Class describing an apparent horizon. More...

#include <spheroid.h>

Inheritance diagram for Lorene::App_hor:

Public Member Functions
	App_hor (const Mg3d &grid_angu, double radius)
	Standard constructor. More...

	App_hor (const Scalar &h_in, const Metric &gamij, const Sym_tensor &Kij)
	Constructor of an apparent horizon embedded in a 3-slice (`Time_slice` ) of 3+1 formalism. More...

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

	App_hor (FILE *)
	Constructor from a file (see `sauve(FILE*)` ) More...

virtual	~App_hor ()
	Destructor. More...

void	operator= (const App_hor &)
	Assignment to another App_hor. More...

bool	check_expansion (double thres=1.e-7) const

const Sym_tensor &	lie_derive_shear (const Scalar &bb, const Scalar &lapse)
	Lie derivative of shear tensor with respect to the evolution vector field. More...

const Sym_tensor &	lie_derive_theta_plus (const Scalar &bb, const Scalar &lapse)
	Lie derivative of the null outgoing expansion rate with respect to the evolution vector field. More...

const Sym_tensor &	lie_derive_theta_minus (const Scalar &bb, const Scalar &lapse)
	Lie derivative of the null ingoing expansion rate with respect to the evolution vector field. More...

const Sym_tensor &	lie_derive_q_ab (const Scalar &bb, const Scalar &lapse)
	Lie derivative of 2-metric with respect to the evolution vector field. More...

const Scalar &	l_non_affinity (const Scalar &bb, const Scalar &lapse)
	non-affinity (or surface gravity) with respect to the outgoing null vector field More...

void	set_ephi (const Scalar &)
	Assigns the conformal Killing vector field to phi. More...

const Scalar &	get_hsurf () const
	Returns the field `h_surf`. More...

const Metric &	get_qab () const
	Returns the metric $q_{ab}$ . More...

const Scalar &	get_ricci () const
	Returns the 2-ricci scalar $R = q^{ab}R_{ab}$ . More...

const Sym_tensor &	get_hh () const
	Returns the symmetric tensor $H_{ab}$ . More...

const Sym_tensor &	get_qq () const
	returns the 3-d degenerate 2-metric $Q_{ab}$ More...

const Tensor &	get_proj () const
	returns the 3-d projector on 2-surface More...

const Tensor &	get_jac2d () const
	returns the 2-d jacobian of coordinate transformation More...

const Scalar &	get_trk () const
	Returns the trace `K` on the 2-surface. More...

const Vector &	get_ll () const
	Returns the vector . More...

const Vector &	get_ss () const
	Returns the vector . More...

const Vector &	get_ephi () const
	Returns the conformal Killing symmetry vector on the 2-surface. More...

const Sym_tensor &	get_jj () const
	Returns the symmetric tensor $J_{ab}$ . More...

const Scalar &	get_fff () const
	Returns the normalization scalar `F`. More...

const Scalar &	get_ggg () const
	Returns the normalization scalar `G`. More...

bool	get_issphere () const
	Returns the flag saying whether or not the horizon is geometrically round. More...

Scalar &	set_hsurf ()
	Sets the field `h_surf`. More...

Metric &	set_qab ()
	Sets the modified metric (non degenerated) $q_{ab}$ . More...

Scalar &	set_ricci ()
	Sets the 2-Ricci scalar $R = q^{ab}R_{ab}$ . More...

Sym_tensor &	set_qq ()
	Sets the degenerated metric $Q_{ab}$ . More...

Tensor &	set_proj ()
	Sets the projector . More...

Sym_tensor &	set_hh ()
	Sets the symmetric tensor $H_{ab}$ . More...

Scalar &	set_trk ()
	Sets the trace `K` on the 2-surface. More...

Vector &	set_ll ()
	Sets the vector . More...

Vector &	set_ss ()
	Sets the vector . More...

Sym_tensor &	set_jj ()
	Sets the symmetric tensor $J_{ab}$ . More...

Scalar &	set_fff ()
	Sets the normalization factor `F`. More...

