Public Member Functions
	Bin_hor (Map_af &mp1, Map_af &mp2)
	Standard constructor. More...

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

	Bin_hor (Map_af &mp1, Map_af &mp2, FILE *fich)
	Constructor from a binary file. More...

virtual	~Bin_hor ()
	Destructor. More...

void	sauve (FILE *fich) const
	Total or partial saves in a binary file. More...

void	write_global (ostream &, double lim_nn, int bound_nn, int bound_psi, int bound_beta, double alpha) const
	Write global quantities in a formatted file. More...

void	operator= (const Bin_hor &)
	Affectation operator. More...

Single_hor &	set (int i)
	Read/write of a component of the system. More...

void	set_omega (double ome)
	Sets the orbital velocity to `ome`. More...

const Single_hor &	operator() (int i) const
	Read only of a component of the system. More...

double	get_omega () const
	Returns the angular velocity. More...

void	init_bin_hor ()
	Initialisation of the system. More...

double	viriel () 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 . More...

void	extrinsic_curvature ()
	Calculation of the extrinsic curvature tensor. More...

void	decouple ()
	Calculates `decouple` which is used to obtain `tkij_auto` and `tkij_comp`. More...

void	set_statiques (double precis, double relax, int bound_nn, double lim_nn, int bound_psi)
	Initialize the systeme to Misner Lindquist solution, that is solving for N and $\Psi$ in the case $\Omega = 0$ . More...

double	coal (double ang_vel, double relax, int nb_om, int nb_it, int bound_nn, double lim_nn, int bound_psi, int bound_beta, double omega_eff, double alpha, ostream &fich_iteration, ostream &fich_correction, ostream &fich_viriel, ostream &fich_kss, int step, int search_mass, double mass_irr, const int sortie=0)
	Solves the equation for a particular angular velocity, the systeme being initialized to Misner-Lindquist solution. More...

void	solve_lapse (double precis, double relax, int bound_nn, double lim_nn)
	Solves the equation for the lapse : The fields are the total values except those with subscript , which are the fields generated by each holes (a = 1, 2). More...

void	solve_psi (double precis, double relax, int bound_psi)
	Solves the equation for the conformal factor : The fields are the total values excpet those with subscript , which are the fields generated by each holes (a = 1, 2). More...

void	solve_shift (double precis, double relax, int bound_beta, double omega_eff)
	Solves the equation for the shift, using the Oohara-Nakarmure scheme : The fields are the total values excpet those with subscript , which are the fields generated by each holes (`a` = 1, 2). More...

void	import_bh (const Bin_hor &bin)
	Function to initialize a Bin_hor from a solution computed with a smaller number of colocation points. More...

double	adm_mass () const
	Calculates the ADM mass of the system. More...

double	komar_mass () const
	Calculates the Komar mass of the system using : $M = \frac{1}{4 \pi} \oint_{\infty} D^i N {\mathrm d} S_i$ . More...

double	ang_mom_hor () const
	Calculates the angular momentum of the black hole using the formula at the horizon. More...

double	ang_mom_adm () const
	Calculates the angular momentum of the black hole. More...

double	proper_distance (const int nr=65) const
	Calculation of the proper distance between the two spheres of inversion, along the x axis. More...

Sym_tensor	hh_Samaya_hole1 ()
	Calculation of the hole1 part of the Post-Newtonian correction to $h^{ij}$ . More...

Sym_tensor	hh_Samaya_hole2 ()
	Calculation of the hole2 part of the Post-Newtonian correction to $h^{ij}$ . More...

void	set_hh_Samaya ()
	Calculation of the Post-Newtonian correction to $h^{ij}$ . More...

Private Attributes
Single_hor	hole1
	Black hole one. More...

Single_hor	hole2
	Black hole two. More...

Single_hor *	holes [2]
	Array on the black holes. More...

double	omega
	Angular velocity. More...

Detailed Description

Definition at line 1337 of file isol_hor.h.

Constructor & Destructor Documentation

◆ Bin_hor() [1/3]

Lorene::Bin_hor::Bin_hor	(	Map_af &	mp1,
		Map_af &	mp2
	)

Standard constructor.

Parameters

mp1	affine mapping for the first black hole
mp2	affine mapping for the second black hole
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 100 of file bin_hor.C.

