Isol_hole Class Reference

Class to compute quasistationary single black hole spacetimes in vacuum. More...

#include <isol_hole.h>

Public Member Functions
	Isol_hole (const Map &mp_i, double Omega_i, bool NorKappa_i, Scalar NoK_i, bool isCF_i=false)
	Standard constructor.
	Isol_hole (const Isol_hole &)
	Copy constructor.
	Isol_hole (const Map &mp_i, double Omega_i, bool NorKappa_i, Scalar NoK_i, bool isCF_i, FILE *fich)
	Constructor from a file (see `sauve(FILE* )`).
virtual	~Isol_hole ()
	Destructor.
void	operator= (const Isol_hole &)
	Assignment to another `Isol_hole`.
void	compute_stat_metric (double precis, double relax, int mer_max, int mer_max2, bool isvoid=true)
	Computes a quasi-stationary 3-slice from the chosen parameters.
void	secmembre_kerr (Sym_tensor &source_hh)
	Computes the rhs of hyperbolic equation for conformal metric assuming statioarity; WARNING; up to now, we are only able to handle void spacetimes.
const Map &	get_mp () const
	Returns the mapping.
double	get_Omega () const
	Returns the rotation rate.
const Scalar &	get_boundN () const
	Returns the boundary value used for the lapse (if it is the one used).
const Scalar &	get_Kappa () const
	Returns the surface gravity value at the boundary (if it is the one used).
const Scalar &	get_lapse () const
	Returns the lapse function N.
const Scalar &	get_conf_fact () const
	Returns the conformal factor.
const Vector &	get_shift () const
	Returns the shift vector $\beta^i$ .
const Sym_tensor &	get_hij () const
	Returns the deviation tensor $h^{ij}$ .
const Sym_tensor &	get_hatA () const
	Returns the rescaled tracefree extrinsic curvature $\hat{A}^{ij}$ .
virtual void	sauve (FILE *) const
	Save in a file.
void	Einstein_errors ()
	Prints out errors in Einstein equations for the data obtained.
Spheroid	hor ()
	Spheroid at the excised boundary associated with the black hole MOTS on the slice.
double	adm_mass ()
	Computation of the ADM mass of the BH spacetime.
double	komar_angmom ()
	Computation of the Komar angular momentum w.r.t.
double	virial_residue ()
	Computation of the Virial residual, as difference at infinity between the ADM mass and the Komar integral associated to the mass.
Protected Member Functions
virtual void	del_deriv () const
	Deletes all the derived quantities.
virtual void	set_der_0x0 () const
	Sets to `0x0` all the pointers on derived quantities.
Protected Attributes
const Map &	mp
	Mapping associated with the star.
double	Omega
bool	NorKappa
	Rotation rate of the horizon in the azimuthal direction.
Scalar	boundNoK
	Indicates if the boundary value for the lapse or the surface gravity is used.
bool	isCF
	Stores the boundary value of the lapse or surface gravity.
Scalar	lapse
	Lapse function.
Scalar	conf_fact
Vector	shift
	Shift vector.
Sym_tensor	hij
	Deviation tensor( non-flat part of the conformal 3-metric on the slice; see Bonazzola et al.
Sym_tensor	hatA
	Rescaled tracefree extrinsic curvature tensor: see Cordero et al.
Spheroid *	p_hor
	Computation of the spheroid associated with the black hole horizon.
double *	p_adm_mass
	Computation of the ADM mass of the BH spacetime.
double *	p_komar_angmom
	Computation of the Komar angular momentum w.r.t.
double *	p_virial_residue
	Computation of the Virial residual, as difference at infinity between the ADM mass and the Komar integral associated to the mass.

Detailed Description

Class to compute quasistationary single black hole spacetimes in vacuum.

It takes as arguments:

A Mapping mp
A rotation rate $\Omega$ of the horizon in the $\varphi$ direction, assumed to be the direction of the rotational symmetry.
A Scalar NoK, storing the boundary value to be verified either for the lapse or the surface gravity at the excised boundary (which is a MOTS in the philosophy of this class). Whether it corresponds to the lapse or the surface gravity is controlled by the boolean NorKappa. (Warning: setting a boundary on Kappa is not implemented yet).
A boolean isCF, to determine whether or not one adopts the conformally flat approximation in the spacetime construction. Set to FALSE by default.

