LORENE
Public Member Functions | Protected Member Functions | Protected Attributes | List of all members
Lorene::App_hor Class Reference

Class describing an apparent horizon. More...

#include <spheroid.h>

Inheritance diagram for Lorene::App_hor:
Lorene::Spheroid

Public Member Functions

 App_hor (const Mg3d &grid_angu, double radius)
 Standard constructor.
 
 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.
 
 App_hor (const App_hor &)
 Copy constructor.
 
 App_hor (FILE *)
 Constructor from a file (see sauve(FILE*) )
 
virtual ~App_hor ()
 Destructor.
 
void operator= (const App_hor &)
 Assignment to another App_hor.
 
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.
 
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.
 
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.
 
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.
 
const Scalar & l_non_affinity (const Scalar &bb, const Scalar &lapse)
 non-affinity (or surface gravity) with respect to the outgoing null vector field
 
void set_ephi (const Scalar &)
 Assigns the conformal Killing vector field to phi.
 
const Scalar & get_hsurf () const
 Returns the field h_surf.
 
const Metric & get_qab () const
 Returns the metric $ q_{ab} $.
 
const Scalar & get_ricci () const
 Returns the 2-ricci scalar $ R = q^{ab}R_{ab} $.
 
const Sym_tensor & get_hh () const
 Returns the symmetric tensor $ H_{ab} $.
 
const Sym_tensor & get_qq () const
 returns the 3-d degenerate 2-metric $ Q_{ab}$
 
const Tensor & get_proj () const
 returns the 3-d projector on 2-surface $ Pi $
 
const Tensor & get_jac2d () const
 returns the 2-d jacobian of coordinate transformation $ J $
 
const Scalar & get_trk () const
 Returns the trace K on the 2-surface.
 
const Vector & get_ll () const
 Returns the vector $ L_a $.
 
const Vector & get_ss () const
 Returns the vector $ S_a $.
 
const Vector & get_ephi () const
 Returns the conformal Killing symmetry vector on the 2-surface.
 
const Sym_tensor & get_jj () const
 Returns the symmetric tensor $ J_{ab} $.
 
const Scalar & get_fff () const
 Returns the normalization scalar F.
 
const Scalar & get_ggg () const
 Returns the normalization scalar G.
 
bool get_issphere () const
 Returns the flag saying whether or not the horizon is geometrically round.
 
Scalar & set_hsurf ()
 Sets the field h_surf.
 
Metric & set_qab ()
 Sets the modified metric (non degenerated) $ q_{ab} $.
 
Scalar & set_ricci ()
 Sets the 2-Ricci scalar $ R = q^{ab}R_{ab} $.
 
Sym_tensor & set_qq ()
 Sets the degenerated metric $ Q_{ab} $.
 
Tensor & set_proj ()
 Sets the projector $ Pi $.
 
Sym_tensor & set_hh ()
 Sets the symmetric tensor $ H_{ab} $.
 
Scalar & set_trk ()
 Sets the trace K on the 2-surface.
 
Vector & set_ll ()
 Sets the vector $ L_a $.
 
Vector & set_ss ()
 Sets the vector $ s_a $.
 
Sym_tensor & set_jj ()
 Sets the symmetric tensor $ J_{ab} $.
 
Scalar & set_fff ()
 Sets the normalization factor F.
 
Scalar & set_ggg ()
 Sets the normalization factor G.
 
bool set_issphere ()
 Sets the boolean linked to geometrical shape of the horizon.
 
void update_from_tslice (const Metric &gamij, const Sym_tensor &Kij)
 Updates from the 3-slice data.
 
const Scalar & sqrt_q () const
 Computes the normal vector field to the 2-surface.
 
double area () const
 Computes the area of the 2-surface.
 
double angu_mom () const
 Computes the angular momentum with respect to a divergence-free vector field tangent to the 2-surface.
 
double mass () const
 Computes the mass as defined from the calculus of angular momentum, done with respect to a divergence free tangent vector field $ phi $.
 
double multipole_mass (const int order) const
 Computes the mass multipole of a given order for the spheroid, assumed to be spherical.
 