References hole1, hole2, and holes.

◆ Bin_hor() [2/3]

Lorene::Bin_hor::Bin_hor ( const Bin_hor & source )

Copy constructor.

Definition at line 110 of file bin_hor.C.

References hole1, hole2, and holes.

◆ Bin_hor() [3/3]

Lorene::Bin_hor::Bin_hor	(	Map_af &	mp1,
		Map_af &	mp2,
		FILE *	fich
	)

Constructor from a binary file.

Parameters

mp1	affine mapping of the first black hole
mp2	affine mapping of the second black hole
fich	file containing the saved `Bin_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 120 of file bin_hor.C.

References Lorene::fread_be(), hole1, hole2, holes, and omega.

◆ ~Bin_hor()

Lorene::Bin_hor::~Bin_hor ( )

virtual

Destructor.

Definition at line 135 of file bin_hor.C.

Member Function Documentation

◆ adm_mass()

double Lorene::Bin_hor::adm_mass ( ) const

Calculates the ADM mass of the system.

Definition at line 86 of file binhor_global.C.

References Lorene::contract(), Lorene::Scalar::derive_con(), Lorene::Single_hor::ff, Lorene::Vector::flux(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Single_hor::hh, hole1, hole2, Lorene::Single_hor::mp, Lorene::Single_hor::psi_auto, Lorene::Tensor::trace(), and Lorene::Map_af::val_r().

◆ ang_mom_adm()

double Lorene::Bin_hor::ang_mom_adm ( ) const

◆ ang_mom_hor()

double Lorene::Bin_hor::ang_mom_hor ( ) const

Calculates the angular momentum of the black hole using the formula at the horizon.

Definition at line 121 of file binhor_global.C.

References Lorene::Single_hor::aa, Lorene::Tensor::change_triad(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Single_hor::get_psi4(), Lorene::Map::get_rot_phi(), hole1, hole2, Lorene::Map_af::integrale_surface(), Lorene::Single_hor::mp, omega, Lorene::Single_hor::psi, Lorene::Single_hor::radius, Lorene::Vector::set(), Lorene::Scalar::std_spectral_base(), Lorene::Map::xa, and Lorene::Map::ya.

◆ coal()

double Lorene::Bin_hor::coal	(	double	ang_vel,
		double	relax,
		int	nb_om,
		int	nb_it,
		int	bound_nn,
		double	lim_nn,
		int	bound_psi,
		int	bound_beta,
		double	omega_eff,
		double	alpha,
		ostream &	fich_iteration,
		ostream &	fich_correction,
		ostream &	fich_viriel,
		ostream &	fich_kss,
		int	step,
		int	search_mass,
		double	mass_irr,
		const int	sortie = `0`
	)

Solves the equation for a particular angular velocity, the systeme being initialized to Misner-Lindquist solution.

Parameters

angu	[input] : angular velocity used for the boundary condition on $\vec{\beta}$ .
relax	[input] : relaxation parameter.
nb_om	[input] : number of intermediates velocities to go from 0 to `omega` , typically 10.
nb_it	[input] : number of iteration when omega is fixed
bound_nn	[input] : type of the boundary condition for the lapse.
lim_nn	[input] : value (double) of the coefficient for the boundary condition. Only used for boundary_nn_Dir(double), boundary_nn_Neu_eff(double) and boundary_nn_Dir_eff(double).
bound_psi	[input] : type of the boundary condition for psi.
bound_nn	[input] : type of the boundary condition for the shift.
step	current step of the iteration
sortie	[input] : flag for the output on files (0 no output files).

Returns: : the virial error.

Definition at line 136 of file binhor_coal.C.

◆ decouple()

void Lorene::Bin_hor::decouple ( )

Calculates decouple which is used to obtain tkij_auto and tkij_comp.

Definition at line 476 of file binhor_kij.C.

References Lorene::Scalar::allocate_all(), Lorene::Map::convert_absolute(), Lorene::cos(), Lorene::Single_hor::decouple, Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Map::get_ori_x(), hole1, hole2, Lorene::Single_hor::mp, Lorene::pow(), Lorene::Map::r, Lorene::Scalar::set_grid_point(), Lorene::sin(), Lorene::Scalar::std_spectral_base(), Lorene::Scalar::val_grid_point(), Lorene::Scalar::val_point(), Lorene::Map::xa, Lorene::Map::ya, and Lorene::Map::za.

