Excised_slice Class Reference

Class to compute single black hole spacetime excised slices. More...

#include <excised_slice.h>

Public Member Functions
	Excised_slice (const Map &mp_i, int hor_type, int scheme_type)
	Standard constructor.
	Excised_slice (const Excised_slice &)
	Copy constructor.
	Excised_slice (const Map &mp_i, int hor_type, int scheme_type, FILE *fich)
	Constructor from a file (see `sauve(FILE* )`).
virtual	~Excised_slice ()
	Destructor.
void	operator= (const Excised_slice &)
	Assignment to another `Excised_slice`.
void	compute_stat_metric (double precis, double Omega_i, bool NorKappa_i, Scalar NoK_i, bool isCF_i=true, double relax=0.2, int mer_max=2000, int mer_max2=200, bool isvoid=true)
	If hor_type=1, computes a quasi-stationary 3-slice from the chosen parameters.
void	secmembre_kerr (Sym_tensor &source_hh)
	If hor_type=1, computes the rhs of hyperbolic equation for conformal metric assuming stationarity; WARNING; up to now, we are only able to handle void spacetimes.
const Map &	get_mp () const
	Returns the mapping.
int	get_type_hor () const
	Returns the type of horizon that performs the excision.
int	get_field_set () const
	Returns the field set chosen for the data.
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 $\hat{A}^{ij}$ (or its TT part if scheme_type=2).
const Vector &	get_Xx () const
	Return the longitudinal part of Einstein Equations if the scheme is appropriate.
int	set_type_hor ()
	Sets the horizon type.
Scalar &	set_lapse ()
	Sets the lapse.
Scalar &	set_conf_fact ()
	Sets the conformal factor.
Vector &	set_shift ()
	Sets the shift vector.
Sym_tensor &	set_hij ()
	Sets the deviation tensor.
Sym_tensor &	set_hatA ()
	Sets the rescaled tracefree extrinsic curvature $\hat{A}^{ij}$ (or its TT part if scheme_type=2).
Vector &	set_Xx ()
	Sets the longitudinal part of Einstein Equations if the scheme is apropriate.
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 slice.
int	type_hor
	Chosen horizon type.
int	field_set
	Chose field set type.
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: rescaled same way as Cordero et al.
Vector	Xx
	Longitudinal part of the extrinsic curvature.
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 single black hole spacetime excised slices.

It takes as arguments:

A Mapping mp
The type of physical surface used to perform the excision:
- 0. General
- 1. Isolated horizon-like
- 2. Dynamical horizon-like
- 3. Inner trapped surface
The type of metric fields that live in the slice:
- 1. FCF quantities are used (Bonazzola et al., 2004)
- 2. FCF-New scheme quantities are used (Cordero et al., 2009) Members are obviously the metric fields living in the slice, and related variables. The aim of this class is to coordinate Resolution of Einstein equations with the right set of boundary conditions, using classes like Spheroid() and Excision_surf(); Disclaimer: the class Isol_hole() is redundant with this class under a set of parameters; therefore it has to go at some point.

Definition at line 40 of file excised_slice.h.

Constructor & Destructor Documentation

Excised_slice::Excised_slice	(	const Map &	mp_i,
		int	hor_type,
		int	scheme_type
	)

Standard constructor.

Parameters:

mp_i

Mapping on which the black hole slice will be defined

hor_type

Type of horizon used for excision:

0. General
1. Isolated horizon-like
2. Dynamical horizon-like
3. Inner trapped surface

scheme_type

Type of scheme use for metric field computation

1. Original FCF scheme (Bonazzola et al., 2004)
2. New FCF scheme (Cordero et al., 2009)

Definition at line 58 of file excised_slice.C.

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

Excised_slice::Excised_slice ( const Excised_slice & ih )

Copy constructor.

Definition at line 84 of file excised_slice.C.

References set_der_0x0().

Excised_slice::Excised_slice	(	const Map &	mp_i,
		int	hor_type,
		int	scheme_type,
		FILE *	fich
	)

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

Parameters:

	mp_i	Mapping on which the black hole slice will be defined
	hor_type	Type of horizon used for excision: 0. General 1. Isolated horizon-like 2. Dynamical horizon-like 3. Inner trapped surface
	scheme_type	Type of scheme use for metric field computation 1. Original FCF scheme (Bonazzola et al., 2004) 2. New FCF scheme (Cordero et al., 2009)
	fich	input file (must have been created by the function `sauve`)

Definition at line 101 of file excised_slice.C.

