Isol_hor Class Reference
[Time evolution (under development)]

Spacelike time-slice of an Isolated Horizon in a 3+1 spacetime with conformal decomposition. More...

#include <isol_hor.h>

Inheritance diagram for Isol_hor:

Public Member Functions
	Isol_hor (Map_af &mpi, int depth_in=3)
	Standard constructor.
	Isol_hor (Map_af &mpi, const Scalar &lapse_in, const Scalar &psi_in, const Vector &shift_in, const Sym_tensor &aa_in, const Metric &gamt, const Sym_tensor &gamt_point, const Scalar &trK, const Scalar &trK_point, const Metric_flat &ff_in, int depth_in=3)
	Constructor from conformal decomposition.
	Isol_hor (const Isol_hor &)
	Copy constructor.
	Isol_hor (Map_af &mp, FILE *fich, bool partial_read, int depth_in=3)
	Constructor from a binary file.
virtual	~Isol_hor ()
	Destructor.
void	operator= (const Isol_hor &)
	Assignment to another Isol_hor.
const Map_af &	get_mp () const
	Returns the mapping (readonly).
Map_af &	set_mp ()
	Read/write of the mapping.
double	get_radius () const
	Returns the radius of the horizon.
void	set_radius (double rad)
	Sets the radius of the horizon to `rad` .
double	get_omega () const
	Returns the angular velocity.
void	set_omega (double ome)
	Sets the angular velocity to `ome` .
double	get_boost_x () const
	Returns the boost velocity in x-direction.
void	set_boost_x (double bo)
	Sets the boost velocity in x-direction to `bo` .
double	get_boost_z () const
	Returns the boost velocity in z-direction.
void	set_boost_z (double bo)
	Sets the boost velocity in z-direction to `bo` .
virtual const Scalar &	n_auto () const
	Lapse function $N_{auto}$ at the current time step `jtime`.
virtual const Scalar &	n_comp () const
	Lapse function $N_{comp}$ at the current time step `jtime`.
virtual const Scalar &	psi_auto () const
	Conformal factor $\Psi_{auto}$ at the current time step `jtime`.
virtual const Scalar &	psi_comp () const
	Conformal factor $\Psi_{comp}$ at the current time step `jtime`.
virtual const Vector &	dnn () const
	Covariant derivative of the lapse function $\overline\nabla_i N$ at the current time step `jtime`.
virtual const Vector &	dpsi () const
	Covariant derivative with respect to the flat metric of the conformal factor $\overline\nabla_i \Psi$ at the current time step `jtime`.
virtual const Vector &	beta_auto () const
	Shift function $\beta^i_{auto}$ at the current time step `jtime`.
virtual const Vector &	beta_comp () const
	Shift function $\beta^i_{comp}$ at the current time step `jtime`.
virtual const Sym_tensor &	aa_auto () const
	Conformal representation $A^{ij}_{auto}$ of the traceless part of the extrinsic curvature: Returns the value at the current time step `jtime`.
virtual const Sym_tensor &	aa_comp () const
	Conformal representation $A^{ij}_{comp}$ of the traceless part of the extrinsic curvature: Returns the value at the current time step `jtime`.
virtual const Scalar &	aa_quad () const
	Conformal representation $A^{ij}A_{ij}$ .
virtual const Metric &	tgam () const
	Conformal metric $\tilde\gamma_{ij} = \Psi^{-4} \gamma_{ij}$ Returns the value at the current time step (`jtime` ).
const Scalar	get_decouple () const
	Returns the function used to construct `tkij_auto` from `tkij_tot` .
void	n_comp (const Isol_hor &comp)
	Imports the part of N due to the companion hole `comp` .
void	psi_comp (const Isol_hor &comp)
	Imports the part of $\Psi$ due to the companion hole `comp` .
void	beta_comp (const Isol_hor &comp)
	Imports the part of $\beta^i$ due to the companion hole `comp`.
double	viriel_seul () 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 .
void	init_bhole ()
	Sets the values of the fields to :.
void	init_met_trK ()
	Sets the 3-metric tilde to the flat metric and gamt_point, trK and trK_point to zero.
void	init_bhole_seul ()
	Initiates for a single black hole.
void	set_psi (const Scalar &psi_in)
	Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .
void	set_nn (const Scalar &nn_in)
	Sets the lapse.
void	set_gamt (const Metric &gam_tilde)
	Sets the conformal metric to gam_tilde.
const Vector	radial_vect_hor () const
	Vector radial normal.
const Vector	tradial_vect_hor () const
	Vector radial normal tilde.
const Scalar	b_tilde () const
	Radial component of the shift with respect to the conformal metric.
const Scalar	darea_hor () const
	Element of area of the horizon.
double	area_hor () const
	Area of the horizon.
double	radius_hor () const
	Radius of the horizon.
double	ang_mom_hor () const
	Angular momentum (modulo).
double	mass_hor () const
	Mass computed at the horizon.
double	kappa_hor () const
	Surface gravity.
double	omega_hor () const
	Orbital velocity.
double	ang_mom_adm () const
	ADM angular Momentum.
Scalar	expansion () const
	Expansion of the outgoing null normal ( $\bf n + \bf s$ ).
void	init_data (int bound_nn, double lim_nn, int bound_psi, int bound_beta, int solve_lapse, int solve_psi, int solve_shift, double precis=1.e-12, double relax_nn=0.5, double relax_psi=0.5, double relax_beta=0.5, int niter=100)
void	init_data_loop (int bound_nn, double lim_nn, int bound_psi, int bound_beta, int solve_lapse, int solve_psi, int solve_shift, double precis=1.e-12, double precis_loop=1.e-12, double relax_nn=1., double relax_psi=1., double relax_beta=1., double relax_loop=1., int niter=100)
void	init_data_spher (int bound_nn, double lim_nn, int bound_psi, int bound_beta, int solve_lapse, int solve_psi, int solve_shift, double precis=1.e-12, double relax=1., int niter=100)
void	init_data_alt (int bound_nn, double lim_nn, int bound_psi, int bound_beta, int solve_lapse, int solve_psi, int solve_shift, double precis=1.e-12, double relax=1., int niter=100)
void	init_data_CTS_gen (int bound_nn, double lim_nn, int bound_psi, int bound_beta, int solve_lapse, int solve_psi, int solve_shift, double precis=1.e-12, double relax_nn=1., double relax_psi=1., double relax_beta=1., int niter=100, double a=1., double zeta=4.)
const Scalar	source_psi () const
	Source for $\Psi$ .
const Scalar	source_nn () const
	Source for `N`.
const Vector	source_beta () const
	Source for $\beta$ .
const Scalar	source_b_tilde () const
	Source for `b_tilde`.
const Vector	source_vector_b () const
	Source for `vector_b`.
const Valeur	boundary_psi_Dir_evol () const
	Dirichlet boundary condition for $\Psi$ (evolution).
const Valeur	boundary_psi_Neu_evol () const
	Neumann boundary condition for $\Psi$ (evolution).
const Valeur	boundary_psi_Dir_spat () const
	Dirichlet boundary condition for $\Psi$ (spatial).
const Valeur	boundary_psi_Neu_spat () const
	Neumann boundary condition for $\Psi$ (spatial).
const Valeur	boundary_psi_app_hor () const
	Neumann boundary condition for $\Psi$ (spatial).
const Valeur	boundary_psi_Dir () const
	Dirichlet boundary condition for $\Psi$ (spatial).
const Valeur	boundary_nn_Dir_kk () const
	Dirichlet boundary condition for `N` using the extrinsic curvature.
const Valeur	boundary_nn_Neu_kk (int nn=1) const
	Neumann boundary condition for `N` using the extrinsic curvature.
const Valeur	boundary_nn_Neu_Cook () const
	Neumann boundary condition for `N` using Cook's boundary condition.
const Valeur	boundary_nn_Dir_eff (double aa) const
	Dirichlet boundary condition for `N` (effectif) $\partial_r N + a N = 0$ .
const Valeur	boundary_nn_Dir_lapl (int mer=1) const
	Dirichlet boundary condition for `N` fixing the divergence of the connection form $\omega$ .
const Valeur	boundary_nn_Neu_eff (double aa) const
	Neumann boundary condition on nn (effectif) $\partial_r N + a N = 0$ .
const Valeur	boundary_nn_Dir (double aa) const
	Dirichlet boundary condition .
const Valeur	boundary_beta_r () const
	Component r of boundary value of $\beta$ .
const Valeur	boundary_beta_theta () const
	Component theta of boundary value of $\beta$ .
const Valeur	boundary_beta_phi (double om) const
	Component phi of boundary value of $\beta$ .
const Valeur	boundary_beta_x (double om) const
	Component x of boundary value of $\beta$ .
const Valeur	boundary_beta_y (double om) const
	Component y of boundary value of $\beta$ .
const Valeur	boundary_beta_z () const
	Component z of boundary value of $\beta$ .
const Valeur	beta_boost_x () const
	Boundary value for a boost in x-direction.
const Valeur	beta_boost_z () const
	Boundary value for a boost in z-direction.
const Vector	vv_bound_cart (double om) const
	Vector for boundary conditions in cartesian.
const Vector	vv_bound_cart_bin (double om, int hole=0) const
	Vector for boundary conditions in cartesian for binary systems.
const Valeur	boundary_vv_x (double om) const
	Component x of boundary value of .
const Valeur	boundary_vv_y (double om) const
	Component y of boundary value of .
const Valeur	boundary_vv_z (double om) const
	Component z of boundary value of .
const Valeur	boundary_vv_x_bin (double om, int hole=0) const
	Component x of boundary value of .
const Valeur	boundary_vv_y_bin (double om, int hole=0) const
	Component y of boundary value of .
const Valeur	boundary_vv_z_bin (double om, int hole=0) const
	Component z of boundary value of .
const Valeur	boundary_b_tilde_Neu () const
	Neumann boundary condition for `b_tilde`.
const Valeur	boundary_b_tilde_Dir () const
	Dirichlet boundary condition for `b_tilde`.
void	update_aa ()
	Conformal representation $A^{ij}$ of the traceless part of the extrinsic curvature: $A^{ij} = \Psi^4 \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .
double	regularisation (const Vector &shift_auto, const Vector &shift_comp, double ang_vel)
	Corrects `shift_auto` in such a way that the total $A^{ij}$ is equal to zero in the horizon, which should ensure the regularity of $K^{ij}$ .
double	regularise_one ()
	Corrects the shift in the innermost shell, so that it remains ${\mathcal{C}}^2$ and that $A^{ij}$ equals zero on the horizon.
void	met_kerr_perturb ()
	Initialisation of the metric tilde from equation (15) of Dain (2002).
void	aa_kerr_ww (double mm, double aa)
double	axi_break () const
	Breaking of the axial symmetry on the horizon.