The main goal of this class is the computation of metric data from those parameters, as well as some global quantities related to the physical characteristics of the spacetime. Those metric data are given on a spacelike 3-slice, assuming a global timelike Killing field and using adapted coordinates.

Definition at line 49 of file isol_hole.h.

Constructor & Destructor Documentation

Isol_hole::Isol_hole	(	const Map &	mp_i,
		double	Omega_i,
		bool	NorKappa_i,
		Scalar	NoK_i,
		bool	isCF_i = `false`
	)

Standard constructor.

Parameters:

	mp_i	Mapping on which the black hole slice will be defined
	Omega_i	rotation rate of the horizon
	NorKappa_i	FALSE: use of boundary value for the lapse TRUE use of boundary value for the surface gravity (Warning! not implemented yet!)
	NoK_i	value either for the lapse or surface gravity.
	isCF_i	FALSE: Full GR 3+1 equations to be verified TRUE: IWM approximation used in determination of the spacetime geometry;

Definition at line 55 of file isol_hole.C.

References boundNoK, Tensor::get_mp(), hatA, hij, lapse, set_der_0x0(), Tensor::set_etat_zero(), and shift.

Isol_hole::Isol_hole ( const Isol_hole & ih )

Copy constructor.

Definition at line 87 of file isol_hole.C.

References set_der_0x0().

Isol_hole::Isol_hole	(	const Map &	mp_i,
		double	Omega_i,
		bool	NorKappa_i,
		Scalar	NoK_i,
		bool	isCF_i,
		FILE *	fich
	)

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

Parameters:

	mp_i	Mapping on which the star will be defined
	Omega_i	rotation rate of the horizon
	NorKappa_i	FALSE: use of boundary value for the lapse TRUE use of boundary value for the surface gravity (Warning! not implemented yet!)
	NoK_i	value either for the lapse or surface gravity.
	isCF_i	FALSE: Full GR 3+1 equations to be verified TRUE: IWM approximation used in determination of the spacetime geometry;
	fich	input file (must have been created by the function `sauve`)

Definition at line 105 of file isol_hole.C.

References set_der_0x0().

Isol_hole::~Isol_hole ( ) [virtual]

Destructor.

Definition at line 129 of file isol_hole.C.

References del_deriv().

Member Function Documentation

double Isol_hole::adm_mass ( )

Computation of the ADM mass of the BH spacetime.

Definition at line 293 of file isol_hole.C.

References Metric_flat::con(), contract(), Metric::cov(), Tensor_sym::derive_con(), Scalar::dsdr(), Unites::ggrav, hij, mp, sqrt(), and Scalar::std_spectral_base().

void Isol_hole::compute_stat_metric	(	double	precis,
		double	relax,
		int	mer_max,
		int	mer_max2,
		bool	isvoid = `true`
	)

Computes a quasi-stationary 3-slice from the chosen parameters.

Parameters:

precis

[input] threshold in the relative difference between the radial shift for two consecutive steps to stop the iterative procedure (default value: 1.e-11)

Definition at line 49 of file Isol_hole/isol_hole_compute_metric.C.

References Scalar::allocate_all(), Tensor::annule(), Tensor::annule_domain(), Scalar::annule_hard(), boundNoK, Valeur::c_cf, Valeur::coef(), Metric::con(), Metric_flat::con(), contract(), Metric::cov(), Scalar::dec_dzpuis(), Tensor::dec_dzpuis(), Scalar::derive_con(), Tensor::derive_con(), Tensor_sym::derive_con(), Tensor::derive_cov(), Scalar::derive_cov(), Tensor_sym::derive_cov(), Sym_tensor::derive_lie(), Metric::determinant(), Sym_tensor::divergence(), Vector::divergence(), Scalar::dsdr(), Vector::eta(), Scalar::get_etat(), Scalar::get_spectral_va(), hatA, hij, Tensor::inc_dzpuis(), Scalar::inc_dzpuis(), isCF, Scalar::laplacian(), lapse, log(), max(), maxabs(), mp, Vector::mu(), Scalar::mult_rsint(), NorKappa, secmembre_kerr(), Vector::set(), Tensor::set(), Scalar::set_dzpuis(), Scalar::set_etat_qcq(), Scalar::set_grid_point(), Scalar::set_spectral_va(), shift, Scalar::sol_elliptic_boundary(), sqrt(), Vector::std_spectral_base(), Scalar::std_spectral_base(), Tensor::trace(), Tensor::up(), Tensor::up_down(), Scalar::val_grid_point(), and Valeur::ylm().

