Base class for black holes. More...

#include <blackhole.h>

Inheritance diagram for Lorene::Black_hole:

Public Member Functions
	Black_hole (Map &mp_i, bool Kerr_schild, double massbh)
	Standard constructor. More...

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

	Black_hole (Map &mp_i, FILE *fich)
	Constructor from a file (see `sauve(FILE*)` ) More...

virtual	~Black_hole ()
	Destructor. More...

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

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

double &	set_mass_bh ()
	Read/write of the gravitational mass of BH [{ m_unit}]. More...

const Map &	get_mp () const
	Returns the mapping. More...

bool	is_kerrschild () const
	Returns `true` for a Kerr-Schild background, `false` for a Conformally flat one. More...

double	get_mass_bh () const
	Returns the gravitational mass of BH [{ m_unit}]. More...

const Scalar &	get_lapconf () const
	Returns lapconf generated by the black hole. More...

const Scalar &	get_lapconf_rs () const
	Returns the part of lapconf from the numerical computation. More...

const Scalar &	get_lapse () const
	Returns the lapse function generated by the black hole. More...

const Vector &	get_shift () const
	Returns the shift vector generated by the black hole. More...

const Vector &	get_shift_rs () const
	Returns the part of the shift vector from the numerical computation. More...

const Scalar &	get_confo () const
	Returns the conformal factor generated by the black hole. More...

virtual void	sauve (FILE *) const
	Save in a file. More...

virtual double	mass_irr () const
	Irreducible mass of the black hole. More...

virtual double	mass_adm () const
	ADM mass. More...

virtual double	mass_kom () const
	Komar mass. More...

virtual double	rad_ah () const
	Radius of the apparent horizon. More...

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. More...

const Tbl &	angu_mom_bh () const
	Total angular momentum. More...

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`. More...

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 direction: 2-D `Valeur`. More...

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 direction: 2-D `Valeur`. More...

const Valeur	bc_shift_z () const
	Boundary condition on the apparent horizon of the black hole for the shift vector of the direction: 2-D `Valeur`. More...

const Valeur	bc_confo () const
	Boundary condition on the apparent horizon of the black hole for the conformal factor: 2-D `Valeur`. More...

void	extr_curv_bh ()
	Computes `taij` , `taij_quad` from `shift` , `lapse` , `confo` . More...

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. More...

void	static_bh (bool neumann, bool first)
	Sets the metric quantities to a spherical, static blach-hole analytic solution. More...

double	rah_iso (bool neumann, bool first) const
	Computes a radius of apparent horizon (excised surface) in isotropic coordinates. More...

const Scalar	r_coord (bool neumann, bool first) const
	Expresses the areal radial coordinate by that in spatially isotropic coordinates. More...

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. More...

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. More...

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. 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...

Protected Attributes
Map &	mp
	Mapping associated with the black hole. More...

bool	kerrschild
	`true` for a Kerr-Schild background, `false` for a conformally flat background More...

double	mass_bh
	Gravitational mass of BH. More...

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

Scalar	lapconf_rs
	Part of lapconf from the numerical computation. More...

Scalar	lapconf_bh
	Part of lapconf from the analytic background. More...

Scalar	lapse
	Lapse function generated by the black hole. More...

Vector	shift
	Shift vector generated by the black hole. More...

Vector	shift_rs
	Part of the shift vector from the numerical computation. More...

Vector	shift_bh
	Part of the shift vector from the analytic background. More...

Scalar	confo
	Conformal factor generated by the black hole. More...

Sym_tensor	taij
	Trace of the extrinsic curvature. More...

Sym_tensor	taij_rs
	Part of the extrinsic curvature tensor. More...

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

Scalar	taij_quad_rs
	Part of the scalar. More...

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

double *	p_mass_irr
	Conformal metric $\tilde \gamma_{ij}$ . More...

double *	p_mass_adm
	Irreducible mass of the black hole. More...

double *	p_mass_kom
	ADM mass. More...

double *	p_rad_ah
	Komar mass. More...

double *	p_spin_am_bh
	Radius of the apparent horizon. More...

Tbl *	p_angu_mom_bh
	Spin angular momentum. More...

Friends
ostream &	operator<< (ostream &, const Black_hole &)
	Display. More...

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_i	Mapping on which the black hole will be defined

Definition at line 74 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 121 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_i	Mapping on which the black hole will be defined
fich	input file (must have been created by the function `sauve` )

Definition at line 145 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::Vector::std_spectral_base(), Lorene::Scalar::std_spectral_base(), taij, taij_quad, taij_quad_rs, and taij_rs.

◆ ~Black_hole()

Lorene::Black_hole::~Black_hole ( )

virtual

Destructor.

Definition at line 197 of file blackhole.C.

References del_deriv().

Member Function Documentation

◆ angu_mom_bh()

const Tbl & Lorene::Black_hole::angu_mom_bh ( ) const

Total angular momentum.