◆ extrinsic_curvature()

void Lorene::Bin_hor::extrinsic_curvature ( )

Calculation of the extrinsic curvature tensor.

aa_auto_evol and aa_auto_comp are also computed.

Definition at line 91 of file binhor_kij.C.

References Lorene::Single_hor::beta_auto, Lorene::Tensor::change_triad(), Lorene::Single_hor::decouple, Lorene::Single_hor::gamt_point, Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), hole1, hole2, Lorene::Single_hor::mp, Lorene::Single_hor::n_auto, Lorene::Single_hor::n_comp, Lorene::Single_hor::nn, Lorene::Vector::ope_killing_conf(), and Lorene::Single_hor::tgam.

◆ get_omega()

double Lorene::Bin_hor::get_omega ( ) const

inline

Returns the angular velocity.

Definition at line 1422 of file isol_hor.h.

References omega.

◆ hh_Samaya_hole1()

Sym_tensor Lorene::Bin_hor::hh_Samaya_hole1 ( )

Calculation of the hole1 part of the Post-Newtonian correction to $h^{ij}$ .

Definition at line 66 of file binhor_hh.C.

References Lorene::Tensor::annule_domain(), Lorene::Vector::change_triad(), Lorene::Metric_flat::con(), Lorene::Scalar::domain(), Lorene::exp(), Lorene::Single_hor::ff, Lorene::Valeur::get_base(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Map::get_ori_x(), Lorene::Map::get_ori_y(), Lorene::Map::get_ori_z(), Lorene::Scalar::get_spectral_va(), hole1, hole2, Lorene::Scalar::import(), Lorene::Single_hor::mp, Lorene::Map::r, Lorene::Scalar::raccord(), Lorene::Coord::set(), Lorene::Vector::set(), Lorene::Tensor::set(), Lorene::Valeur::set_base(), Lorene::Scalar::set_domain(), Lorene::Scalar::set_etat_qcq(), Lorene::Scalar::set_grid_point(), Lorene::Scalar::set_outer_boundary(), Lorene::Scalar::set_spectral_va(), Lorene::sqrt(), Lorene::Scalar::std_spectral_base(), Lorene::Map_af::val_r(), Lorene::Map::x, Lorene::Map::y, and Lorene::Map::z.

◆ hh_Samaya_hole2()

Sym_tensor Lorene::Bin_hor::hh_Samaya_hole2 ( )

Calculation of the hole2 part of the Post-Newtonian correction to $h^{ij}$ .

Definition at line 456 of file binhor_hh.C.

References Lorene::Tensor::annule_domain(), Lorene::Vector::change_triad(), Lorene::Metric_flat::con(), Lorene::Scalar::domain(), Lorene::exp(), Lorene::Single_hor::ff, Lorene::Valeur::get_base(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Map::get_ori_x(), Lorene::Map::get_ori_y(), Lorene::Map::get_ori_z(), Lorene::Scalar::get_spectral_va(), hole1, hole2, Lorene::Scalar::import(), Lorene::Single_hor::mp, Lorene::Map::r, Lorene::Scalar::raccord(), Lorene::Coord::set(), Lorene::Vector::set(), Lorene::Tensor::set(), Lorene::Valeur::set_base(), Lorene::Scalar::set_domain(), Lorene::Scalar::set_etat_qcq(), Lorene::Scalar::set_grid_point(), Lorene::Scalar::set_outer_boundary(), Lorene::Scalar::set_spectral_va(), Lorene::sqrt(), Lorene::Scalar::std_spectral_base(), Lorene::Map_af::val_r(), Lorene::Map::x, Lorene::Map::y, and Lorene::Map::z.

◆ import_bh()

void Lorene::Bin_hor::import_bh ( const Bin_hor & bin )

Function to initialize a Bin_hor from a solution computed with a smaller number of colocation points.

◆ init_bin_hor()

void Lorene::Bin_hor::init_bin_hor ( )

Initialisation of the system.

Each hole is set close to a Schwarzschild one and the parts of the fields generated by the companion are calculated.

The angular velocity is set to zero.