References set_der_0x0().

Excised_slice::~Excised_slice ( ) [virtual]

Destructor.

Definition at line 124 of file excised_slice.C.

References del_deriv().

Member Function Documentation

double Excised_slice::adm_mass ( )

Computation of the ADM mass of the BH spacetime.

Definition at line 288 of file excised_slice.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 Excised_slice::compute_stat_metric	(	double	precis,
		double	Omega_i,
		bool	NorKappa_i,
		Scalar	NoK_i,
		bool	isCF_i = `true`,
		double	relax = `0.2`,
		int	mer_max = `2000`,
		int	mer_max2 = `200`,
		bool	isvoid = `true`
	)

If hor_type=1, 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)
	Omega_i,:	Rotation parameter for the isolated horizon slice. The principal Killing vector associated to this quantity will be by default the $e_{}$ vector.
	NorKappa_i,:	boolean to tell whether boundary condition is put on the surface gravity (true) or the lapse (false)
	NoK_i,:	The corresponding Dirichlet value for this quantity.
	isCF,:	Tells whether the calculation is using the conformal flatness approximation (true) or not (false).
	relax	relaxation coefficient for all metric fields (0: no relaxation)
	mer_max,:	Maximum number of iterations allowed in the main loop
	mer_max,:	Maximum number of iterations allowed in the possible secondary loop for conformal geometry computation.
	isvoid,:	indicates whether or not the spacetime is vacuum. This is useless for now since matter terms are not handled in the class.

Definition at line 37 of file Excised_slice/isol_hole_compute_metric.C.

References Scalar::allocate_all(), Tensor::annule(), Tensor::annule_domain(), Scalar::annule_hard(), 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(), Scalar::laplacian(), lapse, log(), max(), maxabs(), mp, Vector::mu(), Scalar::mult_rsint(), 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(), type_hor, Tensor::up(), Tensor::up_down(), Scalar::val_grid_point(), and Valeur::ylm().

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

Deletes all the derived quantities.

Definition at line 135 of file excised_slice.C.

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

void Excised_slice::Einstein_errors ( )

Prints out errors in Einstein equations for the data obtained.

Definition at line 193 of file excised_slice.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& Excised_slice::get_conf_fact ( ) const [inline]

Returns the conformal factor.

Definition at line 209 of file excised_slice.h.

int Excised_slice::get_field_set ( ) const [inline]

Returns the field set chosen for the data.

Definition at line 203 of file excised_slice.h.

References field_set.

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

Returns the rescaled tracefree extrinsic curvature $\hat{A}^{ij}$ (or its TT part if scheme_type=2).

Definition at line 218 of file excised_slice.h.

References hatA.

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

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

Definition at line 215 of file excised_slice.h.

References hij.

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

Returns the lapse function N.

Definition at line 206 of file excised_slice.h.

References lapse.

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

Returns the mapping.

Definition at line 196 of file excised_slice.h.

References mp.

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

Returns the shift vector $\beta^i$ .

Definition at line 212 of file excised_slice.h.

References shift.

int Excised_slice::get_type_hor ( ) const [inline]

Returns the type of horizon that performs the excision.

Definition at line 199 of file excised_slice.h.

References type_hor.

const Vector& Excised_slice::get_Xx ( ) const [inline]

Return the longitudinal part of Einstein Equations if the scheme is appropriate.

Definition at line 221 of file excised_slice.h.

References field_set, and Xx.

Spheroid Excised_slice::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 246 of file excised_slice.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 Excised_slice::komar_angmom ( )

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

assumed rotational symmetry

Definition at line 308 of file excised_slice.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 Excised_slice::operator= ( const Excised_slice & ih )

Assignment to another Excised_slice.

Definition at line 159 of file excised_slice.C.

References del_deriv(), field_set, hatA, hij, lapse, mp, shift, type_hor, and Xx.

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

Save in a file.

Definition at line 181 of file excised_slice.C.

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

void Excised_slice::secmembre_kerr ( Sym_tensor & source_hh )

If hor_type=1, computes the rhs of hyperbolic equation for conformal metric assuming stationarity; WARNING; up to now, we are only able to handle void spacetimes.

Definition at line 11 of file Excised_slice/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().