Classes
class	Lorene::Bhole
	Black hole. More...

class	Lorene::Bhole_binaire
	Binary black holes system. More...

class	Lorene::Bin_bhns
	Class for computing a black hole - neutron star binary system with comparable mass () More...

class	Lorene::Bin_bhns_extr
	Class for computing a Black hole - Neutron star binary system with an extreme mass ratio. More...

class	Lorene::Binary
	Binary systems. More...

class	Lorene::Binary_xcts
	Binary systems in eXtended Conformal Thin Sandwich formulation. More...

class	Lorene::Black_hole
	Base class for black holes. More...

class	Lorene::Et_bin_bhns_extr
	Class for a neutron star in black hole - neutron star binary systems. More...

class	Lorene::Et_rot_bifluid
	Class for two-fluid rotating relativistic stars. More...

class	Lorene::Et_rot_diff
	Class for differentially rotating stars. More...

class	Lorene::Et_rot_mag
	Class for magnetized (isolator or perfect conductor), rigidly rotating stars. More...

class	Lorene::Etoile
	Base class for stars * DEPRECATED : use class `Star` instead *. More...

class	Lorene::Etoile_bin
	Class for stars in binary system. More...

class	Lorene::Etoile_rot
	Class for isolated rotating stars * DEPRECATED : use class `Star_rot` instead *. More...

class	Lorene::Excision_hor
	Surface where boundary conditions for quantities in the bulk will be calculated It relies on geometrical properties of the associated Spheroid() (* WARNING! under development*) More...

class	Lorene::Excision_surf
	Surface where boundary conditions for quantities in the bulk will be calculated It relies on geometrical properties of the associated Spheroid() (* WARNING! under development*) More...

class	Lorene::Gravastar
	Class for perfect fluid rotating gravastar. More...

class	Lorene::Hole_bhns
	Class for black holes in black hole-neutron star binaries. More...

class	Lorene::Single_hor
	Binary black holes system. More...

class	Lorene::Spheroid
	Spheroidal 2-surfaces embedded in a time-slice of the 3+1 formalism. More...

class	Lorene::Star
	Base class for stars. More...

class	Lorene::Star_bin
	Class for stars in binary system. More...

class	Lorene::Star_bin_xcts
	Class for stars in binary system in eXtended Conformal Thin Sandwich formulation. More...

class	Lorene::Star_bhns
	Class for stars in black hole-neutron star binaries. More...

class	Lorene::Star_rot
	Class for isolated rotating stars. More...

class	Lorene::Star_rot_CFC
	Class for relativistic rotating stars in Conformal Flatness Condition and maximal slicing. More...

class	Lorene::Star_rot_Dirac
	Class for relativistic rotating stars in Dirac gauge and maximal slicing. More...

class	Lorene::Star_rot_Dirac_diff
	Class for relativistic differentially rotating stars in Dirac gauge and maximal slicing. More...

Functions
bool	Lorene::ah_finder (const Metric &gamma, const Sym_tensor &k_dd_in, Valeur &h, Scalar &ex_fcn, double a_axis, double b_axis, double c_axis, bool verbose=true, bool print=false, double precis=1.e-8, double precis_exp=1.e-6, int it_max=200, int it_relax=200, double relax_fac=1.)
	Apparent horizon linked functions. More...

Detailed Description

Function Documentation

◆ ah_finder()

bool Lorene::ah_finder	(	const Metric &	gamma,
		const Sym_tensor &	k_dd_in,
		Valeur &	h,
		Scalar &	ex_fcn,
		double	a_axis,
		double	b_axis,
		double	c_axis,
		bool	verbose = `true`,
		bool	print = `false`,
		double	precis = `1.e-8`,
		double	precis_exp = `1.e-6`,
		int	it_max = `200`,
		int	it_relax = `200`,
		double	relax_fac = `1.`
	)

Apparent horizon linked functions.