double multipole_angu (const int order) const
 Computes the angular multipole of a given order for the spheroid, assumed to be spherical.
 
double epsilon_A_minus_one () const
 Computation of the refined Penrose parameter for axisymmetric spacetimes, and its difference wrt one.
 
double epsilon_P_minus_one () const
 Computation of the classical Penrose parameter, and its difference wrt one.
 
const Scalar & theta_plus () const
 Computes the outgoing null expansion $ \theta_+ $.
 
const Scalar & theta_minus () const
 Computes the ingoing null expansion $ \theta_- $.
 
const Sym_tensor & shear () const
 Computes the shear of the 2-surface $ \sigma_{ab} $.
 
Tensor derive_cov2dflat (const Tensor &uu) const
 Computes the round covariant derivative on the spheroid.
 
const Tensor & delta () const
 Computes the delta coefficients for covariant derivative.
 
Tensor derive_cov2d (const Tensor &uu) const
 Computes the total covariant derivative on the spheroid.
 
virtual void sauve (FILE *) const
 Save in a file.
 

Protected Member Functions

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

Scalar h_surf
 The location of the 2-surface as r = h_surf $(\theta, \varphi)$.
 
Tensor jac2d
 The jacobian of the adaptation of coordinates (contravariant/covariant representation)
 
Tensor proj
 The 3-d projector on the 2-surface (contravariant-covariant form).
 
Sym_tensor qq
 The 3-d covariant degenerated 2-metric on the surface.
 
Vector ss
 The adapted normal vector field to spheroid in the 3-slice.
 
Vector ephi
 The conformal Killing vector field on the 2-surface (set to by default to the axial vector associated with coordinate $ \varphi $)
 
Metric qab
 
Scalar ricci
 Induced metric on the 2-surface $ q_{ab} $.
 
Sym_tensor hh
 The ricci scalar on the 2-surface.
 
Scalar trk
 Trace K of the extrinsic curvature of the 3-slice.
 
Vector ll
 Normal-tangent component of the extrinsic curvature of the 3-slice.
 
Sym_tensor jj
 Tangent components of the extrinsic curvature of the 3-slice.
 
Scalar fff
 Normalization function for the outgoing null vector l.
 
Scalar ggg
 Normalization function for the ingoing null vector k.
 
Scalar zeta
 
bool issphere
 Flag to know whether the horizon is geometrically round or distorted.
 
Scalar * p_sqrt_q
 Surface element $\sqrt{\det q_{ab}} $.
 
double * p_area
 The area of the 2-surface.
 
double * p_angu_mom
 The angular momentum.
 
double * p_mass
 Mass defined from angular momentum.
 
double * p_multipole_mass
 Mass multipole for the spheroid.
 
double * p_multipole_angu
 Angular momentum multipole for the spheroid.
 
double * p_epsilon_A_minus_one
 
double * p_epsilon_P_minus_one
 Refined Penrose parameter, difference wrt one.
 
Scalar * p_theta_plus
 Classical Penrose parameter, difference wrt one.
 
Scalar * p_theta_minus
 Null ingoing expansion.
 
Sym_tensor * p_shear
 The shear tensor.
 
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 721 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 708 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 650 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 1203 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(), Lorene::Tensor::set_etat_zero(), 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 1240 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 954 of file spheroid.C.

References Lorene::Scalar::div_r_dzpuis(), Lorene::Scalar::div_tant(), 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::Tensor::set(), Lorene::Itbl::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 864 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 876 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 736 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 801 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 748 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 1186 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 666 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 925 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 693 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 909 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 889 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_delta

Tensor* Lorene::Spheroid::p_delta
mutableprotectedinherited

Definition at line 168 of file spheroid.h.

◆ p_epsilon_A_minus_one

double* Lorene::Spheroid::p_epsilon_A_minus_one
mutableprotectedinherited

Definition at line 163 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.

◆ qab

Metric Lorene::Spheroid::qab
protectedinherited

Definition at line 115 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.

◆ zeta

Scalar Lorene::Spheroid::zeta
protectedinherited

Definition at line 147 of file spheroid.h.

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