void Isol_hole::del_deriv ( ) const [protected, virtual]

Deletes all the derived quantities.

Definition at line 140 of file isol_hole.C.

References p_adm_mass, p_hor, p_komar_angmom, p_virial_residue, and set_der_0x0().

void Isol_hole::Einstein_errors ( )

Prints out errors in Einstein equations for the data obtained.

Definition at line 198 of file isol_hole.C.

References Metric_flat::con(), contract(), Scalar::dec_dzpuis(), Tensor::dec_dzpuis(), Scalar::derive_con(), Tensor::derive_cov(), Scalar::derive_cov(), Sym_tensor::derive_lie(), Sym_tensor::divergence(), hatA, hij, lapse, maxabs(), mp, pow(), Metric::ricci(), Metric::ricci_scal(), shift, Tensor::std_spectral_base(), Tensor::trace(), Tensor::up(), and Tensor::up_down().

const Scalar& Isol_hole::get_boundN ( ) const [inline]

Returns the boundary value used for the lapse (if it is the one used).

Definition at line 201 of file isol_hole.h.

References boundNoK, and NorKappa.

const Scalar& Isol_hole::get_conf_fact ( ) const [inline]

Returns the conformal factor.

Definition at line 221 of file isol_hole.h.

const Sym_tensor& Isol_hole::get_hatA ( ) const [inline]

Returns the rescaled tracefree extrinsic curvature $\hat{A}^{ij}$ .

Definition at line 230 of file isol_hole.h.

References hatA.

const Sym_tensor& Isol_hole::get_hij ( ) const [inline]

Returns the deviation tensor $h^{ij}$ .

Definition at line 227 of file isol_hole.h.

References hij.

const Scalar& Isol_hole::get_Kappa ( ) const [inline]

Returns the surface gravity value at the boundary (if it is the one used).

Definition at line 209 of file isol_hole.h.

References boundNoK, and NorKappa.

const Scalar& Isol_hole::get_lapse ( ) const [inline]

Returns the lapse function N.

Definition at line 218 of file isol_hole.h.

References lapse.

const Map& Isol_hole::get_mp ( ) const [inline]

Returns the mapping.

Definition at line 195 of file isol_hole.h.

References mp.

double Isol_hole::get_Omega ( ) const [inline]

Returns the rotation rate.

Definition at line 198 of file isol_hole.h.

const Vector& Isol_hole::get_shift ( ) const [inline]

Returns the shift vector $\beta^i$ .

Definition at line 224 of file isol_hole.h.

References shift.

Spheroid Isol_hole::hor ( )

Spheroid at the excised boundary associated with the black hole MOTS on the slice.

Set by default at the position $ r=1 $ .

Definition at line 251 of file isol_hole.C.

References Metric_flat::con(), hatA, hij, mp, pow(), Tensor::std_spectral_base(), Scalar::std_spectral_base(), Tensor::up_down(), and Scalar::val_grid_point().

double Isol_hole::komar_angmom ( )

Computation of the Komar angular momentum w.r.t.

assumed rotational symmetry

Definition at line 313 of file isol_hole.C.

References Metric_flat::con(), Metric::cov(), Tensor::dec_dzpuis(), Unites::ggrav, hatA, hij, mp, Scalar::mult_r_dzpuis(), Scalar::mult_sint(), pow(), sqrt(), Scalar::std_spectral_base(), Tensor::std_spectral_base(), and Tensor::up_down().

void Isol_hole::operator= ( const Isol_hole & ih )

Assignment to another Isol_hole.