Definition at line 164 of file bin_hor.C.

References decouple(), extrinsic_curvature(), hole1, hole2, Lorene::Single_hor::init_bhole(), Lorene::Single_hor::n_comp_import(), Lorene::Single_hor::psi_comp_import(), and set_omega().

◆ komar_mass()

double Lorene::Bin_hor::komar_mass ( ) const

Calculates the Komar mass of the system using : $M = \frac{1}{4 \pi} \oint_{\infty} D^i N {\mathrm d} S_i$ .

Definition at line 104 of file binhor_global.C.

References Lorene::contract(), Lorene::Scalar::derive_con(), Lorene::Scalar::derive_cov(), Lorene::Single_hor::ff, Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Single_hor::hh, hole1, hole2, Lorene::Single_hor::mp, Lorene::Single_hor::n_auto, Lorene::Single_hor::nn, and Lorene::Map_af::val_r().

◆ operator()()

const Single_hor& Lorene::Bin_hor::operator() ( int i ) const

inline

Read only of a component of the system.

i must be equal to 1 or 2.

Definition at line 1417 of file isol_hor.h.

◆ operator=()

void Lorene::Bin_hor::operator= ( const Bin_hor & source )

Affectation operator.

Definition at line 142 of file bin_hor.C.

References hole1, hole2, and omega.

◆ proper_distance()

double Lorene::Bin_hor::proper_distance ( const int nr = 65 ) const

Calculation of the proper distance between the two spheres of inversion, along the x axis.

Parameters

nr	[input] : number of points used for the calculation.

◆ sauve()

void Lorene::Bin_hor::sauve ( FILE * fich ) const

Total or partial saves in a binary file.

Parameters

fich	binary file
partial_save	indicates whether the whole object must be saved.

Definition at line 154 of file bin_hor.C.

References Lorene::fwrite_be(), hole1, hole2, omega, and Lorene::Single_hor::sauve().

◆ set()

Single_hor& Lorene::Bin_hor::set ( int i )

inline

Read/write of a component of the system.

i must be equal to 1 or 2.

Definition at line 1403 of file isol_hor.h.

References holes.

◆ set_hh_Samaya()

void Lorene::Bin_hor::set_hh_Samaya ( )

Calculation of the Post-Newtonian correction to $h^{ij}$ .

Definition at line 789 of file binhor_hh.C.

References Lorene::Single_hor::ang_mom_hor(), Lorene::Cmp::annule(), Lorene::Single_hor::area_hor(), Lorene::Tensor::change_triad(), Lorene::Metric_flat::con(), des_coupe_z(), des_meridian(), Lorene::Single_hor::ff, Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Single_hor::get_radius(), Lorene::Single_hor::hh, hh_Samaya_hole1(), hh_Samaya_hole2(), hole1, hole2, Lorene::Single_hor::mp, Lorene::Map::phi, Lorene::pow(), Lorene::Map::r, Lorene::Scalar::raccord(), Lorene::Single_hor::radius, Lorene::Tensor::set(), Lorene::Tensor::set_etat_qcq(), Lorene::Cmp::std_base_scal(), Lorene::Map::tet, and Lorene::Single_hor::tgam.

◆ set_omega()

void Lorene::Bin_hor::set_omega ( double ome )

inline

Sets the orbital velocity to ome.

Definition at line 1409 of file isol_hor.h.

References hole1, hole2, omega, and Lorene::Single_hor::set_omega().

◆ set_statiques()

void Lorene::Bin_hor::set_statiques	(	double	precis,
		double	relax,
		int	bound_nn,
		double	lim_nn,
		int	bound_psi
	)

Initialize the systeme to Misner Lindquist solution, that is solving for N and $\Psi$ in the case $\Omega = 0$ .

Parameters

precis	[input] : precision for the convergence (on N ).
relax	[input] : relaxation parameter.
bound_nn	[input] : type of the boundary condition for the lapse.
lim_nn	[input] : value (double) of the coefficient for the boundary condition. Only used for boundary_nn_Dir(double), boundary_nn_Neu_eff(double) and boundary_nn_Dir_eff(double).
bound_psi	[input] : type of the boundary condition for psi.

Definition at line 99 of file binhor_coal.C.