Returns: 1-D { Tbl} of size 3, according to \ { angu_mom()(0)} = $J^x$, \ { angu_mom()(1)} = $J^y$, \ { angu_mom()(2)} = $J^z$.

Definition at line 637 of file blackhole_global.C.

References Lorene::Tensor::annule_domain(), Lorene::Tbl::annule_hard(), Lorene::Map::cosp, Lorene::Map::cost, Lorene::Scalar::dec_dzpuis(), Lorene::Map::get_bvect_cart(), Lorene::Map_af::integrale_surface(), mp, p_angu_mom_bh, Lorene::Scalar::raccord(), Lorene::Tbl::set(), Lorene::Tensor::set(), Lorene::Tensor::set_etat_qcq(), Lorene::Map::sinp, Lorene::Map::sint, Lorene::Scalar::std_spectral_base(), taij, Lorene::Map::val_r(), Lorene::Map::x, Lorene::Map::y, and Lorene::Map::z.

◆ bc_confo()

const Valeur Lorene::Black_hole::bc_confo ( ) const

Boundary condition on the apparent horizon of the black hole for the conformal factor: 2-D Valeur.

Definition at line 413 of file blackhole_bc.C.

References confo, Lorene::Map::cosp, Lorene::Map::cost, Lorene::Scalar::dsdr(), Lorene::Mg3d::get_angu(), Lorene::Scalar::get_dzpuis(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), kerrschild, lapconf, mass_bh, mp, Lorene::pow(), Lorene::Map::r, Lorene::Valeur::set(), Lorene::Scalar::set_dzpuis(), shift, Lorene::Map::sinp, Lorene::Map::sint, Lorene::Valeur::std_base_scal(), Lorene::Scalar::std_spectral_base(), and Lorene::Scalar::val_grid_point().

◆ bc_lapconf()

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

Boundary condition on the apparent horizon of the black hole for the lapse function: 2-D Valeur.

Definition at line 74 of file blackhole_bc.C.

References Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), kerrschild, lapconf, mp, Lorene::Map::r, Lorene::Valeur::set(), Lorene::Valeur::std_base_scal(), Lorene::Scalar::std_spectral_base(), and Lorene::Scalar::val_grid_point().

◆ bc_shift_x()

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

Boundary condition on the apparent horizon of the black hole for the shift vector of the direction: 2-D Valeur.

Definition at line 214 of file blackhole_bc.C.

References Lorene::Valeur::base, confo, Lorene::Map::cosp, Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), kerrschild, lapconf, mp, Lorene::pow(), Lorene::Map::r, Lorene::Valeur::set(), Lorene::Map::sint, Lorene::Mg3d::std_base_vect_cart(), Lorene::Scalar::std_spectral_base(), Lorene::Scalar::val_grid_point(), and Lorene::Map::y.

◆ bc_shift_y()

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

Boundary condition on the apparent horizon of the black hole for the shift vector of the direction: 2-D Valeur.

Definition at line 284 of file blackhole_bc.C.

References Lorene::Valeur::base, confo, Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), kerrschild, lapconf, mp, Lorene::pow(), Lorene::Map::r, Lorene::Valeur::set(), Lorene::Map::sinp, Lorene::Map::sint, Lorene::Mg3d::std_base_vect_cart(), Lorene::Scalar::std_spectral_base(), Lorene::Scalar::val_grid_point(), and Lorene::Map::x.

◆ bc_shift_z()

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

Boundary condition on the apparent horizon of the black hole for the shift vector of the direction: 2-D Valeur.

Definition at line 353 of file blackhole_bc.C.

References Lorene::Valeur::base, confo, Lorene::Map::cost, Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), kerrschild, lapconf, mp, Lorene::pow(), Lorene::Map::r, Lorene::Valeur::set(), Lorene::Mg3d::std_base_vect_cart(), Lorene::Scalar::std_spectral_base(), and Lorene::Scalar::val_grid_point().

◆ del_deriv()

void Lorene::Black_hole::del_deriv ( ) const

protectedvirtual

Deletes all the derived quantities.

Reimplemented in Lorene::Hole_bhns.

Definition at line 208 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 73 of file blackhole_eq_spher.C.

References Lorene::Tensor::annule_domain(), bc_confo(), bc_lapconf(), confo, Lorene::contract(), Lorene::Map::cosp, Lorene::Map::cost, Lorene::Scalar::deriv(), extr_curv_bh(), 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_bh, mp, Lorene::Scalar::poisson_dirichlet(), Lorene::Scalar::poisson_neumann(), Lorene::pow(), Lorene::Map::r, r_coord(), Lorene::Scalar::raccord(), Lorene::Vector::set(), Lorene::Tensor::set(), Lorene::Scalar::set_dzpuis(), Lorene::Scalar::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::Vector::std_spectral_base(), Lorene::Scalar::std_spectral_base(), taij, and taij_quad.

◆ extr_curv_bh()

void Lorene::Black_hole::extr_curv_bh ( )

Computes taij , taij_quad from shift , lapse , confo .

