lorene::Vector::std_spectral_base(), taij, taij_quad, taij_quad_rs, and taij_rs.

◆ ~Black_hole()

Lorene::Black_hole::~Black_hole ( )
virtual

Destructor.

Definition at line 194 of file blackhole.C.

References del_deriv().

Member Function Documentation

◆ angu_mom_bh()

◆ bc_confo()

◆ bc_lapconf()

const Valeur Lorene::Black_hole::bc_lapconf ( bool  neumann,
bool  first 
) const

◆ bc_shift_x()

const Valeur Lorene::Black_hole::bc_shift_x ( double  omega_r) const

◆ bc_shift_y()

const Valeur Lorene::Black_hole::bc_shift_y ( double  omega_r) const

◆ bc_shift_z()

const Valeur Lorene::Black_hole::bc_shift_z ( ) const

◆ del_deriv()

void Lorene::Black_hole::del_deriv ( ) const
protectedvirtual

Deletes all the derived quantities.

Reimplemented in Lorene::Hole_bhns.

Definition at line 205 of file blackhole.C.

References p_angu_mom_bh, p_mass_adm, p_mass_irr, p_mass_kom, p_rad_ah, p_spin_am_bh, and set_der_0x0().

◆ equilibrium_spher()

void Lorene::Black_hole::equilibrium_spher ( bool  neumann,
bool  first,
double  spin_omega,
double  precis = 1.e-14,
double  precis_shift = 1.e-8 
)

Computes a spherical, static black-hole by giving boundary conditions on the apparent horizon.

Parameters
neumann[input] true for the neumann bc, false for the dirichlet one for the lapse
first[input] true for the first type of bc, false for the second type
spin_omega[input] spin parameter of the black hole
precis[input] threshold in the relative difference of a metric quantity between two succesive steps to stop the iterative procedure (default value: 1.e-14)
precis_shift[input] threshold in the relative difference of the shift vector between two succesive steps to stop the iterative procedure (default value: 1.e-8)

Definition at line 70 of file blackhole_eq_spher.C.

References Lorene::Tensor::annule_domain(), bc_confo(), bc_lapconf(), bc_shift_x(), bc_shift_y(), bc_shift_z(), confo, Lorene::contract(), Lorene::Map::cosp, Lorene::Map::cost, del_deriv(), Lorene::Scalar::deriv(), Lorene::diffrel(), extr_curv_bh(), Lorene::Scalar::filtre(), Lorene::Mg3d::get_angu(), Lorene::Map::get_bvect_cart(), Lorene::Scalar::get_dzpuis(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Scalar::inc_dzpuis(), kerrschild, lapconf, lapconf_bh, lapconf_rs, lapse, mass_adm(), mass_bh, mass_irr(), mass_kom(), mp, Lorene::Scalar::poisson_dirichlet(), Lorene::Scalar::poisson_neumann(), Lorene::pow(), Lorene::Map::r, r_coord(), Lorene::Scalar::raccord(), rad_ah(), Lorene::Tenseur::set(), Lorene::Tbl::set(), Lorene::Vector::set(), Lorene::Scalar::set_dzpuis(), Lorene::Scalar::set_etat_qcq(), Lorene::Tenseur::set_etat_qcq(), Lorene::Tensor::set_etat_qcq(), Lorene::Tensor::set_etat_zero(), shift, shift_bh, shift_rs, Lorene::Map::sinp, Lorene::Map::sint, Lorene::sqrt(), Lorene::Scalar::std_spectral_base(), Lorene::Vector::std_spectral_base(), taij, and taij_quad.

◆ extr_curv_bh()

◆ get_confo()

const Scalar & Lorene::Black_hole::get_confo ( ) const
inline

Returns the conformal factor generated by the black hole.

Definition at line 241 of file blackhole.h.

References confo.

◆ get_lapconf()

const Scalar & Lorene::Black_hole::get_lapconf ( ) const
inline

Returns lapconf generated by the black hole.

Definition at line 224 of file blackhole.h.

References lapconf.

◆ get_lapconf_rs()

const Scalar & Lorene::Black_hole::get_lapconf_rs ( ) const
inline

Returns the part of lapconf from the numerical computation.

Definition at line 227 of file blackhole.h.

References lapconf_rs.

◆ get_lapse()

const Scalar & Lorene::Black_hole::get_lapse ( ) const
inline

Returns the lapse function generated by the black hole.

Definition at line 230 of file blackhole.h.