Scalar &	set_ggg ()
	Sets the normalization factor `G`. More...

bool	set_issphere ()
	Sets the boolean linked to geometrical shape of the horizon. More...

void	update_from_tslice (const Metric &gamij, const Sym_tensor &Kij)
	Updates from the 3-slice data. More...

const Scalar &	sqrt_q () const
	Computes the normal vector field to the 2-surface. More...

double	area () const
	Computes the area of the 2-surface. More...

double	angu_mom () const
	Computes the angular momentum with respect to a divergence-free vector field tangent to the 2-surface. More...

double	mass () const
	Computes the mass as defined from the calculus of angular momentum, done with respect to a divergence free tangent vector field . More...

double	multipole_mass (const int order) const
	Computes the mass multipole of a given order for the spheroid, assumed to be spherical. More...

double	multipole_angu (const int order) const
	Computes the angular multipole of a given order for the spheroid, assumed to be spherical. More...

double	epsilon_A_minus_one () const
	Computation of the refined Penrose parameter for axisymmetric spacetimes, and its difference wrt one. More...

double	epsilon_P_minus_one () const
	Computation of the classical Penrose parameter, and its difference wrt one. More...

const Scalar &	theta_plus () const
	Computes the outgoing null expansion $\theta_+$ . More...

const Scalar &	theta_minus () const
	Computes the ingoing null expansion $\theta_-$ . More...

const Sym_tensor &	shear () const
	Computes the shear of the 2-surface $\sigma_{ab}$ . More...

Tensor	derive_cov2dflat (const Tensor &uu) const
	Computes the round covariant derivative on the spheroid. More...

const Tensor &	delta () const
	Computes the delta coefficients for covariant derivative. More...

Tensor	derive_cov2d (const Tensor &uu) const
	Computes the total covariant derivative on the spheroid. More...

virtual void	sauve (FILE *) const
	Save in a file. More...

Protected Member Functions
virtual void	del_deriv () const
	Deletes all the derived quantities. More...

void	set_der_0x0 () const
	Sets to `0x0` all the pointers on derived quantities. More...

Protected Attributes
Scalar	h_surf
	The location of the 2-surface as r = `h_surf` $(\theta, \varphi)$ . More...

Tensor	jac2d
	The jacobian of the adaptation of coordinates (contravariant/covariant representation) More...

Tensor	proj
	The 3-d projector on the 2-surface (contravariant-covariant form). More...

Sym_tensor	qq
	The 3-d covariant degenerated 2-metric on the surface. More...

Vector	ss
	The adapted normal vector field to spheroid in the 3-slice. More...

Vector	ephi
	The conformal Killing vector field on the 2-surface (set to by default to the axial vector associated with coordinate $\varphi$ ) More...

Metric	qab

Scalar	ricci
	Induced metric on the 2-surface $q_{ab}$ . More...

Sym_tensor	hh
	The ricci scalar on the 2-surface. More...

Scalar	trk
	Trace K of the extrinsic curvature of the 3-slice. More...

Vector	ll
	Normal-tangent component of the extrinsic curvature of the 3-slice. More...

Sym_tensor	jj
	Tangent components of the extrinsic curvature of the 3-slice. More...

Scalar	fff
	Normalization function for the outgoing null vector l. More...

Scalar	ggg
	Normalization function for the ingoing null vector k. More...

Scalar	zeta

bool	issphere
	Flag to know whether the horizon is geometrically round or distorted. More...

Scalar *	p_sqrt_q
	Surface element $\sqrt{\det q_{ab}}$ . More...

double *	p_area
	The area of the 2-surface. More...

double *	p_angu_mom
	The angular momentum. More...

double *	p_mass
	Mass defined from angular momentum. More...

double *	p_multipole_mass
	Mass multipole for the spheroid. More...

double *	p_multipole_angu
	Angular momentum multipole for the spheroid. More...

double *	p_epsilon_A_minus_one

double *	p_epsilon_P_minus_one
	Refined Penrose parameter, difference wrt one. More...

Scalar *	p_theta_plus
	Classical Penrose parameter, difference wrt one. More...

Scalar *	p_theta_minus
	Null ingoing expansion. More...

Sym_tensor *	p_shear
	The shear tensor. More...

Tensor *	p_delta

Detailed Description

Class describing an apparent horizon.

It is derived from the class Spheroid, with the property that the outgoing null expansion $\theta_+ = 0$ .

Definition at line 408 of file spheroid.h.

Constructor & Destructor Documentation

◆ App_hor() [1/4]

Lorene::App_hor::App_hor	(	const Mg3d &	grid_angu,
		double	radius
	)

Standard constructor.

◆ App_hor() [2/4]

Lorene::App_hor::App_hor	(	const Scalar &	h_in,
		const Metric &	gamij,
		const Sym_tensor &	Kij
	)

Constructor of an apparent horizon embedded in a 3-slice (Time_slice ) of 3+1 formalism.

This is done from the Time_slice data.

Parameters

h_in	: the location of the surface r = h_in
gamij	: the 3-metric on the 3-slice
Kij	: the extrinsic curvature of the 3-slice (covariant representation)

◆ App_hor() [3/4]

Lorene::App_hor::App_hor ( const App_hor & )

Copy constructor.

◆ App_hor() [4/4]

Lorene::App_hor::App_hor ( FILE * )

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

◆ ~App_hor()

virtual Lorene::App_hor::~App_hor ( )

virtual

Destructor.

Member Function Documentation

◆ angu_mom()

double Lorene::Spheroid::angu_mom ( ) const

inherited

Computes the angular momentum with respect to a divergence-free vector field tangent to the 2-surface.

This is defined as

${\cal J} = \int h^2 L_i \phi^i \sqrt{\det q_{ab}} \sin \theta {\rm d}\theta {\rm d}\varphi$

Parameters

phi	: the divergence-free vector field $\phi$

Definition at line 724 of file spheroid.C.

References Lorene::contract(), Lorene::Map::get_bvect_spher(), Lorene::Spheroid::get_ephi(), Lorene::Tensor::get_mp(), Lorene::Spheroid::h_surf, Lorene::Map_af::integrale_surface(), Lorene::Spheroid::jac2d, Lorene::Spheroid::ll, Lorene::Spheroid::p_angu_mom, and Lorene::Spheroid::sqrt_q().

◆ area()

double Lorene::Spheroid::area ( ) const

inherited

Computes the area of the 2-surface.

This is defined as

${\cal A} = \int h^2 \sqrt{\det q_{ab}} \sin \theta {\rm d}\theta {\rm d}\varphi$

Definition at line 711 of file spheroid.C.

References Lorene::Tensor::get_mp(), Lorene::Spheroid::h_surf, Lorene::Map_af::integrale_surface(), Lorene::Spheroid::p_area, and Lorene::Spheroid::sqrt_q().

◆ del_deriv()

void Lorene::Spheroid::del_deriv ( ) const

protectedvirtualinherited

Deletes all the derived quantities.

Definition at line 653 of file spheroid.C.

References Lorene::Spheroid::p_angu_mom, Lorene::Spheroid::p_area, Lorene::Spheroid::p_epsilon_P_minus_one, Lorene::Spheroid::p_mass, Lorene::Spheroid::p_multipole_angu, Lorene::Spheroid::p_multipole_mass, Lorene::Spheroid::p_shear, Lorene::Spheroid::p_sqrt_q, Lorene::Spheroid::p_theta_minus, Lorene::Spheroid::p_theta_plus, and Lorene::Spheroid::set_der_0x0().

◆ delta()

const Tensor & Lorene::Spheroid::delta ( ) const

inherited

Computes the delta coefficients for covariant derivative.

Definition at line 1206 of file spheroid.C.

References Lorene::Metric::con(), Lorene::Metric::cov(), Lorene::Spheroid::derive_cov2dflat(), Lorene::Map::get_bvect_spher(), Lorene::Metric::get_mp(), Lorene::Tensor::set(), and Lorene::Tensor::set_index_type().

◆ derive_cov2d()

Tensor Lorene::Spheroid::derive_cov2d ( const Tensor & uu ) const

inherited

Computes the total covariant derivative on the spheroid.

Definition at line 1243 of file spheroid.C.

References Lorene::contract(), Lorene::Spheroid::delta(), Lorene::Spheroid::derive_cov2dflat(), Lorene::Tensor::get_index_type(), and Lorene::Tensor::get_valence().

◆ derive_cov2dflat()

Tensor Lorene::Spheroid::derive_cov2dflat ( const Tensor & uu ) const

inherited

Computes the round covariant derivative on the spheroid.

Definition at line 957 of file spheroid.C.

References Lorene::Map::get_bvect_spher(), Lorene::Tensor::get_index_type(), Lorene::Tensor::get_mp(), Lorene::Tensor::get_n_comp(), Lorene::Tensor::get_triad(), Lorene::Tensor::get_valence(), Lorene::Tensor::indices(), Lorene::Itbl::set(), Lorene::Tensor::set(), Lorene::Tensor_sym::sym_index1(), and Lorene::Tensor_sym::sym_index2().

◆ epsilon_A_minus_one()

double Lorene::Spheroid::epsilon_A_minus_one ( ) const

inherited

Computation of the refined Penrose parameter for axisymmetric spacetimes, and its difference wrt one.

Definition at line 867 of file spheroid.C.

References Lorene::Spheroid::angu_mom(), Lorene::Spheroid::area(), Lorene::Spheroid::mass(), Lorene::pow(), and Lorene::sqrt().

◆ epsilon_P_minus_one()

double Lorene::Spheroid::epsilon_P_minus_one ( ) const

inherited

Computation of the classical Penrose parameter, and its difference wrt one.

To use in replacement of epsilon_A_minus_one when the computed spacetime is not axisymmetric.

Definition at line 879 of file spheroid.C.

References Lorene::Spheroid::angu_mom(), Lorene::Spheroid::area(), Lorene::Spheroid::mass(), Lorene::Spheroid::p_epsilon_P_minus_one, and Lorene::pow().

◆ get_ephi()

const Vector& Lorene::Spheroid::get_ephi ( ) const

inlineinherited

Returns the conformal Killing symmetry vector on the 2-surface.

Definition at line 253 of file spheroid.h.

References Lorene::Spheroid::ephi.

◆ get_fff()

const Scalar& Lorene::Spheroid::get_fff ( ) const

inlineinherited

Returns the normalization scalar F.

Definition at line 259 of file spheroid.h.

References Lorene::Spheroid::fff.

◆ get_ggg()

const Scalar& Lorene::Spheroid::get_ggg ( ) const

inlineinherited

Returns the normalization scalar G.

Definition at line 262 of file spheroid.h.

References Lorene::Spheroid::ggg.

◆ get_hh()

const Sym_tensor& Lorene::Spheroid::get_hh ( ) const

inlineinherited

Returns the symmetric tensor $H_{ab}$ .

Definition at line 232 of file spheroid.h.

References Lorene::Spheroid::hh.

◆ get_hsurf()

const Scalar& Lorene::Spheroid::get_hsurf ( ) const

inlineinherited

Returns the field h_surf.

Definition at line 223 of file spheroid.h.

References Lorene::Spheroid::h_surf.

◆ get_issphere()

bool Lorene::Spheroid::get_issphere ( ) const

inlineinherited

Returns the flag saying whether or not the horizon is geometrically round.

Definition at line 265 of file spheroid.h.

References Lorene::Spheroid::issphere.

◆ get_jac2d()

const Tensor& Lorene::Spheroid::get_jac2d ( ) const

inlineinherited

returns the 2-d jacobian of coordinate transformation $ J $

Definition at line 241 of file spheroid.h.

References Lorene::Spheroid::jac2d.

◆ get_jj()

const Sym_tensor& Lorene::Spheroid::get_jj ( ) const

inlineinherited

Returns the symmetric tensor $J_{ab}$ .

Definition at line 256 of file spheroid.h.

References Lorene::Spheroid::jj.

◆ get_ll()

const Vector& Lorene::Spheroid::get_ll ( ) const

inlineinherited

Returns the vector $ L_a $ .

Definition at line 247 of file spheroid.h.

References Lorene::Spheroid::ll.

◆ get_proj()

const Tensor& Lorene::Spheroid::get_proj ( ) const

inlineinherited

returns the 3-d projector on 2-surface $ Pi $

Definition at line 238 of file spheroid.h.

References Lorene::Spheroid::proj.

◆ get_qab()

const Metric& Lorene::Spheroid::get_qab ( ) const

inlineinherited

Returns the metric $q_{ab}$ .

Definition at line 226 of file spheroid.h.

◆ get_qq()

const Sym_tensor& Lorene::Spheroid::get_qq ( ) const

inlineinherited

returns the 3-d degenerate 2-metric $Q_{ab}$

Definition at line 235 of file spheroid.h.

References Lorene::Spheroid::qq.

◆ get_ricci()

const Scalar& Lorene::Spheroid::get_ricci ( ) const

inlineinherited

Returns the 2-ricci scalar $R = q^{ab}R_{ab}$ .

Definition at line 229 of file spheroid.h.

References Lorene::Spheroid::ricci.

◆ get_ss()

const Vector& Lorene::Spheroid::get_ss ( ) const

inlineinherited

Returns the vector $ S_a $ .