Definition at line 65 of file blackhole_extr_curv.C.

References Lorene::Tensor::annule_domain(), Lorene::Metric_flat::con(), confo, Lorene::Map::cosp, Lorene::Map::cost, Lorene::Metric_flat::cov(), flat, Lorene::Map::get_bvect_cart(), Lorene::Scalar::inc_dzpuis(), kerrschild, lapconf, mass_bh, mp, Lorene::pow(), Lorene::Map::r, Lorene::Scalar::raccord(), Lorene::Tensor::set(), Lorene::Tensor::set_etat_qcq(), shift, shift_rs, Lorene::Map::sinp, Lorene::Map::sint, Lorene::sqrt(), Lorene::Tensor::std_spectral_base(), Lorene::Scalar::std_spectral_base(), taij, taij_quad, taij_quad_rs, and taij_rs.

◆ 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 [{ 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 69 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_nr(), kerrschild, mp, Lorene::pow(), Lorene::Map::r, rad_ah(), runge_kutta_phi_bh(), runge_kutta_theta_bh(), Lorene::Tbl::set(), Lorene::Tbl::set_etat_qcq(), Lorene::Scalar::set_grid_point(), Lorene::Map::sint, Lorene::Scalar::std_spectral_base(), Lorene::Scalar::val_grid_point(), and Lorene::Scalar::val_point().

◆ mass_adm()

double Lorene::Black_hole::mass_adm ( ) const

virtual

◆ mass_irr()

double Lorene::Black_hole::mass_irr ( ) const

virtual

Irreducible mass of the black hole.

Definition at line 72 of file blackhole_global.C.

References Lorene::Tensor::annule_domain(), confo, Lorene::Map_af::integrale_surface(), mp, p_mass_irr, Lorene::pow(), Lorene::Scalar::raccord(), Lorene::sqrt(), Lorene::Scalar::std_spectral_base(), and Lorene::Map::val_r().

◆ mass_kom()

double Lorene::Black_hole::mass_kom ( ) const

virtual

◆ operator=()

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

Assignment to another Black_hole.

Definition at line 239 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 290 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 69 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 508 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 72 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 70 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 70 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 270 of file blackhole.C.

References confo, kerrschild, lapconf_rs, mass_bh, Lorene::Tensor::sauve(), Lorene::Scalar::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 221 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 [{ 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()

double Lorene::Black_hole::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.

Definition at line 531 of file blackhole_global.C.

References Lorene::Tensor::annule_domain(), confo, Lorene::Map::cosp, Lorene::Map::cost, Lorene::Scalar::dec_dzpuis(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Map_af::integrale_surface(), kerrschild, killing_vect_bh(), mp, p_spin_am_bh, Lorene::pow(), Lorene::Scalar::raccord(), Lorene::Tensor::set(), Lorene::Tensor::set_etat_qcq(), Lorene::Map::sinp, Lorene::Map::sint, Lorene::Scalar::std_spectral_base(), taij, and Lorene::Map::val_r().

◆ 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 63 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(), Lorene::Tensor::set_etat_qcq(), shift, Lorene::Map::sinp, Lorene::Map::sint, Lorene::sqrt(), Lorene::Vector::std_spectral_base(), and Lorene::Scalar::std_spectral_base().

Friends And Related Function Documentation

◆ operator<<

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

friend

Display.

Definition at line 283 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:

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Black_hole() [1/3]

◆ Black_hole() [2/3]

◆ Black_hole() [3/3]

◆ ~Black_hole()

Member Function Documentation

◆ angu_mom_bh()

◆ bc_confo()

◆ bc_lapconf()

◆ bc_shift_x()

◆ bc_shift_y()

◆ bc_shift_z()

◆ del_deriv()

◆ equilibrium_spher()

◆ extr_curv_bh()

◆ get_confo()

◆ get_lapconf()

◆ get_lapconf_rs()

◆ get_lapse()

◆ get_mass_bh()

◆ get_mp()

◆ get_shift()

◆ get_shift_rs()

◆ is_kerrschild()

◆ killing_vect_bh()

◆ mass_adm()

◆ mass_irr()

◆ mass_kom()

◆ operator=()

◆ operator>>()

◆ r_coord()

◆ rad_ah()

◆ rah_iso()

◆ runge_kutta_phi_bh()

◆ runge_kutta_theta_bh()

◆ sauve()

◆ set_der_0x0()

◆ set_mass_bh()

◆ set_mp()

◆ spin_am_bh()

◆ static_bh()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ confo

◆ flat

◆ kerrschild

◆ lapconf

◆ lapconf_bh

◆ lapconf_rs

◆ lapse

◆ mass_bh

◆ mp

◆ p_angu_mom_bh

◆ p_mass_adm

◆ p_mass_irr

◆ p_mass_kom

◆ p_rad_ah

◆ p_spin_am_bh

◆ shift

◆ shift_bh

◆ shift_rs

◆ taij

◆ taij_quad

◆ taij_quad_rs

◆ taij_rs