References lapse.

◆ get_mass_bh()

double Lorene::Black_hole::get_mass_bh ( ) const
inline

Returns the gravitational mass of BH [{\tt m_unit}].

Definition at line 221 of file blackhole.h.

References mass_bh.

◆ get_mp()

const Map & Lorene::Black_hole::get_mp ( ) const
inline

Returns the mapping.

Definition at line 213 of file blackhole.h.

References mp.

◆ get_shift()

const Vector & Lorene::Black_hole::get_shift ( ) const
inline

Returns the shift vector generated by the black hole.

Definition at line 233 of file blackhole.h.

References shift.

◆ get_shift_rs()

const Vector & Lorene::Black_hole::get_shift_rs ( ) const
inline

Returns the part of the shift vector from the numerical computation.

Definition at line 238 of file blackhole.h.

References shift_rs.

◆ is_kerrschild()

bool Lorene::Black_hole::is_kerrschild ( ) const
inline

Returns true for a Kerr-Schild background, false for a Conformally flat one.

Definition at line 218 of file blackhole.h.

References kerrschild.

◆ killing_vect_bh()

Vector Lorene::Black_hole::killing_vect_bh ( const Tbl xi_i,
const double phi_i,
const double theta_i,
const int nrk_phi,
const int nrk_theta 
) const

Compute the Killing vector of a black hole normalized so that its affine length is 2 M_PI.

Parameters
xi_i[input] initial set of the Killing vectors at the starting point on the equator
phi_i[input] initial phi coordinate at which the integration starts
theta_i[input] initial theta coordinate at which the integration starts
nrk_phi[input] number of the Runge-Kutta integration between two successive collocation points for the phi direction
nrk_theta[input] number of the Runge-Kutta integration between two successive collocation points for the theta direction

Definition at line 66 of file blackhole_killing.C.

References confo, Lorene::Map::get_bvect_spher(), Lorene::Tbl::get_dim(), Lorene::Map::get_mg(), Lorene::Tbl::get_ndim(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), kerrschild, mp, Lorene::pow(), Lorene::Map::r, rad_ah(), runge_kutta_phi_bh(), runge_kutta_theta_bh(), Lorene::Tbl::set(), Lorene::Vector::set(), Lorene::Tbl::set_etat_qcq(), Lorene::Tensor::set_etat_qcq(), Lorene::Scalar::set_grid_point(), Lorene::Map::sint, Lorene::Scalar::std_spectral_base(), Lorene::Vector::std_spectral_base(), Lorene::Scalar::val_grid_point(), and Lorene::Scalar::val_point().

◆ mass_adm()

◆ mass_irr()

double Lorene::Black_hole::mass_irr ( ) const
virtual

◆ mass_kom()

◆ operator=()

void Lorene::Black_hole::operator= ( const Black_hole bh)

Assignment to another Black_hole.

Definition at line 236 of file blackhole.C.

References confo, del_deriv(), flat, kerrschild, lapconf, lapconf_bh, lapconf_rs, lapse, mass_bh, mp, shift, shift_bh, shift_rs, taij, taij_quad, taij_quad_rs, and taij_rs.

◆ operator>>()

ostream & Lorene::Black_hole::operator>> ( ostream ost) const
protectedvirtual

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

Reimplemented in Lorene::Hole_bhns.

Definition at line 287 of file blackhole.C.

References confo, Lorene::Map::get_mg(), Lorene::Mg3d::get_nt(), kerrschild, lapconf, lapse, mass_adm(), mass_bh, mass_irr(), mass_kom(), mp, shift, and Lorene::Scalar::val_grid_point().

◆ r_coord()

const Scalar Lorene::Black_hole::r_coord ( bool  neumann,
bool  first 
) const

Expresses the areal radial coordinate by that in spatially isotropic coordinates.

Parameters
neumann[input] true for the neumann bc, false for the dirichlet one for the lapse
first[input] true for the first type of bc, false for the second type

Definition at line 66 of file blackhole_r_coord.C.

References Lorene::Tensor::annule_domain(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::log(), mass_bh, mp, Lorene::Map::r, Lorene::Scalar::raccord(), Lorene::Scalar::set_grid_point(), Lorene::sqrt(), Lorene::Scalar::std_spectral_base(), and Lorene::Scalar::val_grid_point().

◆ rad_ah()

double Lorene::Black_hole::rad_ah ( ) const
virtual

Radius of the apparent horizon.

Definition at line 505 of file blackhole_global.C.

References mp, p_rad_ah, Lorene::Map::r, Lorene::Scalar::std_spectral_base(), and Lorene::Scalar::val_grid_point().

◆ rah_iso()

double Lorene::Black_hole::rah_iso ( bool  neumann,
bool  first 
) const

Computes a radius of apparent horizon (excised surface) in isotropic coordinates.

Parameters
neumann[input] true for the neumann bc, false for the dirichlet one for the lapse
first[input] true for the first type of bc, false for the second type

Definition at line 69 of file blackhole_rah_iso.C.

References Lorene::exp(), and Lorene::sqrt().

◆ runge_kutta_phi_bh()

Tbl Lorene::Black_hole::runge_kutta_phi_bh ( const Tbl xi_i,
const double phi_i,
const int nrk 
) const

Compute a forth-order Runge-Kutta integration to the phi direction for the solution of the Killing vectors on the equator.

Parameters
xi_i[input] initial set of the Killing vectors at the starting point on the equator
phi_i[input] initial phi coordinate at which the integration starts
nrk[input] number of the Runge-Kutta integration between two successive collocation points

Definition at line 67 of file blackhole_rk_phi.C.

References confo, Lorene::Scalar::dsdt(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), kerrschild, Lorene::Scalar::lapang(), mp, rad_ah(), Lorene::Tbl::set(), Lorene::Tbl::set_etat_qcq(), Lorene::Scalar::std_spectral_base(), and Lorene::Scalar::val_point().

◆ runge_kutta_theta_bh()

Tbl Lorene::Black_hole::runge_kutta_theta_bh ( const Tbl xi_i,
const double theta_i,
const double phi,
const int nrk 
) const

Compute a forth-order Runge-Kutta integration to the theta direction for the solution of the Killing vectors.

Parameters
xi_i[input] initial set of the Killing vectors at the starting point on the equator
theta_i[input] initial theta coordinate at which the integration starts
phi[input] fixed phi coordinate during integration to the theta direction
nrk[input] number of the Runge-Kutta integration between two successive collocation points

Definition at line 67 of file blackhole_rk_theta.C.

References confo, Lorene::Map::get_mg(), Lorene::Mg3d::get_nt(), kerrschild, Lorene::Scalar::lapang(), mp, rad_ah(), Lorene::Tbl::set(), Lorene::Tbl::set_etat_qcq(), Lorene::Scalar::std_spectral_base(), Lorene::Scalar::stdsdp(), and Lorene::Scalar::val_point().

◆ sauve()

void Lorene::Black_hole::sauve ( FILE fich) const
virtual

Save in a file.

Reimplemented in Lorene::Hole_bhns.

Definition at line 267 of file blackhole.C.

References confo, kerrschild, lapconf_rs, mass_bh, Lorene::Scalar::sauve(), Lorene::Tensor::sauve(), and shift_rs.

◆ set_der_0x0()

void Lorene::Black_hole::set_der_0x0 ( ) const
protected

Sets to 0x0 all the pointers on derived quantities.

Definition at line 218 of file blackhole.C.

References p_angu_mom_bh, p_mass_adm, p_mass_irr, p_mass_kom, p_rad_ah, and p_spin_am_bh.

◆ set_mass_bh()

double & Lorene::Black_hole::set_mass_bh ( )
inline

Read/write of the gravitational mass of BH [{\tt m_unit}].

Definition at line 207 of file blackhole.h.

References mass_bh.

◆ set_mp()

Map & Lorene::Black_hole::set_mp ( )
inline

Read/write of the mapping.

Definition at line 204 of file blackhole.h.

References mp.

◆ spin_am_bh()

◆ static_bh()

void Lorene::Black_hole::static_bh ( bool  neumann,
bool  first 
)

Sets the metric quantities to a spherical, static blach-hole analytic solution.

Parameters
neumann[input] true for the neumann bc, false for the dirichlet one for the lapse
first[input] true for the first type of bc, false for the second type

Definition at line 60 of file blackhole_static.C.

References Lorene::Tensor::annule_domain(), confo, Lorene::Map::cosp, Lorene::Map::cost, Lorene::Map::get_bvect_cart(), kerrschild, lapconf, lapse, mass_bh, mp, Lorene::pow(), Lorene::Map::r, r_coord(), Lorene::Scalar::raccord(), Lorene::Vector::set(), Lorene::Tensor::set_etat_qcq(), shift, Lorene::Map::sinp, Lorene::Map::sint, Lorene::sqrt(), Lorene::Scalar::std_spectral_base(), and Lorene::Vector::std_spectral_base().