References Lorene::diffrelmax(), extrinsic_curvature(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), hole1, hole2, init_bin_hor(), Lorene::Single_hor::init_met_trK(), Lorene::Single_hor::mp, Lorene::Single_hor::n_auto, set_omega(), solve_lapse(), and solve_psi().

◆ solve_lapse()

void Lorene::Bin_hor::solve_lapse	(	double	precis,
		double	relax,
		int	bound_nn,
		double	lim_nn
	)

Solves the equation for the lapse : The fields are the total values except those with subscript $_a$ , which are the fields generated by each holes (a = 1, 2).

Parameters

precis	[input] : precision, for the boudary conditions are obtained by iteration.
relax	[input] : relaxation parameter.
bound_nn	[input] : type of the boundary condition at the horizon.
lim_nn	[input] : value (double) of the coefficient for the boundary condition. Only used for boundary_nn_Dir(double), boundary_nn_Neu_eff(double) and boundary_nn_Dir_eff(double).

Definition at line 127 of file binhor_equations.C.

◆ solve_psi()

void Lorene::Bin_hor::solve_psi	(	double	precis,
		double	relax,
		int	bound_psi
	)

Solves the equation for the conformal factor : The fields are the total values excpet those with subscript $_a$ , which are the fields generated by each holes (a = 1, 2).

Parameters

precis	[input] : precision, for the boudary conditions are being obtained by iteration.
relax	[input] : relaxation parameter.
bound_psi	[input] : type of the boundary condition at the horizon.

Definition at line 304 of file binhor_equations.C.

◆ solve_shift()

void Lorene::Bin_hor::solve_shift	(	double	precis,
		double	relax,
		int	bound_beta,
		double	omega_eff
	)

Solves the equation for the shift, using the Oohara-Nakarmure scheme : The fields are the total values excpet those with subscript $_a$ , which are the fields generated by each holes (a = 1, 2).

Parameters

precis	[input] : precision for the solver, the boundary conditions and the inversion of the operator being obtained by iteration.
relax	[input] : relaxation parameter.
bound_beta	[input] : type of the boundary condition at the horizon.

Definition at line 456 of file binhor_equations.C.

◆ viriel()

double Lorene::Bin_hor::viriel ( ) 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 .

Definition at line 74 of file binhor_viriel.C.

References Lorene::Scalar::asymptot(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), hole1, hole2, Lorene::Single_hor::mp, Lorene::Single_hor::n_auto, and Lorene::Single_hor::psi_auto.

◆ write_global()

void Lorene::Bin_hor::write_global	(	ostream &	ost,
		double	lim_nn,
		int	bound_nn,
		int	bound_psi,
		int	bound_beta,
		double	alpha
	)		const

Write global quantities in a formatted file.

This file can be read by an external program.

Definition at line 181 of file bin_hor.C.

Member Data Documentation

◆ hole1

Single_hor Lorene::Bin_hor::hole1

private

Black hole one.

Definition at line 1342 of file isol_hor.h.

◆ hole2

Single_hor Lorene::Bin_hor::hole2

private

Black hole two.

Definition at line 1343 of file isol_hor.h.

◆ holes

Single_hor* Lorene::Bin_hor::holes[2]

private

Array on the black holes.

Definition at line 1346 of file isol_hor.h.

◆ omega

double Lorene::Bin_hor::omega

private

Angular velocity.

Definition at line 1348 of file isol_hor.h.

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

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Bin_hor() [1/3]

◆ Bin_hor() [2/3]

◆ Bin_hor() [3/3]

◆ ~Bin_hor()

Member Function Documentation

◆ adm_mass()

◆ ang_mom_adm()

◆ ang_mom_hor()

◆ coal()

◆ decouple()

◆ extrinsic_curvature()

◆ get_omega()

◆ hh_Samaya_hole1()

◆ hh_Samaya_hole2()

◆ import_bh()

◆ init_bin_hor()

◆ komar_mass()

◆ operator()()

◆ operator=()

◆ proper_distance()

◆ sauve()

◆ set()

◆ set_hh_Samaya()

◆ set_omega()

◆ set_statiques()

◆ solve_lapse()

◆ solve_psi()

◆ solve_shift()

◆ viriel()

◆ write_global()

Member Data Documentation

◆ hole1

◆ hole2

◆ holes

◆ omega