Definition at line 250 of file spheroid.h.

References Lorene::Spheroid::ss.

◆ get_trk()

const Scalar& Lorene::Spheroid::get_trk ( ) const

inlineinherited

Returns the trace K on the 2-surface.

Definition at line 244 of file spheroid.h.

References Lorene::Spheroid::trk.

◆ l_non_affinity()

const Scalar& Lorene::App_hor::l_non_affinity	(	const Scalar &	bb,
		const Scalar &	lapse
	)

non-affinity (or surface gravity) with respect to the outgoing null vector field

◆ lie_derive_q_ab()

const Sym_tensor& Lorene::App_hor::lie_derive_q_ab	(	const Scalar &	bb,
		const Scalar &	lapse
	)

Lie derivative of 2-metric with respect to the evolution vector field.

◆ lie_derive_shear()

const Sym_tensor& Lorene::App_hor::lie_derive_shear	(	const Scalar &	bb,
		const Scalar &	lapse
	)

Lie derivative of shear tensor with respect to the evolution vector field.

◆ lie_derive_theta_minus()

const Sym_tensor& Lorene::App_hor::lie_derive_theta_minus	(	const Scalar &	bb,
		const Scalar &	lapse
	)

Lie derivative of the null ingoing expansion rate with respect to the evolution vector field.

◆ lie_derive_theta_plus()

const Sym_tensor& Lorene::App_hor::lie_derive_theta_plus	(	const Scalar &	bb,
		const Scalar &	lapse
	)

Lie derivative of the null outgoing expansion rate with respect to the evolution vector field.

◆ mass()

double Lorene::Spheroid::mass ( ) const

inherited

Computes the mass as defined from the calculus of angular momentum, done with respect to a divergence free tangent vector field $ phi $ .

Spheroid has to be a real sphere (flag issphere true), of constant radius

$R_{s}$

. defined as

$M = \frac{1}{2 R_{s}} \sqrt{R_{s}^{4} + 4{\cal J}^{2}}$

Definition at line 739 of file spheroid.C.

References Lorene::Spheroid::angu_mom(), Lorene::Spheroid::area(), Lorene::Spheroid::p_mass, and Lorene::sqrt().

◆ multipole_angu()

double Lorene::Spheroid::multipole_angu ( const int order ) const

inherited

Computes the angular multipole of a given order for the spheroid, assumed to be spherical.

$ phi $ is a divergence free tangent vector field. WARNING:order has to be strictly higher than zero (no topological defects here...), and an odd number for technical reasons.

Definition at line 804 of file spheroid.C.

References Lorene::Spheroid::area(), Lorene::contract(), Lorene::Map::get_bvect_spher(), Lorene::Spheroid::get_ephi(), Lorene::Tensor::get_mp(), Lorene::Spheroid::h_surf, Lorene::Map_af::integrale_surface(), Lorene::Spheroid::jac2d, Lorene::Spheroid::ll, Lorene::Spheroid::p_multipole_angu, Lorene::Scalar::set_spectral_va(), Lorene::sqrt(), Lorene::Spheroid::sqrt_q(), Lorene::Scalar::std_spectral_base(), and Lorene::Valeur::ylm().

◆ multipole_mass()

double Lorene::Spheroid::multipole_mass ( const int order ) const

inherited

Computes the mass multipole of a given order for the spheroid, assumed to be spherical.

WARNING: For technical reasons, only even orders are supported by the code.

Definition at line 751 of file spheroid.C.

References Lorene::Spheroid::area(), Lorene::Tensor::get_mp(), Lorene::Spheroid::get_ricci(), Lorene::Spheroid::h_surf, Lorene::Map_af::integrale_surface(), Lorene::Spheroid::mass(), Lorene::Spheroid::p_multipole_mass, Lorene::Scalar::set_spectral_va(), Lorene::sqrt(), Lorene::Spheroid::sqrt_q(), Lorene::Scalar::std_spectral_base(), and Lorene::Valeur::ylm().

◆ operator=()

void Lorene::App_hor::operator= ( const App_hor & )

Assignment to another App_hor.

◆ sauve()

void Lorene::Spheroid::sauve ( FILE * ) const

virtualinherited

Save in a file.

Definition at line 1189 of file spheroid.C.

◆ set_der_0x0()

void Lorene::Spheroid::set_der_0x0 ( ) const

protectedinherited

Sets to 0x0 all the pointers on derived quantities.

Definition at line 669 of file spheroid.C.

References Lorene::Spheroid::p_angu_mom, Lorene::Spheroid::p_area, Lorene::Spheroid::p_epsilon_P_minus_one, Lorene::Spheroid::p_mass, Lorene::Spheroid::p_multipole_angu, Lorene::Spheroid::p_multipole_mass, Lorene::Spheroid::p_shear, Lorene::Spheroid::p_sqrt_q, Lorene::Spheroid::p_theta_minus, and Lorene::Spheroid::p_theta_plus.

◆ set_ephi()

void Lorene::Spheroid::set_ephi ( const Scalar & )

inherited

Assigns the conformal Killing vector field to phi.

◆ set_fff()

Scalar& Lorene::Spheroid::set_fff ( )

inlineinherited

Sets the normalization factor F.

Definition at line 298 of file spheroid.h.

References Lorene::Spheroid::del_deriv(), and Lorene::Spheroid::fff.

◆ set_ggg()

Scalar& Lorene::Spheroid::set_ggg ( )

inlineinherited

Sets the normalization factor G.

Definition at line 301 of file spheroid.h.

References Lorene::Spheroid::del_deriv(), and Lorene::Spheroid::ggg.

◆ set_hh()

Sym_tensor& Lorene::Spheroid::set_hh ( )

inlineinherited

Sets the symmetric tensor $H_{ab}$ .

Definition at line 283 of file spheroid.h.

References Lorene::Spheroid::del_deriv(), and Lorene::Spheroid::hh.

◆ set_hsurf()

Scalar& Lorene::Spheroid::set_hsurf ( )

inlineinherited

Sets the field h_surf.

Definition at line 268 of file spheroid.h.

References Lorene::Spheroid::del_deriv(), and Lorene::Spheroid::h_surf.

◆ set_issphere()

bool Lorene::Spheroid::set_issphere ( )

inlineinherited

Sets the boolean linked to geometrical shape of the horizon.

Definition at line 304 of file spheroid.h.

References Lorene::Spheroid::del_deriv(), and Lorene::Spheroid::issphere.

◆ set_jj()

Sym_tensor& Lorene::Spheroid::set_jj ( )

inlineinherited

Sets the symmetric tensor $J_{ab}$ .

Definition at line 295 of file spheroid.h.

References Lorene::Spheroid::del_deriv(), and Lorene::Spheroid::jj.

◆ set_ll()

Vector& Lorene::Spheroid::set_ll ( )

inlineinherited

Sets the vector $ L_a $ .

Definition at line 289 of file spheroid.h.

References Lorene::Spheroid::del_deriv(), and Lorene::Spheroid::ll.

◆ set_proj()

Tensor& Lorene::Spheroid::set_proj ( )

inlineinherited

Sets the projector $ Pi $ .

Definition at line 280 of file spheroid.h.

References Lorene::Spheroid::del_deriv(), and Lorene::Spheroid::proj.

◆ set_qab()

Metric& Lorene::Spheroid::set_qab ( )

inlineinherited

Sets the modified metric (non degenerated) $q_{ab}$ .

Definition at line 271 of file spheroid.h.

References Lorene::Spheroid::del_deriv().

◆ set_qq()

Sym_tensor& Lorene::Spheroid::set_qq ( )

inlineinherited

Sets the degenerated metric $Q_{ab}$ .

Definition at line 277 of file spheroid.h.

References Lorene::Spheroid::del_deriv(), and Lorene::Spheroid::qq.

◆ set_ricci()

Scalar& Lorene::Spheroid::set_ricci ( )

inlineinherited

Sets the 2-Ricci scalar $R = q^{ab}R_{ab}$ .

Definition at line 274 of file spheroid.h.

References Lorene::Spheroid::del_deriv(), and Lorene::Spheroid::ricci.

◆ set_ss()

Vector& Lorene::Spheroid::set_ss ( )

inlineinherited

Sets the vector $ s_a $ .

Definition at line 292 of file spheroid.h.

References Lorene::Spheroid::del_deriv(), and Lorene::Spheroid::ss.

◆ set_trk()

Scalar& Lorene::Spheroid::set_trk ( )

inlineinherited

Sets the trace K on the 2-surface.

Definition at line 286 of file spheroid.h.

References Lorene::Spheroid::del_deriv(), and Lorene::Spheroid::trk.