Apparent horizon finder.()

Find the apparent horizon (AH) on a spatial slice for given 3-metric $\gamma_{ij}$ and extrinsic curvature $K_{ij}$ . Method: We solve the apparent-horizon equation $\Theta=0$ (where $\Theta$ is the expansion function of the outgoing null geodesic) as a generalized angular Poisson equation ( $\Delta_{\theta\phi}u+\lambda u=\sigma$ ) in the form:

$\Delta_{\theta\phi}h - 2h = \Psi^4 |DF| h^2\Theta + \Delta_{\theta\phi}h - 2h$

where $h=h(\theta,\phi)$ (h) is the 2-surface of the AH, $\Psi$ is the conformal factor, and $|DF|:= (\gamma^{ij}D_iFD_jF)^{1/2}$ (where $F$ is the level set function $F:=r-h(\theta,\phi)$ and $D_i$ is the covariant derivative w.r.t. $\gamma_{ij}$ ).
We solve the above equation iteratively with the right hand side of the equation as a source term.

Parameters

gamma	: [input] the 3-metric $\gamma_{ij}$ w.r.t. which the AH is to be found.
k_dd_in	: [input] the extrinsic curvature $K_{ij}$ .
Valeur	h : [output] the 2-surface of the apparent horizon
Scalar	ex_fcn : [output] the expansion function defined from the level set function $F:= r - h(\theta,\phi)$
a_axis	: [input] the initial guess for is a triaxial ellipsoidal surface with a_axis the axis along the x-axis of the Cartesian grid
b_axis	: [input] axis along the y-axis (cf a_axis)
c_axis	: [input] axis along the z-axis (cf a_axis)
bool	print : [input] screen printout during iterations? (default: false)
precis	: [input] threshold in the relative difference between the 2-surface of two consecutive steps to stop the iterative procedure (default value: 1.e-8)
precis_exp	: [input] maximum error of the expansion function evaluated on the 2-surface (should be zero by definition) after the iteration is stopped (default value: 1.e-6)
it_max	: [input] maximum number of steps (default value: 200)
it_relax	: [input] step at which relaxation is switched on (default value: 200)
relax_fac	: [input] relaxation factor (default value: 1 for no relaxation)

Returns: bool ah_flag : a flag to indicate whether an apparent horizon is found

Definition at line 97 of file app_hor_finder.C.

References Lorene::abs(), Lorene::Scalar::allocate_all(), Lorene::Valeur::annule_hard(), Lorene::Valeur::c, Lorene::Valeur::c_cf, Lorene::Valeur::coef_i(), Lorene::Metric::con(), Lorene::Metric_flat::con(), Lorene::Metric::connect(), Lorene::contract(), Lorene::Map::cosp, Lorene::Map::cost, Lorene::Scalar::derive_con(), Lorene::Tensor::derive_cov(), Lorene::Scalar::derive_cov(), Lorene::Metric::determinant(), Lorene::Metric_flat::determinant(), Lorene::diffrel(), Lorene::Vector::divergence(), Lorene::Map::flat_met_spher(), Lorene::Mg3d::get_angu(), Lorene::Map::get_bvect_spher(), Lorene::Connection::get_delta(), Lorene::Map::get_mg(), Lorene::Metric::get_mp(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::max(), Lorene::min(), Lorene::Map::phi, Lorene::Mtbl_cf::poisson_angu(), Lorene::pow(), Lorene::Map::r, Lorene::Valeur::set(), Lorene::Scalar::set_etat_zero(), Lorene::Scalar::set_grid_point(), Lorene::Map::sinp, Lorene::Map::sint, Lorene::sqrt(), Lorene::Valeur::std_base_scal(), Lorene::Scalar::std_spectral_base(), Lorene::Map::tet, Lorene::Tensor::trace(), Lorene::Scalar::val_point(), Lorene::Valeur::ylm(), and Lorene::Valeur::ylm_i().

Classes

Functions

Detailed Description

Function Documentation

◆ ah_finder()