void	adapt_hor (double c_min, double c_max)
virtual void	sauve (FILE *fich, bool partial_save) const
	Total or partial saves in a binary file.
virtual void	set_psi_del_npsi (const Scalar &psi_in)
	Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .
virtual void	set_psi_del_n (const Scalar &psi_in)
	Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .
virtual void	set_npsi_del_psi (const Scalar &npsi_in)
	Sets the factor $N\Psi$ at the current time step (`jtime` ) and deletes the value of $\Psi$ .
virtual void	set_npsi_del_n (const Scalar &npsi_in)
	Sets the factor $N\Psi$ at the current time step (`jtime` ) and deletes the value of N.
virtual void	set_hh (const Sym_tensor &hh_in)
	Sets the deviation $h^{ij}$ of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ .
virtual void	set_hata (const Sym_tensor &hata_in)
	Sets the conformal representation $\hat{A}{ij}$ of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .
virtual void	set_hata_TT (const Sym_tensor_tt &hata_tt)
	Sets the TT part of $\hat{A}^{ij}$ (see member `hata_evol` ).
virtual void	set_hata_from_XAB (Param par_bc=0x0, Param par_mat=0x0)
	Sets the conformal representation $\hat{A}{ij}$ of the traceless part of the extrinsic curvature from its potentials A, $\tilde{B}$ and .
virtual const Scalar &	nn () const
	Lapse function N at the current time step (`jtime` ).
virtual const Sym_tensor &	gam_dd () const
	Induced metric (covariant components $\gamma_{ij}$ ) at the current time step (`jtime` ).
virtual const Sym_tensor &	gam_uu () const
	Induced metric (contravariant components $\gamma^{ij}$ ) at the current time step (`jtime` ).
virtual const Sym_tensor &	k_dd () const
	Extrinsic curvature tensor (covariant components $K_{ij}$ ) at the current time step (`jtime` ).
virtual const Sym_tensor &	k_uu () const
	Extrinsic curvature tensor (contravariant components $K^{ij}$ ) at the current time step (`jtime` ).
virtual const Scalar &	A_hata () const
	Returns the potential A of $\hat{A}^{ij}$ .
virtual const Scalar &	B_hata () const
	Returns the potential $\tilde{B}$ of $\hat{A}^{ij}$ .
virtual const Scalar &	psi () const
	Conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .
const Scalar &	psi4 () const
	Factor $\Psi^4$ at the current time step (`jtime` ).
const Scalar &	ln_psi () const
	Logarithm of $\Psi$ at the current time step (`jtime` ).
virtual const Scalar &	npsi () const
	Factor $N\Psi$ at the current time step (`jtime` ).
virtual const Sym_tensor &	hh (Param =0x0, Param =0x0) const
	Deviation $h^{ij}$ of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ .
virtual const Sym_tensor &	hata () const
	Conformal representation $\hat{A}^{ij}$ of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .
virtual Sym_tensor	aa () const
	Conformal representation $A^{ij}$ of the traceless part of the extrinsic curvature: $A^{ij} = \Psi^4 \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .
virtual const Scalar &	trk () const
	Trace K of the extrinsic curvature at the current time step (`jtime` ).
virtual const Vector &	hdirac () const
	Vector $H^i = {\cal D}_j \tilde\gamma^{ij}$ which vanishes in Dirac gauge.
virtual const Vector &	vec_X (int method_poisson=6) const
	Vector representing the longitudinal part of $\hat{A}^{ij}$ .
void	compute_X_from_momentum_constraint (const Vector &hat_S, const Sym_tensor_tt &hata_tt, int iter_max=200, double precis=1.e-12, double relax=0.8, int methode_poisson=6)
	Computes the vector from the conformally-rescaled momentum $\hat{S}^i = \Psi^6 S^i$ , using the momentum constraint.
void	set_scheme_order (int ord)
	Sets the order of the finite-differences scheme.
int	get_scheme_order () const
	Gets the order of the finite-differences scheme.
int	get_latest_j () const
	Gets the latest value of time step index.
const Evolution_std< double > &	get_time () const
	Gets the time coordinate t at successive time steps.
virtual const Vector &	beta () const
	shift vector $\beta^i$ at the current time step (`jtime` )
const Metric &	gam () const
	Induced metric $\mathbf{\gamma}$ at the current time step (`jtime` ).
Tbl	check_hamiltonian_constraint (const Scalar *energy_density=0x0, ostream &ost=cout, bool verb=true) const
	Checks the level at which the hamiltonian constraint is verified.
Tbl	check_momentum_constraint (const Vector *momentum_density=0x0, ostream &ost=cout, bool verb=true) const
	Checks the level at which the momentum constraints are verified.
Tbl	check_dynamical_equations (const Sym_tensor strain_tensor=0x0, const Scalar energy_density=0x0, ostream &ost=cout, bool verb=true) const
	Checks the level at which the dynamical equations are verified.
virtual double	adm_mass () const
	Returns the ADM mass (geometrical units) at the current step.
void	save (const char *rootname) const
	Saves in a binary file.
Protected Member Functions
virtual ostream &	operator>> (ostream &) const
	Operator >> (virtual function called by the operator<<).
virtual void	del_deriv () const
	Deletes all the derived quantities.
void	set_der_0x0 () const
	Sets to `0x0` all the pointers on derived quantities.
Protected Attributes
Map_af &	mp
	Affine mapping.
int	nz
	Number of zones.
double	radius
	Radius of the horizon in LORENE's units.
double	omega
	Angular velocity in LORENE's units.
double	boost_x
	Boost velocity in x-direction.
double	boost_z
	Boost velocity in z-direction.
double	regul
	Intensity of the correction on the shift vector.
Evolution_std< Scalar >	n_auto_evol
	Values at successive time steps of the lapse function $N_{auto}$ .
Evolution_std< Scalar >	n_comp_evol
	Values at successive time steps of the lapse function $N_{comp}$ .
Evolution_std< Scalar >	psi_auto_evol
	Values at successive time steps of the conformal factor $\Psi_{auto}$ .
Evolution_std< Scalar >	psi_comp_evol
	Values at successive time steps of the lapse function $\Psi_{comp}$ .
Evolution_std< Vector >	dn_evol
	Values at successive time steps of the covariant derivative of the lapse with respect to the flat metric $\overline\nabla_i N$ .
Evolution_std< Vector >	dpsi_evol
	Values at successive time steps of the covariant derivative of the conformal factor $\overline\nabla_i \Psi$ .
Evolution_std< Vector >	beta_auto_evol
	Values at successive time steps of the shift function $\beta^i_{auto}$ .
Evolution_std< Vector >	beta_comp_evol
	Values at successive time steps of the shift function $\beta^i_{comp}$ .
Evolution_std< Sym_tensor >	aa_auto_evol
	Values at successive time steps of the components $A^{ij}_{auto}$ of the conformal representation of the traceless part of the extrinsic curvature:.
Evolution_std< Sym_tensor >	aa_comp_evol
	Values at successive time steps of the components $A^{ij}_{comp}$ of the conformal representation of the traceless part of the extrinsic curvature:.
Evolution_std< Sym_tensor >	aa_nn
	Values at successive time steps of the components $A^{ij}*2N$ .
Evolution_std< Scalar >	aa_quad_evol
	Values at successive time steps of the components $A^{ij}A_{ij}$ .
Metric	met_gamt
	3 metric tilde
Sym_tensor	gamt_point
	Time derivative of the 3-metric tilde.
Scalar	trK
	Trace of the extrinsic curvature.
Scalar	trK_point
	Time derivative of the trace of the extrinsic curvature.
Scalar	decouple
	Function used to construct $A^{ij}_{auto}$ from the total $A^{ij}$ .
const Metric_flat &	ff
	Pointer on the flat metric $f_{ij}$ with respect to which the conformal decomposition is performed.
Evolution_std< Scalar >	psi_evol
	Values at successive time steps of the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .
Evolution_std< Scalar >	npsi_evol
	Values at successive time steps of the factor $N\Psi$ .
Evolution_std< Sym_tensor >	hh_evol
	Values at successive time steps of the components $h^{ij}$ .
Evolution_std< Sym_tensor >	hata_evol
	Values at successive time steps of the components $\hat{A}^{ij}$ .
Evolution_std< Scalar >	A_hata_evol
	Potential A associated with the symmetric tensor $\hat{A}^{ij}_{TT}$ .
Evolution_std< Scalar >	B_hata_evol
	Potential $\tilde{B}$ associated with the symmetric tensor $\hat{A}^{ij}_{TT}$ .
Metric *	p_tgamma
	Pointer on the conformal metric $\tilde\gamma_{ij}$ at the current time step (`jtime`).
Scalar *	p_psi4
	Pointer on the factor $\Psi^4$ at the current time step (`jtime`).
Scalar *	p_ln_psi
	Pointer on the logarithm of $\Psi$ at the current time step (`jtime`).
Vector *	p_hdirac
	Pointer on the vector $H^i = {\cal D}_j \tilde\gamma^{ij}$ (which vanishes in Dirac gauge), at the current time step (`jtime`).
Vector *	p_vec_X
	Pointer on the vector representing the longitudinal part of $\hat{A}^{ij}$ .
int	depth
	Number of stored time slices.
int	scheme_order
	Order of the finite-differences scheme for the computation of time derivatives.
int	jtime
	Time step index of the latest slice.
Evolution_std< double >	the_time
	Time label of each slice.
Evolution_std< Sym_tensor >	gam_dd_evol
	Values at successive time steps of the covariant components of the induced metric $\gamma_{ij}$ .
Evolution_std< Sym_tensor >	gam_uu_evol
	Values at successive time steps of the contravariant components of the induced metric $\gamma^{ij}$ .
Evolution_std< Sym_tensor >	k_dd_evol
	Values at successive time steps of the covariant components of the extrinsic curvature tensor $K_{ij}$ .
Evolution_std< Sym_tensor >	k_uu_evol
	Values at successive time steps of the contravariant components of the extrinsic curvature tensor $K^{ij}$ .
Evolution_std< Scalar >	n_evol
	Values at successive time steps of the lapse function N.
Evolution_std< Vector >	beta_evol
	Values at successive time steps of the shift vector $\beta^i$ .
Evolution_std< Scalar >	trk_evol
	Values at successive time steps of the trace K of the extrinsic curvature.
Evolution_full< Tbl >	adm_mass_evol
	ADM mass at each time step, since the creation of the slice.
Metric *	p_gamma
	Pointer on the induced metric at the current time step (`jtime`).
Friends
class	Bin_hor
ostream &	operator<< (ostream &, const Time_slice &)
	Display.