Friends And Related Symbol Documentation

◆ operator<<

ostream & operator<< ( ostream ost,
const Black_hole bh 
)
friend

Display.

Definition at line 280 of file blackhole.C.

Member Data Documentation

◆ confo

Scalar Lorene::Black_hole::confo
protected

Conformal factor generated by the black hole.

Definition at line 118 of file blackhole.h.

◆ flat

Metric_flat Lorene::Black_hole::flat
protected

Flat metric defined on the mapping (Spherical components with respect to the mapping of the black hole ).

Definition at line 143 of file blackhole.h.

◆ kerrschild

bool Lorene::Black_hole::kerrschild
protected

true for a Kerr-Schild background, false for a conformally flat background

Definition at line 85 of file blackhole.h.

◆ lapconf

Scalar Lorene::Black_hole::lapconf
protected

A function (lapse function * conformal factor) lapconf generated by the black hole.

Definition at line 97 of file blackhole.h.

◆ lapconf_bh

Scalar Lorene::Black_hole::lapconf_bh
protected

Part of lapconf from the analytic background.

Definition at line 103 of file blackhole.h.

◆ lapconf_rs

Scalar Lorene::Black_hole::lapconf_rs
protected

Part of lapconf from the numerical computation.

Definition at line 100 of file blackhole.h.

◆ lapse

Scalar Lorene::Black_hole::lapse
protected

Lapse function generated by the black hole.

Definition at line 106 of file blackhole.h.

◆ mass_bh

double Lorene::Black_hole::mass_bh
protected

Gravitational mass of BH.

Definition at line 88 of file blackhole.h.

◆ mp

Map& Lorene::Black_hole::mp
protected

Mapping associated with the black hole.

Definition at line 80 of file blackhole.h.

◆ p_angu_mom_bh

Tbl* Lorene::Black_hole::p_angu_mom_bh
mutableprotected

Spin angular momentum.

Total angular momentum of the black hole

Definition at line 162 of file blackhole.h.

◆ p_mass_adm

double* Lorene::Black_hole::p_mass_adm
mutableprotected

Irreducible mass of the black hole.

Definition at line 153 of file blackhole.h.

◆ p_mass_irr

double* Lorene::Black_hole::p_mass_irr
mutableprotected

Conformal metric $\tilde \gamma_{ij}$.

Definition at line 151 of file blackhole.h.

◆ p_mass_kom

double* Lorene::Black_hole::p_mass_kom
mutableprotected

ADM mass.

Definition at line 155 of file blackhole.h.

◆ p_rad_ah

double* Lorene::Black_hole::p_rad_ah
mutableprotected

Komar mass.

Definition at line 157 of file blackhole.h.

◆ p_spin_am_bh

double* Lorene::Black_hole::p_spin_am_bh
mutableprotected

Radius of the apparent horizon.

Definition at line 159 of file blackhole.h.

◆ shift

Vector Lorene::Black_hole::shift
protected

Shift vector generated by the black hole.

Definition at line 109 of file blackhole.h.

◆ shift_bh

Vector Lorene::Black_hole::shift_bh
protected

Part of the shift vector from the analytic background.

Definition at line 115 of file blackhole.h.

◆ shift_rs

Vector Lorene::Black_hole::shift_rs
protected

Part of the shift vector from the numerical computation.

Definition at line 112 of file blackhole.h.

◆ taij

Sym_tensor Lorene::Black_hole::taij
protected

Trace of the extrinsic curvature.

Extrinsic curvature tensor $\ A^{ij}$ generated by shift , lapse , and confo .

Definition at line 127 of file blackhole.h.

◆ taij_quad

Scalar Lorene::Black_hole::taij_quad
protected

Part of the scalar $\eta_{ik} \eta_{jl} A^{ij} A^{kl}$ generated by $A_{ij}$.

Definition at line 135 of file blackhole.h.

◆ taij_quad_rs

Scalar Lorene::Black_hole::taij_quad_rs
protected

Part of the scalar.

Definition at line 138 of file blackhole.h.

◆ taij_rs

Sym_tensor Lorene::Black_hole::taij_rs
protected

Part of the extrinsic curvature tensor.

Definition at line 130 of file blackhole.h.


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