◆ shear()

const Sym_tensor & Lorene::Spheroid::shear ( ) const

inherited

Computes the shear of the 2-surface $\sigma_{ab}$ .

Definition at line 928 of file spheroid.C.

References Lorene::Metric::cov(), Lorene::Spheroid::fff, Lorene::Spheroid::hh, Lorene::Spheroid::jj, Lorene::Spheroid::p_shear, Lorene::Tensor::std_spectral_base(), and Lorene::Tensor::trace().

◆ sqrt_q()

const Scalar & Lorene::Spheroid::sqrt_q ( ) const

inherited

Computes the normal vector field to the 2-surface.

Computes the square root of the determinant of $q_{ab}$ .

Definition at line 696 of file spheroid.C.

References Lorene::Spheroid::get_qq(), Lorene::Spheroid::p_sqrt_q, Lorene::sqrt(), and Lorene::Scalar::std_spectral_base().

◆ theta_minus()

const Scalar & Lorene::Spheroid::theta_minus ( ) const

inherited

Computes the ingoing null expansion $\theta_-$ .

Definition at line 912 of file spheroid.C.

References Lorene::Spheroid::ggg, Lorene::Spheroid::hh, Lorene::Spheroid::jj, Lorene::Spheroid::p_theta_minus, Lorene::Scalar::std_spectral_base(), and Lorene::Tensor::trace().

◆ theta_plus()

const Scalar & Lorene::Spheroid::theta_plus ( ) const

inherited

Computes the outgoing null expansion $\theta_+$ .

Definition at line 892 of file spheroid.C.

References Lorene::Spheroid::fff, Lorene::Spheroid::hh, Lorene::Spheroid::jj, Lorene::Spheroid::p_theta_plus, Lorene::Scalar::set_spectral_va(), Lorene::Scalar::std_spectral_base(), Lorene::Tensor::trace(), and Lorene::Valeur::ylm().

◆ update_from_tslice()

void Lorene::Spheroid::update_from_tslice	(	const Metric &	gamij,
		const Sym_tensor &	Kij
	)

inherited

Updates from the 3-slice data.

Member Data Documentation

◆ ephi

Vector Lorene::Spheroid::ephi

protectedinherited

The conformal Killing vector field on the 2-surface (set to by default to the axial vector associated with coordinate $\varphi$ )

Definition at line 113 of file spheroid.h.

◆ fff

Scalar Lorene::Spheroid::fff

protectedinherited

Normalization function for the outgoing null vector l.

Definition at line 138 of file spheroid.h.

◆ ggg

Scalar Lorene::Spheroid::ggg

protectedinherited

Normalization function for the ingoing null vector k.

Definition at line 143 of file spheroid.h.

◆ h_surf

Scalar Lorene::Spheroid::h_surf

protectedinherited

The location of the 2-surface as r = h_surf $(\theta, \varphi)$ .

Definition at line 91 of file spheroid.h.

◆ hh

Sym_tensor Lorene::Spheroid::hh

protectedinherited

The ricci scalar on the 2-surface.

Extrinsic curvature of the 2-surface in the 3-slice. $H_{ab}$ (covariant representation)

Definition at line 122 of file spheroid.h.

◆ issphere

bool Lorene::Spheroid::issphere

protectedinherited

Flag to know whether the horizon is geometrically round or distorted.

Definition at line 151 of file spheroid.h.

◆ jac2d

Tensor Lorene::Spheroid::jac2d

protectedinherited

The jacobian of the adaptation of coordinates (contravariant/covariant representation)

Definition at line 96 of file spheroid.h.

◆ jj

Sym_tensor Lorene::Spheroid::jj

protectedinherited

Tangent components of the extrinsic curvature of the 3-slice.

$J_{ab}$ (covariant representation)

Definition at line 134 of file spheroid.h.

◆ ll

Vector Lorene::Spheroid::ll

protectedinherited

Normal-tangent component of the extrinsic curvature of the 3-slice.

$ L_a $ (covariant representation)

Definition at line 129 of file spheroid.h.

◆ p_angu_mom

double* Lorene::Spheroid::p_angu_mom

mutableprotectedinherited

The angular momentum.

Definition at line 159 of file spheroid.h.

◆ p_area

double* Lorene::Spheroid::p_area

mutableprotectedinherited

The area of the 2-surface.

Definition at line 158 of file spheroid.h.

◆ p_epsilon_P_minus_one

double* Lorene::Spheroid::p_epsilon_P_minus_one

mutableprotectedinherited

Refined Penrose parameter, difference wrt one.

Definition at line 164 of file spheroid.h.

◆ p_mass

double* Lorene::Spheroid::p_mass

mutableprotectedinherited

Mass defined from angular momentum.

Definition at line 160 of file spheroid.h.

◆ p_multipole_angu

double* Lorene::Spheroid::p_multipole_angu

mutableprotectedinherited

Angular momentum multipole for the spheroid.

Definition at line 162 of file spheroid.h.

◆ p_multipole_mass

double* Lorene::Spheroid::p_multipole_mass

mutableprotectedinherited

Mass multipole for the spheroid.

Definition at line 161 of file spheroid.h.

◆ p_shear

Sym_tensor* Lorene::Spheroid::p_shear

mutableprotectedinherited

The shear tensor.

Definition at line 167 of file spheroid.h.

◆ p_sqrt_q

Scalar* Lorene::Spheroid::p_sqrt_q

mutableprotectedinherited

Surface element $\sqrt{\det q_{ab}}$ .

Definition at line 157 of file spheroid.h.

◆ p_theta_minus

Scalar* Lorene::Spheroid::p_theta_minus

mutableprotectedinherited

Null ingoing expansion.

Definition at line 166 of file spheroid.h.

◆ p_theta_plus

Scalar* Lorene::Spheroid::p_theta_plus

mutableprotectedinherited

Classical Penrose parameter, difference wrt one.

Null outgoing expansion

Definition at line 165 of file spheroid.h.

◆ proj

Tensor Lorene::Spheroid::proj

protectedinherited

The 3-d projector on the 2-surface (contravariant-covariant form).

Definition at line 100 of file spheroid.h.

◆ qq

Sym_tensor Lorene::Spheroid::qq

protectedinherited

The 3-d covariant degenerated 2-metric on the surface.

Definition at line 104 of file spheroid.h.

◆ ricci

Scalar Lorene::Spheroid::ricci

protectedinherited

Induced metric on the 2-surface $q_{ab}$ .

Definition at line 117 of file spheroid.h.

◆ ss

Vector Lorene::Spheroid::ss

protectedinherited

The adapted normal vector field to spheroid in the 3-slice.

Definition at line 108 of file spheroid.h.

◆ trk

Scalar Lorene::Spheroid::trk

protectedinherited

Trace K of the extrinsic curvature of the 3-slice.

Definition at line 124 of file spheroid.h.

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

spheroid.h

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ App_hor() [1/4]

◆ App_hor() [2/4]

◆ App_hor() [3/4]

◆ App_hor() [4/4]

◆ ~App_hor()

Member Function Documentation

◆ angu_mom()

◆ area()

◆ del_deriv()

◆ delta()

◆ derive_cov2d()

◆ derive_cov2dflat()

◆ epsilon_A_minus_one()

◆ epsilon_P_minus_one()

◆ get_ephi()

◆ get_fff()

◆ get_ggg()

◆ get_hh()

◆ get_hsurf()

◆ get_issphere()

◆ get_jac2d()

◆ get_jj()

◆ get_ll()

◆ get_proj()

◆ get_qab()

◆ get_qq()

◆ get_ricci()

◆ get_ss()

◆ get_trk()

◆ l_non_affinity()

◆ lie_derive_q_ab()

◆ lie_derive_shear()

◆ lie_derive_theta_minus()

◆ lie_derive_theta_plus()

◆ mass()

◆ multipole_angu()

◆ multipole_mass()

◆ operator=()

◆ sauve()

◆ set_der_0x0()

◆ set_ephi()

◆ set_fff()

◆ set_ggg()

◆ set_hh()

◆ set_hsurf()

◆ set_issphere()

◆ set_jj()

◆ set_ll()

◆ set_proj()

◆ set_qab()

◆ set_qq()

◆ set_ricci()

◆ set_ss()

◆ set_trk()

◆ shear()

◆ sqrt_q()

◆ theta_minus()

◆ theta_plus()

◆ update_from_tslice()

Member Data Documentation

◆ ephi

◆ fff

◆ ggg

◆ h_surf

◆ hh

◆ issphere

◆ jac2d

◆ jj

◆ ll

◆ p_angu_mom

◆ p_area

◆ p_epsilon_P_minus_one

◆ p_mass

◆ p_multipole_angu

◆ p_multipole_mass