Detailed Description

Spacelike time-slice of an Isolated Horizon in a 3+1 spacetime with conformal decomposition.

No gauge choice imposed. ()

Definition at line 252 of file isol_hor.h.

Constructor & Destructor Documentation

Isol_hor::Isol_hor	(	Map_af &	mpi,
		int	depth_in = `3`
	)

Standard constructor.

Parameters:

	mpi	affine mapping
	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 172 of file isol_hor.C.

Isol_hor::Isol_hor	(	Map_af &	mpi,
		const Scalar &	lapse_in,
		const Scalar &	psi_in,
		const Vector &	shift_in,
		const Sym_tensor &	aa_in,
		const Metric &	gamt,
		const Sym_tensor &	gamt_point,
		const Scalar &	trK,
		const Scalar &	trK_point,
		const Metric_flat &	ff_in,
		int	depth_in = `3`
	)

Constructor from conformal decomposition.

Parameters:

	mpi	affine mapping
	lapse_in	lapse function N
	psi_in	conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$
	shift_in	shift vector
	aa_in	conformal representation $A^{ij}$ of the traceless part of the extrinsic curvature: $A^{ij} = \Psi^4 \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$
	gamt	3-metric tilde
	gamt_point	time derivative of the 3-metric tilde
	trK	trace K of the extrinsic curvature
	trK_point	time derivative of the trace K of the extrinsic curvature
	ff_in	reference flat metric with respect to which the conformal decomposition is performed
	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 189 of file isol_hor.C.

References Metric_flat::con(), Metric::con(), Time_slice_conf::ff, Time_slice_conf::hh_evol, Time_slice::jtime, met_gamt, Time_slice::the_time, trK, Time_slice::trk_evol, and Evolution_std< TyT >::update().

Isol_hor::Isol_hor ( const Isol_hor & isolhor_in )

Copy constructor.

Definition at line 218 of file isol_hor.C.

Isol_hor::Isol_hor	(	Map_af &	mp,
		FILE *	fich,
		bool	partial_read,
		int	depth_in = `3`
	)

Constructor from a binary file.

Parameters:

	mpi	affine mapping
	fich	file containing the saved `isol_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 249 of file isol_hor.C.

References beta_auto_evol, boost_x, boost_z, Metric_flat::con(), Time_slice::depth, Time_slice_conf::ff, fread_be(), gamt_point, Map::get_bvect_spher(), Map::get_mg(), Time_slice_conf::hh_evol, Time_slice::jtime, met_gamt, mp, n_auto_evol, omega, psi_auto_evol, Time_slice_conf::psi_evol, Time_slice::the_time, trK, Time_slice::trk_evol, trK_point, and Evolution_std< TyT >::update().

Isol_hor::~Isol_hor ( ) [virtual]

Destructor.

Definition at line 332 of file isol_hor.C.

Member Function Documentation

const Scalar & Time_slice_conf::A_hata ( ) const [virtual, inherited]

Returns the potential A of $\hat{A}^{ij}$ .

See the documentation of Sym_tensor for details. Returns the value at the current time step (jtime ).

Definition at line 660 of file time_slice_conf.C.

References Time_slice_conf::A_hata_evol, Time_slice_conf::hata_evol, Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::the_time, and Evolution_std< TyT >::update().

Sym_tensor Time_slice_conf::aa ( ) const [virtual, inherited]

Conformal representation $A^{ij}$ of the traceless part of the extrinsic curvature: $A^{ij} = \Psi^4 \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .

Returns the value at the current time step (jtime ).

Definition at line 761 of file time_slice_conf.C.

References Time_slice_conf::hata(), Time_slice_conf::psi(), and Time_slice_conf::psi4().

const Sym_tensor & Isol_hor::aa_auto ( ) const [virtual]

Conformal representation $A^{ij}_{auto}$ of the traceless part of the extrinsic curvature: Returns the value at the current time step jtime.

Definition at line 499 of file isol_hor.C.

References aa_auto_evol, Evolution< TyT >::is_known(), and Time_slice::jtime.

const Sym_tensor & Isol_hor::aa_comp ( ) const [virtual]

Conformal representation $A^{ij}_{comp}$ of the traceless part of the extrinsic curvature: Returns the value at the current time step jtime.

Definition at line 505 of file isol_hor.C.

References aa_comp_evol, Evolution< TyT >::is_known(), and Time_slice::jtime.

const Scalar & Isol_hor::aa_quad ( ) const [virtual]

Conformal representation $A^{ij}A_{ij}$ .

Returns the value at the current time step jtime.

Definition at line 880 of file isol_hor.C.

References Time_slice_conf::aa(), aa_quad_evol, contract(), Evolution< TyT >::is_known(), Time_slice::jtime, met_gamt, Time_slice_conf::psi4(), Time_slice::the_time, and Evolution_std< TyT >::update().

double Time_slice::adm_mass ( ) const [virtual, inherited]

Returns the ADM mass (geometrical units) at the current step.

Moreover this method updates adm_mass_evol if necessary.

Reimplemented in Tslice_dirac_max.

Definition at line 70 of file tslice_adm_mass.C.

References Time_slice::adm_mass_evol, Tensor::derive_con(), Tensor_sym::derive_con(), Vector::flux(), Time_slice::gam_dd(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_nzone(), Tbl::get_taille(), Time_slice::jtime, Tbl::set(), Tbl::set_etat_qcq(), Time_slice::the_time, Tensor::trace(), Tensor::up(), Evolution_full< TyT >::update(), and Map::val_r().

double Isol_hor::ang_mom_adm ( ) const

ADM angular Momentum.

Definition at line 244 of file phys_param.C.

References Time_slice_conf::gam_dd(), Map_af::integrale_surface_infini(), Time_slice_conf::k_dd(), mp, Scalar::mult_rsint(), and Time_slice_conf::trk().

double Isol_hor::ang_mom_hor ( ) const

Angular momentum (modulo).

Definition at line 174 of file phys_param.C.

References contract(), darea_hor(), Time_slice_conf::ff, Metric::get_mp(), Metric_flat::get_triad(), Map_af::integrale_surface(), Time_slice_conf::k_dd(), mp, radial_vect_hor(), radius, and Vector::set().

double Isol_hor::area_hor ( ) const

Area of the horizon.

Definition at line 153 of file phys_param.C.

References darea_hor(), Map_af::integrale_surface(), mp, Scalar::raccord(), and radius.

double Isol_hor::axi_break ( ) const

Breaking of the axial symmetry on the horizon.

Definition at line 1083 of file isol_hor.C.

References contract(), darea_hor(), Time_slice_conf::ff, Time_slice::gam(), Time_slice_conf::gam_uu(), Metric::get_mp(), Metric_flat::get_triad(), Map_af::integrale_surface(), mp, radius_hor(), Vector::set(), and Tensor::up_down().

const Scalar & Time_slice_conf::B_hata ( ) const [virtual, inherited]

Returns the potential $\tilde{B}$ of $\hat{A}^{ij}$ .

See the documentation of Sym_tensor_tt for details. Returns the value at the current time step (jtime ).

Definition at line 674 of file time_slice_conf.C.

References Time_slice_conf::A_hata_evol, Time_slice_conf::B_hata_evol, Time_slice_conf::hata_evol, Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::the_time, and Evolution_std< TyT >::update().

const Scalar Isol_hor::b_tilde ( ) const

Radial component of the shift with respect to the conformal metric.

Definition at line 132 of file phys_param.C.

References Time_slice::beta(), contract(), Tensor::down(), met_gamt, and Metric::radial_vect().

const Vector & Time_slice::beta ( ) const [virtual, inherited]

shift vector $\beta^i$ at the current time step (jtime )

Definition at line 83 of file time_slice_access.C.

References Time_slice::beta_evol, Evolution< TyT >::is_known(), and Time_slice::jtime.

const Vector & Isol_hor::beta_auto ( ) const [virtual]

Shift function $\beta^i_{auto}$ at the current time step jtime.

Definition at line 487 of file isol_hor.C.

References beta_auto_evol, Evolution< TyT >::is_known(), and Time_slice::jtime.

const Valeur Isol_hor::beta_boost_x ( ) const

Boundary value for a boost in x-direction.

Definition at line 1140 of file bound_hor.C.

References boost_x, Mg3d::get_angu(), Map::get_mg(), mp, and Mg3d::std_base_vect_cart().

const Valeur Isol_hor::beta_boost_z ( ) const

Boundary value for a boost in z-direction.

Definition at line 1151 of file bound_hor.C.

References boost_z, Mg3d::get_angu(), Map::get_mg(), mp, and Mg3d::std_base_vect_cart().

void Isol_hor::beta_comp ( const Isol_hor & comp )

Imports the part of $\beta^i$ due to the companion hole comp.

The total $\beta^i$ is then calculated.

Definition at line 708 of file isol_hor.C.

References beta_auto(), beta_comp(), beta_comp_evol, Time_slice::beta_evol, Map::get_bvect_cart(), Map::get_bvect_spher(), Time_slice::jtime, mp, Time_slice::the_time, and Evolution_std< TyT >::update().

const Vector & Isol_hor::beta_comp ( ) const [virtual]

Shift function $\beta^i_{comp}$ at the current time step jtime.

Definition at line 493 of file isol_hor.C.

References beta_comp_evol, Evolution< TyT >::is_known(), and Time_slice::jtime.

const Valeur Isol_hor::boundary_b_tilde_Dir ( ) const

Dirichlet boundary condition for b_tilde.

Definition at line 1208 of file bound_hor.C.

References b_tilde(), contract(), Tensor::derive_cov(), Time_slice_conf::ff, Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Scalar::inc_dzpuis(), met_gamt, mp, Metric::radial_vect(), and Scalar::std_spectral_base().

const Valeur Isol_hor::boundary_b_tilde_Neu ( ) const

Neumann boundary condition for b_tilde.

Definition at line 1165 of file bound_hor.C.

References b_tilde(), contract(), Scalar::derive_cov(), Tensor::derive_cov(), Time_slice_conf::ff, Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Scalar::inc_dzpuis(), met_gamt, mp, Metric::radial_vect(), and Scalar::std_spectral_base().

const Valeur Isol_hor::boundary_beta_phi ( double om ) const

Component phi of boundary value of $\beta$ .

Definition at line 974 of file bound_hor.C.

References Valeur::base, Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Scalar::get_spectral_va(), mp, Scalar::mult_rsint(), Time_slice_conf::nn(), radial_vect_hor(), Scalar::std_spectral_base(), and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_beta_r ( ) const

Component r of boundary value of $\beta$ .

Definition at line 893 of file bound_hor.C.

References Mg3d::get_angu(), Valeur::get_base(), Base_val::get_base_p(), Base_val::get_base_r(), Base_val::get_base_t(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Scalar::get_spectral_va(), mp, Time_slice_conf::nn(), norme(), radial_vect_hor(), and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_beta_theta ( ) const

Component theta of boundary value of $\beta$ .

Definition at line 934 of file bound_hor.C.

References Mg3d::get_angu(), Base_val::get_base_p(), Base_val::get_base_r(), Base_val::get_base_t(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), mp, Time_slice_conf::nn(), radial_vect_hor(), and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_beta_x ( double om ) const

Component x of boundary value of $\beta$ .

Definition at line 1017 of file bound_hor.C.

References Vector::change_triad(), Map::cosp, Map::cost, Time_slice::gam(), Mg3d::get_angu(), Map::get_bvect_cart(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Map::get_rot_phi(), mp, Time_slice_conf::nn(), Metric::radial_vect(), Tensor::set(), Map::sinp, Map::sint, Mg3d::std_base_vect_cart(), Scalar::val_grid_point(), and Map::ya.

const Valeur Isol_hor::boundary_beta_y ( double om ) const

Component y of boundary value of $\beta$ .

Definition at line 1067 of file bound_hor.C.

References Vector::change_triad(), Map::cosp, Map::cost, Time_slice::gam(), Mg3d::get_angu(), Map::get_bvect_cart(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Map::get_rot_phi(), mp, Time_slice_conf::nn(), Metric::radial_vect(), Tensor::set(), Map::sinp, Map::sint, Mg3d::std_base_vect_cart(), Scalar::val_grid_point(), and Map::xa.

const Valeur Isol_hor::boundary_beta_z ( ) const

Component z of boundary value of $\beta$ .

Definition at line 1117 of file bound_hor.C.

References Vector::change_triad(), Time_slice::gam(), Mg3d::get_angu(), Map::get_bvect_cart(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), mp, Time_slice_conf::nn(), Metric::radial_vect(), and Mg3d::std_base_vect_cart().

const Valeur Isol_hor::boundary_nn_Dir ( double aa ) const

Dirichlet boundary condition $ N = a $ .

Definition at line 643 of file bound_hor.C.

References Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), mp, Time_slice_conf::nn(), and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_nn_Dir_eff ( double aa ) const

Dirichlet boundary condition for N (effectif) $\partial_r N + a N = 0$ .

Definition at line 582 of file bound_hor.C.

References Scalar::dec_dzpuis(), Scalar::derive_cov(), Time_slice_conf::ff, Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), mp, Time_slice_conf::nn(), and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_nn_Dir_kk ( ) const

Dirichlet boundary condition for N using the extrinsic curvature.

Definition at line 367 of file bound_hor.C.

References contract(), Time_slice_conf::ff, Time_slice::gam(), Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Scalar::inc_dzpuis(), Time_slice_conf::k_dd(), mp, Time_slice_conf::nn(), Scalar::std_spectral_base(), and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_nn_Dir_lapl ( int mer = 1 ) const

Dirichlet boundary condition for N fixing the divergence of the connection form $\omega$ .

Definition at line 689 of file bound_hor.C.

References Metric_flat::con(), contract(), Metric_flat::cov(), Scalar::dec_dzpuis(), Tensor::derive_con(), Scalar::derive_cov(), Tensor::derive_cov(), Vector::divergence(), Tensor::down(), exp(), Time_slice_conf::ff, Time_slice::gam(), Time_slice_conf::gam_uu(), Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Scalar::inc_dzpuis(), Map_af::integrale_surface(), Time_slice_conf::k_dd(), Scalar::lapang(), log(), met_gamt, mp, Time_slice_conf::nn(), Scalar::poisson_angu(), pow(), Time_slice_conf::psi(), Map::r, Metric::radial_vect(), radius, Tensor::set(), Scalar::set_dzpuis(), Scalar::std_spectral_base(), Time_slice_conf::trk(), Tensor::up_down(), and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_nn_Neu_Cook ( ) const

Neumann boundary condition for N using Cook's boundary condition.

Definition at line 485 of file bound_hor.C.

References contract(), Scalar::derive_cov(), Vector::divergence(), Tensor::down(), Time_slice_conf::ff, Time_slice::gam(), Time_slice_conf::gam_uu(), Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Scalar::inc_dzpuis(), Time_slice_conf::k_dd(), Scalar::lapang(), log(), met_gamt, mp, Time_slice_conf::nn(), pow(), Time_slice_conf::psi(), Map::r, Metric::radial_vect(), Vector::set(), Scalar::std_spectral_base(), Time_slice_conf::trk(), and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_nn_Neu_eff ( double aa ) const

Neumann boundary condition on nn (effectif) $\partial_r N + a N = 0$ .

Definition at line 618 of file bound_hor.C.

References Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), mp, Time_slice_conf::nn(), and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_nn_Neu_kk ( int nn = 1 ) const

Neumann boundary condition for N using the extrinsic curvature.

Definition at line 416 of file bound_hor.C.

References aa_auto(), contract(), Metric::cov(), Scalar::derive_cov(), Time_slice_conf::ff, Time_slice::gam(), Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Scalar::inc_dzpuis(), Time_slice_conf::k_dd(), kappa_hor(), met_gamt, mp, Time_slice_conf::nn(), Time_slice_conf::psi(), Metric::radial_vect(), Scalar::std_spectral_base(), Time_slice_conf::trk(), Tensor::up_down(), and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_psi_app_hor ( ) const

Neumann boundary condition for $\Psi$ (spatial).

Definition at line 293 of file bound_hor.C.

References Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), mp, Time_slice_conf::psi(), radius, and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_psi_Dir ( ) const

Dirichlet boundary condition for $\Psi$ (spatial).

Definition at line 320 of file bound_hor.C.

References Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), mp, Time_slice_conf::psi(), Scalar::std_spectral_base(), and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_psi_Dir_evol ( ) const

Dirichlet boundary condition for $\Psi$ (evolution).

Definition at line 170 of file bound_hor.C.

References Time_slice::beta(), contract(), Time_slice_conf::ff, Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), mp, Time_slice_conf::nn(), Time_slice_conf::psi(), Time_slice_conf::trk(), and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_psi_Dir_spat ( ) const

Dirichlet boundary condition for $\Psi$ (spatial).

Definition at line 227 of file bound_hor.C.

References contract(), Vector::divergence(), Time_slice_conf::ff, Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Scalar::inc_dzpuis(), Time_slice_conf::k_dd(), mp, Time_slice_conf::psi(), Scalar::std_spectral_base(), tradial_vect_hor(), Time_slice_conf::trk(), and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_psi_Neu_evol ( ) const

Neumann boundary condition for $\Psi$ (evolution).

Definition at line 199 of file bound_hor.C.

References Time_slice::beta(), Scalar::derive_cov(), Vector::divergence(), Time_slice_conf::ff, Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), mp, Time_slice_conf::nn(), Time_slice_conf::psi(), Time_slice_conf::trk(), and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_psi_Neu_spat ( ) const

Neumann boundary condition for $\Psi$ (spatial).

Definition at line 263 of file bound_hor.C.

References contract(), Scalar::derive_cov(), Vector::divergence(), Time_slice_conf::ff, Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Time_slice_conf::k_dd(), mp, Time_slice_conf::psi(), tradial_vect_hor(), Time_slice_conf::trk(), and Scalar::val_grid_point().

const Valeur Isol_hor::boundary_vv_x ( double om ) const

Component x of boundary value of $ V^i $ .

Definition at line 1489 of file bound_hor.C.

References Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), mp, Vector::set(), Mg3d::std_base_vect_cart(), Scalar::val_grid_point(), and vv_bound_cart().

const Valeur Isol_hor::boundary_vv_x_bin	(	double	om,
		int	hole = `0`
	)			const

Component x of boundary value of $ V^i $ .

Definition at line 1568 of file bound_hor.C.

References Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), mp, Vector::set(), Mg3d::std_base_vect_cart(), Scalar::val_grid_point(), and vv_bound_cart_bin().

const Valeur Isol_hor::boundary_vv_y ( double om ) const

Component y of boundary value of $ V^i $ .

Definition at line 1517 of file bound_hor.C.

References Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), mp, Vector::set(), Mg3d::std_base_vect_cart(), Scalar::val_grid_point(), and vv_bound_cart().

const Valeur Isol_hor::boundary_vv_y_bin	(	double	om,
		int	hole = `0`
	)			const

Component y of boundary value of $ V^i $ .

Definition at line 1595 of file bound_hor.C.

References Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), mp, Vector::set(), Mg3d::std_base_vect_cart(), Scalar::val_grid_point(), and vv_bound_cart_bin().

const Valeur Isol_hor::boundary_vv_z ( double om ) const

Component z of boundary value of $ V^i $ .

Definition at line 1543 of file bound_hor.C.

References Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), mp, Vector::set(), Mg3d::std_base_vect_cart(), Scalar::val_grid_point(), and vv_bound_cart().

const Valeur Isol_hor::boundary_vv_z_bin	(	double	om,
		int	hole = `0`
	)			const

Component z of boundary value of $ V^i $ .

Definition at line 1621 of file bound_hor.C.

References Mg3d::get_angu(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), mp, Vector::set(), Mg3d::std_base_vect_cart(), Scalar::val_grid_point(), and vv_bound_cart_bin().

Tbl Time_slice::check_dynamical_equations	(	const Sym_tensor *	strain_tensor = `0x0`,
		const Scalar *	energy_density = `0x0`,
		ostream &	ost = `cout`,
		bool	verb = `true`
	)			const `[inherited]`

Checks the level at which the dynamical equations are verified.

$\frac{\partial K_{ij}}{\partial t} - \pounds_{\mbox{\boldmath{$\beta $}}} K_{ij} = - D_i D_j N + N \left[ R_{ij} - 2 K_{ik} K^k_{\ j} + K K_{ij} + 4\pi \left( (S-E)\gamma_{ij} - 2 S_{ij} \right) \right]$

Parameters:

	strain_tensor	: a pointer on the strain_tensor $S_{ij}$ measured by the Eulerian observer of 4-velocity $\mbox{\boldmath{$n $}}$ ; if this is the null pointer, it is assumed that $S_{ij}$ = 0 (vacuum).
	energy_density	: a pointer on the energy density E (see `check_hamiltonian_constraint`)
	ost	: output stream for a formatted output of the result

Returns:: Tbl 3D of size the number of domains times 3 times 3 (corresponding to the rank-2 tensor, with the symmetry in the components) containing the absolute ( if = 0 ) or the relative (in presence of matter) error in max version.

Definition at line 135 of file tslice_check_einstein.C.

References Tensor::annule_domain(), Time_slice::beta(), Metric::con(), contract(), Tensor::derive_con(), Scalar::derive_con(), Sym_tensor::derive_lie(), Time_slice::gam(), Tbl::get_dim(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_nzone(), Time_slice::jtime, Time_slice::k_dd(), Time_slice::k_dd_evol, Time_slice::k_uu(), maxabs(), Time_slice::nn(), Tensor_sym::position(), Metric::ricci(), Time_slice::scheme_order, Itbl::set(), Evolution< TyT >::time_derive(), Tensor::trace(), Time_slice::trk(), and Tensor::up_down().

Tbl Time_slice::check_hamiltonian_constraint	(	const Scalar *	energy_density = `0x0`,
		ostream &	ost = `cout`,
		bool	verb = `true`
	)			const `[inherited]`

Checks the level at which the hamiltonian constraint is verified.

$R + K^2 - K_{ij}K^{ij} = 16\pi E$

Parameters:

	energy_density	: a pointer on the energy density E measured by the Eulerian observer of 4-velocity $\mbox{\boldmath{$n $}}$ ; if this is the null pointer, it is assumed that E = 0 (vacuum).
	ost	: output stream for a formatted output of the result

Returns:: Tbl of size the number of domains containing the absolute ( if E = 0 ) or the relative (in presence of matter) error in max version.

Definition at line 75 of file tslice_check_einstein.C.

References contract(), Scalar::dec_dzpuis(), Time_slice::gam(), Time_slice::k_dd(), Time_slice::k_uu(), maxabs(), Metric::ricci_scal(), and Time_slice::trk().

Tbl Time_slice::check_momentum_constraint	(	const Vector *	momentum_density = `0x0`,
		ostream &	ost = `cout`,
		bool	verb = `true`
	)			const `[inherited]`

Checks the level at which the momentum constraints are verified.

$D_j K_i^{\ j} - D_i K = 8 \pi J_i$

Parameters:

	momentum_density	: a pointer on the momentum density measured by the Eulerian observer of 4-velocity $\mbox{\boldmath{$n $}}$ ; if this is the null pointer, it is assumed that = 0 (vacuum).
	ost	: output stream for a formatted output of the result

Returns:: Tbl 2D of size the number of domains times 3 (components)containing the absolute ( if = 0 ) or the relative (in presence of matter) error in max version.

Definition at line 105 of file tslice_check_einstein.C.

References Scalar::derive_con(), Sym_tensor::divergence(), Time_slice::gam(), Tensor::get_index_type(), Time_slice::k_uu(), maxabs(), and Time_slice::trk().

void Time_slice_conf::compute_X_from_momentum_constraint	(	const Vector &	hat_S,
		const Sym_tensor_tt &	hata_tt,
		int	iter_max = `200`,
		double	precis = `1.e-12`,
		double	relax = `0.8`,
		int	methode_poisson = `6`
	)			`[inherited]`

Computes the vector $ X^i $ from the conformally-rescaled momentum $\hat{S}^i = \Psi^6 S^i$ , using the momentum constraint.

Definition at line 833 of file time_slice_conf.C.

References abs(), contract(), Tensor::get_index_type(), max(), and Vector::poisson().

const Scalar Isol_hor::darea_hor ( ) const

Element of area of the horizon.

Definition at line 142 of file phys_param.C.

References Time_slice_conf::gam_dd(), sqrt(), and Scalar::std_spectral_base().

void Time_slice_conf::del_deriv ( ) const [protected, virtual, inherited]

Deletes all the derived quantities.

Reimplemented from Time_slice.

Definition at line 343 of file time_slice_conf.C.

References Time_slice_conf::p_hdirac, Time_slice_conf::p_ln_psi, Time_slice_conf::p_psi4, Time_slice_conf::p_tgamma, Time_slice_conf::p_vec_X, and Time_slice_conf::set_der_0x0().

const Vector & Isol_hor::dnn ( ) const [virtual]

Covariant derivative of the lapse function $\overline\nabla_i N$ at the current time step jtime.

Definition at line 475 of file isol_hor.C.

References dn_evol, Evolution< TyT >::is_known(), and Time_slice::jtime.

const Vector & Isol_hor::dpsi ( ) const [virtual]

Covariant derivative with respect to the flat metric of the conformal factor $\overline\nabla_i \Psi$ at the current time step jtime.

Definition at line 481 of file isol_hor.C.

References dpsi_evol, Evolution< TyT >::is_known(), and Time_slice::jtime.

Scalar Isol_hor::expansion ( ) const

Expansion of the outgoing null normal ( $\bf n + \bf s$ ).

Definition at line 259 of file phys_param.C.

References contract(), Time_slice::gam(), Time_slice_conf::k_dd(), and Time_slice_conf::trk().

const Metric & Time_slice::gam ( ) const [inherited]

Induced metric $\mathbf{\gamma}$ at the current time step (jtime ).

Definition at line 91 of file time_slice_access.C.

References Time_slice::gam_dd(), and Time_slice::p_gamma.

const Sym_tensor & Time_slice_conf::gam_dd ( ) const [virtual, inherited]

Induced metric (covariant components $\gamma_{ij}$ ) at the current time step (jtime ).

Reimplemented from Time_slice.

Definition at line 604 of file time_slice_conf.C.

References Time_slice::gam_dd_evol, Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice_conf::psi4(), Time_slice_conf::tgam(), Time_slice::the_time, and Evolution_std< TyT >::update().

const Sym_tensor & Time_slice_conf::gam_uu ( ) const [virtual, inherited]

Induced metric (contravariant components $\gamma^{ij}$ ) at the current time step (jtime ).

Reimplemented from Time_slice.

Definition at line 615 of file time_slice_conf.C.

References Time_slice::gam_uu_evol, Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice_conf::psi4(), Time_slice_conf::tgam(), Time_slice::the_time, and Evolution_std< TyT >::update().

double Isol_hor::get_boost_x ( ) const [inline]

Returns the boost velocity in x-direction.

Definition at line 443 of file isol_hor.h.

References boost_x.

double Isol_hor::get_boost_z ( ) const [inline]

Returns the boost velocity in z-direction.

Definition at line 452 of file isol_hor.h.

References boost_z.

const Scalar Isol_hor::get_decouple ( ) const [inline]

Returns the function used to construct tkij_auto from tkij_tot .

Definition at line 517 of file isol_hor.h.

References decouple.

int Time_slice::get_latest_j ( ) const [inline, inherited]

Gets the latest value of time step index.

Definition at line 339 of file time_slice.h.

References Time_slice::jtime.

const Map_af& Isol_hor::get_mp ( ) const [inline]

Returns the mapping (readonly).

Definition at line 416 of file isol_hor.h.

References mp.

double Isol_hor::get_omega ( ) const [inline]

Returns the angular velocity.

Definition at line 434 of file isol_hor.h.

References omega.

double Isol_hor::get_radius ( ) const [inline]

Returns the radius of the horizon.

Definition at line 424 of file isol_hor.h.

References radius.

int Time_slice::get_scheme_order ( ) const [inline, inherited]

Gets the order of the finite-differences scheme.

Definition at line 336 of file time_slice.h.

References Time_slice::scheme_order.

const Evolution_std<double>& Time_slice::get_time ( ) const [inline, inherited]

Gets the time coordinate t at successive time steps.

Definition at line 342 of file time_slice.h.

References Time_slice::the_time.

const Sym_tensor & Time_slice_conf::hata ( ) const [virtual, inherited]

Conformal representation $\hat{A}^{ij}$ of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .

Returns the value at the current time step (jtime ).

Definition at line 768 of file time_slice_conf.C.

References Time_slice::beta(), Sym_tensor::derive_lie(), Vector::divergence(), Time_slice_conf::ff, Time_slice_conf::hata_evol, Time_slice_conf::hh(), Time_slice_conf::hh_evol, Tensor::inc_dzpuis(), Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice_conf::nn(), Vector::ope_killing_conf(), Time_slice_conf::psi(), Time_slice_conf::psi4(), Time_slice::scheme_order, Time_slice::the_time, Evolution< TyT >::time_derive(), and Evolution_std< TyT >::update().

const Vector & Time_slice_conf::hdirac ( ) const [virtual, inherited]

Vector $H^i = {\cal D}_j \tilde\gamma^{ij}$ which vanishes in Dirac gauge.

Reimplemented in Tslice_dirac_max.

Definition at line 811 of file time_slice_conf.C.

References Time_slice_conf::ff, Time_slice_conf::hh(), and Time_slice_conf::p_hdirac.

const Sym_tensor & Time_slice_conf::hh	(	Param *	= `0x0`,
		Param *	= `0x0`
	)			const `[virtual, inherited]`

Deviation $h^{ij}$ of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ .

Returns the value at the current time step (jtime ).

Reimplemented in Tslice_dirac_max.

Definition at line 754 of file time_slice_conf.C.

References Time_slice_conf::hh_evol, Evolution< TyT >::is_known(), and Time_slice::jtime.

void Isol_hor::init_bhole ( )

Sets the values of the fields to :.

n_auto $= \frac{1}{2}-2\frac{a}{r}$
n_comp $= \frac{1}{2}$
psi_auto $= \frac{1}{2}+\frac{a}{r}$
psi_comp $= \frac{1}{2}$

a being the radius of the hole, the other fields being set to zero.

Definition at line 729 of file isol_hor.C.

References Scalar::annule(), beta_auto_evol, beta_comp_evol, Time_slice::beta_evol, dn_evol, dpsi_evol, Time_slice_conf::ff, Map::get_bvect_spher(), Time_slice::jtime, mp, n_auto(), n_auto_evol, n_comp(), n_comp_evol, Time_slice::n_evol, Time_slice_conf::nn(), Time_slice_conf::psi(), psi_auto(), psi_auto_evol, psi_comp(), psi_comp_evol, Time_slice_conf::psi_evol, Map::r, Scalar::raccord(), radius, Coord::set(), Scalar::set_dzpuis(), Scalar::std_spectral_base(), Time_slice::the_time, and Evolution_std< TyT >::update().

void Isol_hor::init_bhole_seul ( )

Initiates for a single black hole.

WARNING It supposes that the boost is zero and should only be used for an isolated black hole..

Definition at line 793 of file isol_hor.C.

References Scalar::annule(), beta_auto_evol, beta_comp_evol, Time_slice::beta_evol, dn_evol, dpsi_evol, Time_slice_conf::ff, Map::get_bvect_spher(), Map::get_mg(), Time_slice::jtime, mp, n_auto_evol, n_comp_evol, Time_slice::n_evol, Time_slice_conf::nn(), Time_slice_conf::psi(), psi_auto_evol, psi_comp_evol, Time_slice_conf::psi_evol, Map::r, Scalar::raccord(), radius, Scalar::set_dzpuis(), Scalar::set_etat_zero(), Scalar::set_outer_boundary(), Scalar::std_spectral_base(), Time_slice::the_time, and Evolution_std< TyT >::update().

void Isol_hor::init_met_trK ( )

Sets the 3-metric tilde to the flat metric and gamt_point, trK and trK_point to zero.

Definition at line 781 of file isol_hor.C.

References Map::flat_met_spher(), gamt_point, met_gamt, mp, Scalar::set_etat_zero(), Tensor::set_etat_zero(), trK, and trK_point.

const Sym_tensor & Time_slice_conf::k_dd ( ) const [virtual, inherited]

Extrinsic curvature tensor (covariant components $K_{ij}$ ) at the current time step (jtime ).

Reimplemented from Time_slice.

Definition at line 626 of file time_slice_conf.C.

References Time_slice::gam(), Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::k_dd_evol, Time_slice_conf::k_uu(), Time_slice::the_time, and Evolution_std< TyT >::update().

const Sym_tensor & Time_slice_conf::k_uu ( ) const [virtual, inherited]

Extrinsic curvature tensor (contravariant components $K^{ij}$ ) at the current time step (jtime ).

Reimplemented from Time_slice.

Definition at line 639 of file time_slice_conf.C.

References Time_slice::gam(), Time_slice_conf::hata(), Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::k_uu_evol, Time_slice_conf::psi(), Time_slice_conf::psi4(), Time_slice::the_time, Time_slice_conf::trk(), and Evolution_std< TyT >::update().

double Isol_hor::kappa_hor ( ) const

Surface gravity.

Definition at line 214 of file phys_param.C.

References ang_mom_hor(), pow(), radius_hor(), and sqrt().

const Scalar & Time_slice_conf::ln_psi ( ) const [inherited]

Logarithm of $\Psi$ at the current time step (jtime ).

Definition at line 715 of file time_slice_conf.C.

References log(), Time_slice_conf::p_ln_psi, Time_slice_conf::psi(), and Scalar::std_spectral_base().

double Isol_hor::mass_hor ( ) const

Mass computed at the horizon.

Definition at line 202 of file phys_param.C.

References ang_mom_hor(), pow(), radius_hor(), and sqrt().

void Isol_hor::met_kerr_perturb ( )

Initialisation of the metric tilde from equation (15) of Dain (2002).

The determinant of this conformal metric is not one.

Definition at line 891 of file isol_hor.C.

References Metric_flat::con(), Metric::con(), Metric::cov(), Metric::determinant(), Time_slice_conf::ff, Time_slice::gam(), Time_slice_conf::hh_evol, Time_slice::jtime, met_gamt, norme(), pow(), set_psi(), Scalar::std_spectral_base(), Time_slice::the_time, and Evolution_std< TyT >::update().

const Scalar & Isol_hor::n_auto ( ) const [virtual]

Lapse function $N_{auto}$ at the current time step jtime.

Definition at line 451 of file isol_hor.C.

References Evolution< TyT >::is_known(), Time_slice::jtime, and n_auto_evol.

void Isol_hor::n_comp ( const Isol_hor & comp )

Imports the part of N due to the companion hole comp .

The total N is then calculated.

It also imports the covariant derivative of N and construct the total $\nabla_i N$ .

Definition at line 573 of file isol_hor.C.

References Scalar::derive_cov(), dn_evol, Time_slice_conf::ff, Map::get_bvect_cart(), Map::get_bvect_spher(), Scalar::import(), Time_slice::jtime, mp, n_auto(), n_comp_evol, Time_slice::n_evol, Scalar::std_spectral_base(), Time_slice::the_time, and Evolution_std< TyT >::update().

const Scalar & Isol_hor::n_comp ( ) const [virtual]

Lapse function $N_{comp}$ at the current time step jtime.

Definition at line 457 of file isol_hor.C.

References Evolution< TyT >::is_known(), Time_slice::jtime, and n_comp_evol.

const Scalar & Time_slice_conf::nn ( ) const [virtual, inherited]

Lapse function N at the current time step (jtime ).

Reimplemented from Time_slice.

Definition at line 587 of file time_slice_conf.C.

References Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::n_evol, Time_slice_conf::npsi_evol, Time_slice_conf::psi_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

const Scalar & Time_slice_conf::npsi ( ) const [virtual, inherited]

Factor $N\Psi$ at the current time step (jtime ).

Definition at line 728 of file time_slice_conf.C.

References Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::n_evol, Time_slice_conf::npsi_evol, Time_slice_conf::psi_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

double Isol_hor::omega_hor ( ) const

Orbital velocity.

Definition at line 229 of file phys_param.C.

References ang_mom_hor(), pow(), radius_hor(), and sqrt().

void Isol_hor::operator= ( const Isol_hor & isolhor_in )

Assignment to another Isol_hor.

Reimplemented from Time_slice_conf.

Definition at line 339 of file isol_hor.C.

References aa_auto_evol, aa_comp_evol, aa_nn, aa_quad_evol, beta_auto_evol, beta_comp_evol, boost_x, boost_z, decouple, dn_evol, dpsi_evol, gamt_point, met_gamt, mp, n_auto_evol, n_comp_evol, nz, omega, psi_auto_evol, psi_comp_evol, radius, regul, trK, and trK_point.

ostream & Isol_hor::operator>> ( ostream & flux ) const [protected, virtual]

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

Reimplemented from Time_slice.

Definition at line 374 of file isol_hor.C.

References Time_slice::adm_mass(), ang_mom_adm(), ang_mom_hor(), area_hor(), boost_x, boost_z, mass_hor(), omega_hor(), and radius.

const Scalar & Time_slice_conf::psi ( ) const [virtual, inherited]

Conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .

$\Psi$ is defined by

$\Psi := \left( \frac{\det\gamma_{ij}}{\det f_{ij}} \right) ^{1/12}$

Returns the value at the current time step (jtime ).

Definition at line 689 of file time_slice_conf.C.

References Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::n_evol, Time_slice_conf::npsi_evol, Time_slice_conf::psi_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

const Scalar & Time_slice_conf::psi4 ( ) const [inherited]

Factor $\Psi^4$ at the current time step (jtime ).

Definition at line 703 of file time_slice_conf.C.

References Time_slice_conf::p_psi4, pow(), Time_slice_conf::psi(), and Scalar::std_spectral_base().

const Scalar & Isol_hor::psi_auto ( ) const [virtual]

Conformal factor $\Psi_{auto}$ at the current time step jtime.

Definition at line 463 of file isol_hor.C.

References Evolution< TyT >::is_known(), Time_slice::jtime, and psi_auto_evol.

void Isol_hor::psi_comp ( const Isol_hor & comp )

Imports the part of $\Psi$ due to the companion hole comp .

The total $\Psi$ is then calculated.

It also imports the covariant derivative of $\Psi$ and construct the total $\nabla_i \Psi$ .

Definition at line 665 of file isol_hor.C.

References Scalar::derive_cov(), dpsi_evol, Time_slice_conf::ff, Map::get_bvect_cart(), Map::get_bvect_spher(), Scalar::import(), Time_slice::jtime, mp, psi_auto(), psi_comp_evol, Time_slice_conf::psi_evol, Scalar::std_spectral_base(), Time_slice::the_time, and Evolution_std< TyT >::update().

const Scalar & Isol_hor::psi_comp ( ) const [virtual]

Conformal factor $\Psi_{comp}$ at the current time step jtime.

Definition at line 469 of file isol_hor.C.

References Evolution< TyT >::is_known(), Time_slice::jtime, and psi_comp_evol.

const Vector Isol_hor::radial_vect_hor ( ) const

Vector radial normal.

Definition at line 91 of file phys_param.C.

References Time_slice_conf::ff, Time_slice_conf::gam_uu(), Metric::get_mp(), Metric_flat::get_triad(), Vector::set(), sqrt(), and Vector::std_spectral_base().

double Isol_hor::radius_hor ( ) const

Radius of the horizon.

Definition at line 163 of file phys_param.C.

References area_hor(), and pow().

double Isol_hor::regularisation	(	const Vector &	shift_auto,
		const Vector &	shift_comp,
		double	ang_vel
	)

Corrects shift_auto in such a way that the total $A^{ij}$ is equal to zero in the horizon, which should ensure the regularity of $K^{ij}$ .

WARNING : this should only be used for a black hole in a binary system Bin_hor.

Parameters:

comp

[input]: the part of $\beta^i$ generated by the companion hole.

Definition at line 84 of file regularisation.C.

References Cmp::annule(), Tensor::annule_domain(), beta_auto_evol, Valeur::c, Vector::change_triad(), Valeur::coef_i(), diffrelmax(), Map::get_bvect_cart(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Map::get_rot_phi(), Scalar::get_spectral_va(), Tensor::get_triad(), Time_slice::jtime, norme(), nz, pow(), Vector::set(), Valeur::set_etat_c_qcq(), Scalar::set_spectral_va(), Vector::std_spectral_base(), Time_slice::the_time, and Evolution_std< TyT >::update().

double Isol_hor::regularise_one ( )

Corrects the shift in the innermost shell, so that it remains ${\mathcal{C}}^2$ and that $A^{ij}$ equals zero on the horizon.

return the relative difference between the shift before and after the regularisation.

WARNING this should only be used for an isolated black hole.

Definition at line 179 of file regularisation.C.

References Cmp::annule(), Tensor::annule_domain(), Time_slice::beta(), Time_slice::beta_evol, boost_x, boost_z, Vector::change_triad(), Valeur::coef_i(), diffrelmax(), Map::get_bvect_cart(), Map::get_bvect_spher(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Time_slice::jtime, mp, norme(), nz, omega, pow(), Map::r, Vector::set(), Valeur::set_etat_c_qcq(), Scalar::set_spectral_va(), Vector::std_spectral_base(), Time_slice::the_time, Evolution_std< TyT >::update(), Map_af::val_r(), Map::x, and Map::y.

void Isol_hor::sauve	(	FILE *	fich,
		bool	partial_save
	)			const `[virtual]`

Total or partial saves in a binary file.

Parameters:

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

Reimplemented from Time_slice.

Definition at line 397 of file isol_hor.C.

References beta_auto_evol, boost_x, boost_z, Metric::con(), Time_slice::depth, fwrite_be(), gamt_point, Evolution< TyT >::is_known(), Time_slice::jtime, met_gamt, n_auto_evol, omega, psi_auto_evol, Time_slice_conf::psi_evol, Scalar::sauve(), Tensor_sym::sauve(), trK, and trK_point.

void Time_slice::save ( const char * rootname ) const [inherited]

Saves in a binary file.

The saved data is sufficient to restore the whole time slice via the constructor from file.

Parameters:

rootname

root for the file name; the current time step index will be appended to it.

Definition at line 457 of file time_slice.C.

References Time_slice::beta(), Time_slice::depth, fwrite_be(), Map::get_mg(), Tensor::get_mp(), Tensor::get_triad(), Time_slice::jtime, Time_slice::nn(), Time_slice::sauve(), Base_vect::sauve(), Map::sauve(), and Mg3d::sauve().

void Isol_hor::set_boost_x ( double bo ) [inline]

Sets the boost velocity in x-direction to bo .

Definition at line 447 of file isol_hor.h.

References boost_x.

void Isol_hor::set_boost_z ( double bo ) [inline]

Sets the boost velocity in z-direction to bo .

Definition at line 456 of file isol_hor.h.

References boost_z.

void Time_slice_conf::set_der_0x0 ( ) const [protected, inherited]

Sets to 0x0 all the pointers on derived quantities.

Reimplemented from Time_slice.

Definition at line 357 of file time_slice_conf.C.

References Time_slice_conf::p_hdirac, Time_slice_conf::p_ln_psi, Time_slice_conf::p_psi4, Time_slice_conf::p_tgamma, and Time_slice_conf::p_vec_X.

void Isol_hor::set_gamt ( const Metric & gam_tilde )

Sets the conformal metric to gam_tilde.

Definition at line 546 of file isol_hor.C.

References Metric_flat::con(), Metric::con(), Evolution< TyT >::downdate(), Time_slice_conf::ff, Time_slice::gam_dd_evol, Time_slice::gam_uu_evol, Time_slice_conf::hh_evol, Time_slice::jtime, Time_slice::k_dd_evol, Time_slice::k_uu_evol, met_gamt, Time_slice::p_gamma, Time_slice_conf::p_tgamma, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::set_hata ( const Sym_tensor & hata_in ) [virtual, inherited]

Sets the conformal representation $\hat{A}{ij}$ of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .

Sets the value at the current time step (jtime ), and updates the potentials A_hata_evol, B_hata_evol and p_vec_X accordingly.

Definition at line 530 of file time_slice_conf.C.

References Time_slice_conf::A_hata_evol, Time_slice_conf::B_hata_evol, Evolution< TyT >::downdate(), Time_slice_conf::hata_evol, Time_slice::jtime, Time_slice::k_dd_evol, Time_slice::k_uu_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::set_hata_from_XAB	(	Param *	par_bc = `0x0`,
		Param *	par_mat = `0x0`
	)			`[virtual, inherited]`

Sets the conformal representation $\hat{A}{ij}$ of the traceless part of the extrinsic curvature from its potentials A, $\tilde{B}$ and $ X^i $ .

These potentials must be up-to-date. It sets the value at the current time step (jtime ).

Definition at line 562 of file time_slice_conf.C.

References Time_slice_conf::A_hata_evol, Time_slice_conf::B_hata_evol, Evolution< TyT >::downdate(), Time_slice_conf::ff, Tensor::get_mp(), Time_slice_conf::hata_evol, Map::inc_dzpuis(), Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice::k_dd_evol, Time_slice::k_uu_evol, Vector::ope_killing_conf(), Time_slice_conf::p_vec_X, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::set_hata_TT ( const Sym_tensor_tt & hata_tt ) [virtual, inherited]

Sets the TT part of $\hat{A}^{ij}$ (see member hata_evol ).

Sets the value at current time-step (jtime ) and updates the potentials A and $\tilde{B}$ .

Definition at line 542 of file time_slice_conf.C.

References Time_slice_conf::A_hata_evol, Time_slice_conf::B_hata_evol, Sym_tensor::compute_A(), Sym_tensor::compute_tilde_B_tt(), Scalar::dec_dzpuis(), Evolution< TyT >::downdate(), Scalar::get_dzpuis(), Time_slice_conf::hata_evol, Time_slice::jtime, Time_slice::k_dd_evol, Time_slice::k_uu_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::set_hh ( const Sym_tensor & hh_in ) [virtual, inherited]

Sets the deviation $h^{ij}$ of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ .

$h^{ij}$ must be such that $\det\tilde\gamma^{ij} = f^{-1}$ . Sets the value at the current time step (jtime ).

Reimplemented in Tslice_dirac_max.

Definition at line 485 of file time_slice_conf.C.

References Time_slice::adm_mass_evol, Metric_flat::con(), Metric_flat::determinant(), Evolution< TyT >::downdate(), Time_slice_conf::ff, Time_slice::gam_dd_evol, Time_slice::gam_uu_evol, Time_slice_conf::hh_evol, Time_slice::jtime, max(), maxabs(), Time_slice::p_gamma, Time_slice_conf::p_hdirac, Time_slice_conf::p_tgamma, Time_slice::the_time, and Evolution_std< TyT >::update().

Map_af& Isol_hor::set_mp ( ) [inline]

Read/write of the mapping.

Definition at line 419 of file isol_hor.h.

References mp.

void Isol_hor::set_nn ( const Scalar & nn_in )

Sets the lapse.

Definition at line 536 of file isol_hor.C.

References aa_quad_evol, Evolution< TyT >::downdate(), Time_slice_conf::hata_evol, Time_slice::jtime, Time_slice::k_dd_evol, Time_slice::k_uu_evol, Time_slice::n_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::set_npsi_del_n ( const Scalar & npsi_in ) [virtual, inherited]

Sets the factor $N\Psi$ at the current time step (jtime ) and deletes the value of N.

Definition at line 474 of file time_slice_conf.C.

References Time_slice::adm_mass_evol, Evolution< TyT >::downdate(), Time_slice::jtime, Time_slice::n_evol, Time_slice_conf::npsi_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::set_npsi_del_psi ( const Scalar & npsi_in ) [virtual, inherited]

Sets the factor $N\Psi$ at the current time step (jtime ) and deletes the value of $\Psi$ .

Definition at line 449 of file time_slice_conf.C.

References Time_slice::adm_mass_evol, Evolution< TyT >::downdate(), Time_slice::gam_dd_evol, Time_slice::gam_uu_evol, Time_slice::jtime, Time_slice_conf::npsi_evol, Time_slice::p_gamma, Time_slice_conf::p_ln_psi, Time_slice_conf::p_psi4, Time_slice_conf::psi_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

void Isol_hor::set_omega ( double ome ) [inline]

Sets the angular velocity to ome .

Definition at line 438 of file isol_hor.h.

References omega.

void Isol_hor::set_psi ( const Scalar & psi_in )

Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .

$\Psi$ is defined by

$\Psi := \left( \frac{\det\gamma_{ij}}{\det f_{ij}} \right) ^{1/12}$

Sets the value at the current time step (jtime ) and delete all quantities which depend on $\Psi$ .

Definition at line 511 of file isol_hor.C.

References Time_slice::adm_mass_evol, Evolution< TyT >::downdate(), Time_slice::gam_dd_evol, Time_slice::gam_uu_evol, Time_slice::jtime, Time_slice::k_dd_evol, Time_slice::k_uu_evol, Time_slice::p_gamma, Time_slice_conf::p_ln_psi, Time_slice_conf::p_psi4, Time_slice_conf::psi_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::set_psi_del_n ( const Scalar & psi_in ) [virtual, inherited]

Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .

$\Psi$ is defined by

$\Psi := \left( \frac{\det\gamma_{ij}}{\det f_{ij}} \right) ^{1/12}$

Sets the value at the current time step (jtime ) and deletes the value of N.

Definition at line 424 of file time_slice_conf.C.

References Time_slice::adm_mass_evol, Evolution< TyT >::downdate(), Time_slice::gam_dd_evol, Time_slice::gam_uu_evol, Time_slice::jtime, Time_slice::n_evol, Time_slice::p_gamma, Time_slice_conf::p_ln_psi, Time_slice_conf::p_psi4, Time_slice_conf::psi_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

void Time_slice_conf::set_psi_del_npsi ( const Scalar & psi_in ) [virtual, inherited]

Sets the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .

$\Psi$ is defined by

$\Psi := \left( \frac{\det\gamma_{ij}}{\det f_{ij}} \right) ^{1/12}$

Sets the value at the current time step (jtime ) and deletes the value of $N\Psi$ .

Definition at line 400 of file time_slice_conf.C.

References Time_slice::adm_mass_evol, Evolution< TyT >::downdate(), Time_slice::gam_dd_evol, Time_slice::gam_uu_evol, Time_slice::jtime, Time_slice_conf::npsi_evol, Time_slice::p_gamma, Time_slice_conf::p_ln_psi, Time_slice_conf::p_psi4, Time_slice_conf::psi_evol, Time_slice::the_time, and Evolution_std< TyT >::update().

void Isol_hor::set_radius ( double rad ) [inline]

Sets the radius of the horizon to rad .

Definition at line 429 of file isol_hor.h.

References radius.

void Time_slice::set_scheme_order ( int ord ) [inline, inherited]

Sets the order of the finite-differences scheme.

Definition at line 327 of file time_slice.h.

References Time_slice::scheme_order.

const Scalar Isol_hor::source_b_tilde ( ) const

Source for b_tilde.

const Vector Isol_hor::source_beta ( ) const

Source for $\beta$ .

Definition at line 186 of file sources_hor.C.

References Time_slice_conf::aa(), Tensor::annule_domain(), Time_slice::beta(), Metric::connect(), contract(), Scalar::derive_con(), Scalar::derive_cov(), Vector::derive_lie(), Vector::divergence(), Sym_tensor::divergence(), Time_slice_conf::ff, gamt_point, Connection::get_delta(), Metric_flat::get_triad(), Time_slice_conf::hdirac(), Time_slice_conf::hh(), Tensor::inc_dzpuis(), Time_slice_conf::ln_psi(), met_gamt, mp, Time_slice_conf::nn(), and trK.

const Scalar Isol_hor::source_nn ( ) const

Source for N.

Definition at line 141 of file sources_hor.C.

References aa_quad(), Tensor::annule_domain(), Time_slice::beta(), contract(), Scalar::derive_con(), Tensor::derive_cov(), Scalar::derive_cov(), Time_slice_conf::ff, Metric_flat::get_triad(), Time_slice_conf::hdirac(), Time_slice_conf::hh(), Scalar::inc_dzpuis(), Time_slice_conf::ln_psi(), met_gamt, mp, Time_slice_conf::nn(), Time_slice_conf::psi4(), trK, and trK_point.

const Scalar Isol_hor::source_psi ( ) const

Source for $\Psi$ .

Definition at line 104 of file sources_hor.C.

References aa_quad(), Tensor::annule_domain(), contract(), Tensor::derive_cov(), Scalar::derive_cov(), Time_slice_conf::ff, Metric_flat::get_triad(), Time_slice_conf::hdirac(), Time_slice_conf::hh(), Scalar::inc_dzpuis(), met_gamt, mp, Time_slice_conf::psi(), Time_slice_conf::psi4(), Metric::ricci_scal(), and trK.

const Vector Isol_hor::source_vector_b ( ) const

Source for vector_b.

virtual const Metric& Isol_hor::tgam ( ) const [inline, virtual]

Conformal metric $\tilde\gamma_{ij} = \Psi^{-4} \gamma_{ij}$ Returns the value at the current time step (jtime ).

Reimplemented from Time_slice_conf.

Definition at line 512 of file isol_hor.h.

References met_gamt.

const Vector Isol_hor::tradial_vect_hor ( ) const

Vector radial normal tilde.

Definition at line 112 of file phys_param.C.

References Metric::con(), Time_slice_conf::ff, Metric::get_mp(), Metric_flat::get_triad(), met_gamt, Vector::set(), sqrt(), and Vector::std_spectral_base().

const Scalar & Time_slice_conf::trk ( ) const [virtual, inherited]

Trace K of the extrinsic curvature at the current time step (jtime ).

Reimplemented from Time_slice.

Reimplemented in Tslice_dirac_max.

Definition at line 792 of file time_slice_conf.C.

References Time_slice::beta(), contract(), Vector::divergence(), Time_slice_conf::ff, Scalar::inc_dzpuis(), Evolution< TyT >::is_known(), Time_slice::jtime, Time_slice_conf::ln_psi(), Time_slice_conf::nn(), Time_slice_conf::psi(), Time_slice_conf::psi_evol, Time_slice::scheme_order, Time_slice::the_time, Evolution< TyT >::time_derive(), Time_slice::trk_evol, and Evolution_std< TyT >::update().

void Isol_hor::update_aa ( )

Conformal representation $A^{ij}$ of the traceless part of the extrinsic curvature: $A^{ij} = \Psi^4 \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ .

Definition at line 838 of file isol_hor.C.

References aa_quad_evol, Time_slice::beta(), contract(), gamt_point, Map::get_bvect_spher(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Time_slice::jtime, met_gamt, mp, Time_slice_conf::nn(), Vector::ope_killing_conf(), Time_slice_conf::psi(), Time_slice_conf::psi4(), regul, regularise_one(), Time_slice_conf::set_hata(), Time_slice::the_time, and Evolution_std< TyT >::update().

const Vector & Time_slice_conf::vec_X ( int method_poisson = 6 ) const [virtual, inherited]

Vector $ X^i $ representing the longitudinal part of $\hat{A}^{ij}$ .

(see the documentation of hata_evol)

Definition at line 821 of file time_slice_conf.C.

References Time_slice_conf::ff, Time_slice_conf::hata_evol, Evolution< TyT >::is_known(), Time_slice::jtime, and Time_slice_conf::p_vec_X.

double Isol_hor::viriel_seul ( ) 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 .

WARNING this should only be used for an isolated black hole.

const Vector Isol_hor::vv_bound_cart ( double om ) const

Vector $ V^i $ for boundary conditions in cartesian.

Definition at line 1247 of file bound_hor.C.

References Scalar::annule_hard(), b_tilde(), Time_slice::beta(), Vector::change_triad(), Metric::con(), contract(), Map::cosp, Map::cost, Scalar::dec_dzpuis(), Tensor::derive_cov(), Tensor::down(), Time_slice_conf::ff, Time_slice::gam(), Map::get_bvect_cart(), Map::get_bvect_spher(), Map::get_mg(), Map::get_rot_phi(), Scalar::inc_dzpuis(), kappa_hor(), met_gamt, mp, Time_slice_conf::nn(), Metric::radial_vect(), Vector::set(), Tensor::set(), Coord::set(), Scalar::set_dzpuis(), Map::sinp, Map::sint, Mg3d::std_base_vect_cart(), Time_slice_conf::trk(), Map::xa, and Map::ya.

const Vector Isol_hor::vv_bound_cart_bin	(	double	om,
		int	hole = `0`
	)			const

Vector $ V^i $ for boundary conditions in cartesian for binary systems.

Definition at line 1375 of file bound_hor.C.

References Map::get_bvect_cart(), and mp.

Friends And Related Function Documentation

ostream& operator<<	(	ostream &	,
		const Time_slice &
	)			`[friend, inherited]`

Display.

Member Data Documentation

Evolution_std<Scalar> Time_slice_conf::A_hata_evol [mutable, protected, inherited]

Potential A associated with the symmetric tensor $\hat{A}^{ij}_{TT}$ .

(see documentation of Sym_tensor::p_aaa).

Definition at line 543 of file time_slice.h.

Evolution_std<Sym_tensor> Isol_hor::aa_auto_evol [mutable, protected]

Values at successive time steps of the components $A^{ij}_{auto}$ of the conformal representation of the traceless part of the extrinsic curvature:.

Definition at line 308 of file isol_hor.h.

Evolution_std<Sym_tensor> Isol_hor::aa_comp_evol [mutable, protected]

Values at successive time steps of the components $A^{ij}_{comp}$ of the conformal representation of the traceless part of the extrinsic curvature:.

Definition at line 314 of file isol_hor.h.

Evolution_std<Sym_tensor> Isol_hor::aa_nn [mutable, protected]

Values at successive time steps of the components $A^{ij}*2N$ .

Definition at line 318 of file isol_hor.h.

Evolution_std<Scalar> Isol_hor::aa_quad_evol [mutable, protected]

Values at successive time steps of the components $A^{ij}A_{ij}$ .

Definition at line 321 of file isol_hor.h.

Evolution_full<Tbl> Time_slice::adm_mass_evol [mutable, protected, inherited]

ADM mass at each time step, since the creation of the slice.

At a given time step j, adm_mass_evol[j] is a 1-D Tbl of size the number nz of domains, containing the "ADM mass" evaluated at the outer boundary of each domain. The true ADM mass is thus the last value, i.e. adm_mass_evol[j](nz-1).

Definition at line 229 of file time_slice.h.

Evolution_std<Scalar> Time_slice_conf::B_hata_evol [mutable, protected, inherited]

Potential $\tilde{B}$ associated with the symmetric tensor $\hat{A}^{ij}_{TT}$ .

(see documentation of Sym_tensor::p_tilde_b).

Definition at line 548 of file time_slice.h.

Evolution_std<Vector> Isol_hor::beta_auto_evol [mutable, protected]

Values at successive time steps of the shift function $\beta^i_{auto}$ .

Definition at line 299 of file isol_hor.h.

Evolution_std<Vector> Isol_hor::beta_comp_evol [mutable, protected]

Values at successive time steps of the shift function $\beta^i_{comp}$ .

Definition at line 302 of file isol_hor.h.

Evolution_std<Vector> Time_slice::beta_evol [mutable, protected, inherited]

Values at successive time steps of the shift vector $\beta^i$ .

Definition at line 215 of file time_slice.h.

double Isol_hor::boost_x [protected]

Boost velocity in x-direction.

Definition at line 270 of file isol_hor.h.

double Isol_hor::boost_z [protected]

Boost velocity in z-direction.

Definition at line 273 of file isol_hor.h.

Scalar Isol_hor::decouple [protected]

Function used to construct $A^{ij}_{auto}$ from the total $A^{ij}$ .

Only used for a binary system.

Mainly this Scalar is 1 around the hole and 0 around the companion and the sum of decouple for the hole and his companion is 1 everywhere.

Definition at line 343 of file isol_hor.h.

int Time_slice::depth [protected, inherited]

Number of stored time slices.

Definition at line 175 of file time_slice.h.

Evolution_std<Vector> Isol_hor::dn_evol [mutable, protected]

Values at successive time steps of the covariant derivative of the lapse with respect to the flat metric $\overline\nabla_i N$ .

Definition at line 292 of file isol_hor.h.

Evolution_std<Vector> Isol_hor::dpsi_evol [mutable, protected]

Values at successive time steps of the covariant derivative of the conformal factor $\overline\nabla_i \Psi$ .

Definition at line 296 of file isol_hor.h.

const Metric_flat& Time_slice_conf::ff [protected, inherited]

Pointer on the flat metric $f_{ij}$ with respect to which the conformal decomposition is performed.

Definition at line 503 of file time_slice.h.

Evolution_std<Sym_tensor> Time_slice::gam_dd_evol [mutable, protected, inherited]

Values at successive time steps of the covariant components of the induced metric $\gamma_{ij}$ .

Definition at line 194 of file time_slice.h.

Evolution_std<Sym_tensor> Time_slice::gam_uu_evol [mutable, protected, inherited]

Values at successive time steps of the contravariant components of the induced metric $\gamma^{ij}$ .

Definition at line 199 of file time_slice.h.

Sym_tensor Isol_hor::gamt_point [protected]

Time derivative of the 3-metric tilde.

Definition at line 327 of file isol_hor.h.

Evolution_std<Sym_tensor> Time_slice_conf::hata_evol [mutable, protected, inherited]

Values at successive time steps of the components $\hat{A}^{ij}$ .

It is the conformal representation of the traceless part of the extrinsic curvature: $\hat{A}^{ij} = \Psi^{10} \left( K^{ij} - \frac{1}{3} K \gamma^{ij} \right)$ . One can uniquely (up to the boundary conditions) define the decomposition: $\hat{A}^{ij} = {\cal D}^i X^j + {\cal D}^j X^i - \frac{2}{3} {\cal D}_k X^k f^{ij} + \hat{A}^{ij}_{TT}$ , where $ X^i $ represents the longitudinal part and $\hat{A}^{ij}_{TT}$ is the transverse-traceless part.

Definition at line 538 of file time_slice.h.

Evolution_std<Sym_tensor> Time_slice_conf::hh_evol [mutable, protected, inherited]

Values at successive time steps of the components $h^{ij}$ .

It is the deviation of the conformal metric $\tilde\gamma^{ij}$ from the flat metric $f^{ij}$ : $\tilde\gamma^{ij} = f^{ij} + h^{ij}$ .

Definition at line 526 of file time_slice.h.

int Time_slice::jtime [protected, inherited]

Time step index of the latest slice.

Definition at line 186 of file time_slice.h.

Evolution_std<Sym_tensor> Time_slice::k_dd_evol [mutable, protected, inherited]

Values at successive time steps of the covariant components of the extrinsic curvature tensor $K_{ij}$ .

Definition at line 204 of file time_slice.h.

Evolution_std<Sym_tensor> Time_slice::k_uu_evol [mutable, protected, inherited]

Values at successive time steps of the contravariant components of the extrinsic curvature tensor $K^{ij}$ .

Definition at line 209 of file time_slice.h.

Metric Isol_hor::met_gamt [protected]

3 metric tilde

Definition at line 324 of file isol_hor.h.

Map_af& Isol_hor::mp [protected]

Affine mapping.

Definition at line 258 of file isol_hor.h.

Evolution_std<Scalar> Isol_hor::n_auto_evol [mutable, protected]

Values at successive time steps of the lapse function $N_{auto}$ .

Definition at line 279 of file isol_hor.h.

Evolution_std<Scalar> Isol_hor::n_comp_evol [mutable, protected]

Values at successive time steps of the lapse function $N_{comp}$ .

Definition at line 282 of file isol_hor.h.

Evolution_std<Scalar> Time_slice::n_evol [mutable, protected, inherited]

Values at successive time steps of the lapse function N.

Definition at line 212 of file time_slice.h.

Evolution_std<Scalar> Time_slice_conf::npsi_evol [mutable, protected, inherited]

Values at successive time steps of the factor $N\Psi$ .

Definition at line 518 of file time_slice.h.

int Isol_hor::nz [protected]

Number of zones.

Definition at line 261 of file isol_hor.h.

double Isol_hor::omega [protected]

Angular velocity in LORENE's units.

Definition at line 267 of file isol_hor.h.

Metric* Time_slice::p_gamma [mutable, protected, inherited]

Pointer on the induced metric at the current time step (jtime).

Definition at line 235 of file time_slice.h.

Vector* Time_slice_conf::p_hdirac [mutable, protected, inherited]

Pointer on the vector $H^i = {\cal D}_j \tilde\gamma^{ij}$ (which vanishes in Dirac gauge), at the current time step (jtime).

Definition at line 567 of file time_slice.h.

Scalar* Time_slice_conf::p_ln_psi [mutable, protected, inherited]

Pointer on the logarithm of $\Psi$ at the current time step (jtime).

Definition at line 562 of file time_slice.h.

Scalar* Time_slice_conf::p_psi4 [mutable, protected, inherited]

Pointer on the factor $\Psi^4$ at the current time step (jtime).

Definition at line 559 of file time_slice.h.

Metric* Time_slice_conf::p_tgamma [mutable, protected, inherited]

Pointer on the conformal metric $\tilde\gamma_{ij}$ at the current time step (jtime).

Definition at line 556 of file time_slice.h.

Vector* Time_slice_conf::p_vec_X [mutable, protected, inherited]

Pointer on the vector $ X^i $ representing the longitudinal part of $\hat{A}^{ij}$ .

(see the documentation of hata_evol)

Definition at line 573 of file time_slice.h.

Evolution_std<Scalar> Isol_hor::psi_auto_evol [mutable, protected]

Values at successive time steps of the conformal factor $\Psi_{auto}$ .

Definition at line 285 of file isol_hor.h.

Evolution_std<Scalar> Isol_hor::psi_comp_evol [mutable, protected]

Values at successive time steps of the lapse function $\Psi_{comp}$ .

Definition at line 288 of file isol_hor.h.

Evolution_std<Scalar> Time_slice_conf::psi_evol [mutable, protected, inherited]

Values at successive time steps of the conformal factor $\Psi$ relating the physical metric $\gamma_{ij}$ to the conformal one: $\gamma_{ij} = \Psi^4 \tilde\gamma_{ij}$ .

$\Psi$ is defined by

$\Psi := \left( \frac{\det\gamma_{ij}}{\det f_{ij}} \right) ^{1/12}$

Definition at line 513 of file time_slice.h.

double Isol_hor::radius [protected]

Radius of the horizon in LORENE's units.

Definition at line 264 of file isol_hor.h.

double Isol_hor::regul [protected]

Intensity of the correction on the shift vector.

Definition at line 276 of file isol_hor.h.

int Time_slice::scheme_order [protected, inherited]

Order of the finite-differences scheme for the computation of time derivatives.

This order is not constant and can be adjusted via set_scheme_order() .

Definition at line 183 of file time_slice.h.

Evolution_std<double> Time_slice::the_time [protected, inherited]

Time label of each slice.

Definition at line 189 of file time_slice.h.

Scalar Isol_hor::trK [protected]

Trace of the extrinsic curvature.

Definition at line 330 of file isol_hor.h.

Evolution_std<Scalar> Time_slice::trk_evol [mutable, protected, inherited]

Values at successive time steps of the trace K of the extrinsic curvature.

Definition at line 220 of file time_slice.h.

Scalar Isol_hor::trK_point [protected]

Time derivative of the trace of the extrinsic curvature.

Definition at line 333 of file isol_hor.h.

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

Isol_hor Class Reference [Time evolution (under development)]

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

Isol_hor Class Reference
[Time evolution (under development)]