Definition at line 164 of file isol_hole.C.

References boundNoK, del_deriv(), hatA, hij, isCF, lapse, mp, NorKappa, and shift.

void Isol_hole::sauve ( FILE * fich ) const [virtual]

Save in a file.

Definition at line 187 of file isol_hole.C.

References hatA, hij, lapse, Tensor_sym::sauve(), Tensor::sauve(), Scalar::sauve(), and shift.

void Isol_hole::secmembre_kerr ( Sym_tensor & source_hh )

Computes the rhs of hyperbolic equation for conformal metric assuming statioarity; WARNING; up to now, we are only able to handle void spacetimes.

Definition at line 17 of file Isol_hole/secmembre_hij_stat.C.

References Tensor::annule_domain(), Scalar::annule_hard(), Metric_flat::con(), contract(), Metric::cov(), Tensor_sym::derive_con(), Scalar::derive_con(), Tensor::derive_cov(), Scalar::derive_cov(), Tensor_sym::derive_cov(), Scalar::derive_lie(), Sym_tensor::derive_lie(), Vector::divergence(), Map::get_bvect_spher(), Map::get_mg(), Tensor::get_mp(), hatA, hij, Tensor::inc_dzpuis(), Scalar::inc_dzpuis(), Tenseur::inc_dzpuis(), lapse, log(), Vector::ope_killing_conf(), Vector::set(), Tensor::set(), shift, sqrt(), Vector::std_spectral_base(), Tensor::std_spectral_base(), Scalar::std_spectral_base(), and Tensor::trace().

void Isol_hole::set_der_0x0 ( ) const [protected, virtual]

Sets to 0x0 all the pointers on derived quantities.

Definition at line 149 of file isol_hole.C.

References p_adm_mass, p_hor, p_komar_angmom, and p_virial_residue.

double Isol_hole::virial_residue ( )

Computation of the Virial residual, as difference at infinity between the ADM mass and the Komar integral associated to the mass.

Definition at line 338 of file isol_hole.C.

References Scalar::asymptot(), Map::get_mg(), Mg3d::get_nzone(), lapse, and mp.

Member Data Documentation

Scalar Isol_hole::boundNoK [protected]

Indicates if the boundary value for the lapse or the surface gravity is used.

Definition at line 64 of file isol_hole.h.

Sym_tensor Isol_hole::hatA [protected]

Rescaled tracefree extrinsic curvature tensor: see Cordero et al.

( * 2009).

Definition at line 91 of file isol_hole.h.

Sym_tensor Isol_hole::hij [protected]

Deviation tensor( non-flat part of the conformal 3-metric on the slice; see Bonazzola et al.

(2004)).

Definition at line 86 of file isol_hole.h.

bool Isol_hole::isCF [protected]

Stores the boundary value of the lapse or surface gravity.

Indicates if the CF approximation is used.

Definition at line 68 of file isol_hole.h.

Scalar Isol_hole::lapse [protected]

Lapse function.

Definition at line 75 of file isol_hole.h.

const Map& Isol_hole::mp [protected]

Mapping associated with the star.

Definition at line 54 of file isol_hole.h.

bool Isol_hole::NorKappa [protected]

Rotation rate of the horizon in the azimuthal direction.

Definition at line 60 of file isol_hole.h.

double* Isol_hole::p_adm_mass [mutable, protected]

Computation of the ADM mass of the BH spacetime.

Definition at line 102 of file isol_hole.h.

Spheroid* Isol_hole::p_hor [mutable, protected]

Computation of the spheroid associated with the black hole horizon.

Definition at line 100 of file isol_hole.h.

double* Isol_hole::p_komar_angmom [mutable, protected]

Computation of the Komar angular momentum w.r.t.

assumed rotational symmetry

Definition at line 107 of file isol_hole.h.

double* Isol_hole::p_virial_residue [mutable, protected]

Computation of the Virial residual, as difference at infinity between the ADM mass and the Komar integral associated to the mass.

Definition at line 112 of file isol_hole.h.

Vector Isol_hole::shift [protected]

Shift vector.

Definition at line 81 of file isol_hole.h.

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

Isol_hole Class Reference

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation