App_hor Class Reference

Class describing an apparent horizon. More...

#include <spheroid.h>

Inheritance diagram for App_hor:
Spheroid

List of all members.

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

Friends

ostream & operator<< (ostream &, const Spheroid &)
 Display.

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 404 of file spheroid.h.

Constructor & Destructor Documentation

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

Standard constructor.

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::App_hor ( const App_hor &   ) 

Copy constructor.

App_hor::App_hor ( FILE *   ) 

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

virtual App_hor::~App_hor (  )  [virtual]

Destructor.

Member Function Documentation

double 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 717 of file spheroid.C.

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

double 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 704 of file spheroid.C.

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

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

Deletes all the derived quantities.

Definition at line 646 of file spheroid.C.

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

const Tensor & Spheroid::delta (  )  const [inherited]

Computes the delta coefficients for covariant derivative.

Definition at line 1199 of file spheroid.C.

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

Tensor Spheroid::derive_cov2d ( const Tensor &  uu  )  const [inherited]

Computes the total covariant derivative on the spheroid.

Definition at line 1236 of file spheroid.C.

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

Tensor Spheroid::derive_cov2dflat ( const Tensor &  uu  )  const [inherited]

Computes the round covariant derivative on the spheroid.

Definition at line 950 of file spheroid.C.

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

double Spheroid::epsilon_A_minus_one (  )  const [inherited]

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

Definition at line 860 of file spheroid.C.

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

double 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 872 of file spheroid.C.

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

const Vector& Spheroid::get_ephi (  )  const [inline, inherited]

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

Definition at line 249 of file spheroid.h.

References Spheroid::ephi.

const Scalar& Spheroid::get_fff (  )  const [inline, inherited]

Returns the normalization scalar F.

Definition at line 255 of file spheroid.h.

References Spheroid::fff.

const Scalar& Spheroid::get_ggg (  )  const [inline, inherited]

Returns the normalization scalar G.

Definition at line 258 of file spheroid.h.

References Spheroid::ggg.

const Sym_tensor& Spheroid::get_hh (  )  const [inline, inherited]

Returns the symmetric tensor $ H_{ab} $.

Definition at line 228 of file spheroid.h.

References Spheroid::hh.

const Scalar& Spheroid::get_hsurf (  )  const [inline, inherited]

Returns the field h_surf.

Definition at line 219 of file spheroid.h.

References Spheroid::h_surf.

bool Spheroid::get_issphere (  )  const [inline, inherited]

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

Definition at line 261 of file spheroid.h.

References Spheroid::issphere.

const Tensor& Spheroid::get_jac2d (  )  const [inline, inherited]

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

Definition at line 237 of file spheroid.h.

References Spheroid::jac2d.

const Sym_tensor& Spheroid::get_jj (  )  const [inline, inherited]

Returns the symmetric tensor $ J_{ab} $.

Definition at line 252 of file spheroid.h.

References Spheroid::jj.

const Vector& Spheroid::get_ll (  )  const [inline, inherited]

Returns the vector $ L_a $.

Definition at line 243 of file spheroid.h.

References Spheroid::ll.

const Tensor& Spheroid::get_proj (  )  const [inline, inherited]

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

Definition at line 234 of file spheroid.h.

References Spheroid::proj.

const Metric& Spheroid::get_qab (  )  const [inline, inherited]

Returns the metric $ q_{ab} $.

Definition at line 222 of file spheroid.h.

const Sym_tensor& Spheroid::get_qq (  )  const [inline, inherited]

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

Definition at line 231 of file spheroid.h.

References Spheroid::qq.

const Scalar& Spheroid::get_ricci (  )  const [inline, inherited]

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

Definition at line 225 of file spheroid.h.

References Spheroid::ricci.

const Vector& Spheroid::get_ss (  )  const [inline, inherited]

Returns the vector $ S_a $.

Definition at line 246 of file spheroid.h.

References Spheroid::ss.

const Scalar& Spheroid::get_trk (  )  const [inline, inherited]

Returns the trace K on the 2-surface.

Definition at line 240 of file spheroid.h.

References Spheroid::trk.

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

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

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

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

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

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

const Sym_tensor& 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.

const Sym_tensor& 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.

double 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 732 of file spheroid.C.

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

double 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 797 of file spheroid.C.

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

double 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 744 of file spheroid.C.

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

void App_hor::operator= ( const App_hor &   ) 

Assignment to another App_hor.

Reimplemented from Spheroid.

void Spheroid::sauve ( FILE *   )  const [virtual, inherited]

Save in a file.

Definition at line 1182 of file spheroid.C.

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

Sets to 0x0 all the pointers on derived quantities.

Definition at line 662 of file spheroid.C.

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

void Spheroid::set_ephi ( const Scalar &   )  [inherited]

Assigns the conformal Killing vector field to phi.

Scalar& Spheroid::set_fff (  )  [inline, inherited]

Sets the normalization factor F.

Definition at line 294 of file spheroid.h.

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

Scalar& Spheroid::set_ggg (  )  [inline, inherited]

Sets the normalization factor G.

Definition at line 297 of file spheroid.h.

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

Sym_tensor& Spheroid::set_hh (  )  [inline, inherited]

Sets the symmetric tensor $ H_{ab} $.

Definition at line 279 of file spheroid.h.

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

Scalar& Spheroid::set_hsurf (  )  [inline, inherited]

Sets the field h_surf.

Definition at line 264 of file spheroid.h.

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

bool Spheroid::set_issphere (  )  [inline, inherited]

Sets the boolean linked to geometrical shape of the horizon.

Definition at line 300 of file spheroid.h.

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

Sym_tensor& Spheroid::set_jj (  )  [inline, inherited]

Sets the symmetric tensor $ J_{ab} $.

Definition at line 291 of file spheroid.h.

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

Vector& Spheroid::set_ll (  )  [inline, inherited]

Sets the vector $ L_a $.

Definition at line 285 of file spheroid.h.

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

Tensor& Spheroid::set_proj (  )  [inline, inherited]

Sets the projector $ Pi $.

Definition at line 276 of file spheroid.h.

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

Metric& Spheroid::set_qab (  )  [inline, inherited]

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

Definition at line 267 of file spheroid.h.

References Spheroid::del_deriv().

Sym_tensor& Spheroid::set_qq (  )  [inline, inherited]

Sets the degenerated metric $ Q_{ab} $.

Definition at line 273 of file spheroid.h.

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

Scalar& Spheroid::set_ricci (  )  [inline, inherited]

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

Definition at line 270 of file spheroid.h.

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

Vector& Spheroid::set_ss (  )  [inline, inherited]

Sets the vector $ s_a $.

Definition at line 288 of file spheroid.h.

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

Scalar& Spheroid::set_trk (  )  [inline, inherited]

Sets the trace K on the 2-surface.

Definition at line 282 of file spheroid.h.

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

const Sym_tensor & Spheroid::shear (  )  const [inherited]

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

Definition at line 921 of file spheroid.C.

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

const Scalar & 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 689 of file spheroid.C.

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

const Scalar & Spheroid::theta_minus (  )  const [inherited]

Computes the ingoing null expansion $ \theta_- $.

Definition at line 905 of file spheroid.C.

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

const Scalar & Spheroid::theta_plus (  )  const [inherited]

Computes the outgoing null expansion $ \theta_+ $.

Definition at line 885 of file spheroid.C.

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

void Spheroid::update_from_tslice ( const Metric &  gamij,
const Sym_tensor &  Kij 
) [inherited]

Updates from the 3-slice data.

Friends And Related Function Documentation

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

Display.

Member Data Documentation

Vector Spheroid::ephi [protected, inherited]

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

Definition at line 109 of file spheroid.h.

Scalar Spheroid::fff [protected, inherited]

Normalization function for the outgoing null vector l.

Definition at line 134 of file spheroid.h.

Scalar Spheroid::ggg [protected, inherited]

Normalization function for the ingoing null vector k.

Definition at line 139 of file spheroid.h.

Scalar Spheroid::h_surf [protected, inherited]

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

Definition at line 87 of file spheroid.h.

Sym_tensor Spheroid::hh [protected, inherited]

The ricci scalar on the 2-surface.

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

Definition at line 118 of file spheroid.h.

bool Spheroid::issphere [protected, inherited]

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

Definition at line 147 of file spheroid.h.

Tensor Spheroid::jac2d [protected, inherited]

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

Definition at line 92 of file spheroid.h.

Sym_tensor Spheroid::jj [protected, inherited]

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

$ J_{ab} $ (covariant representation)

Definition at line 130 of file spheroid.h.

Vector Spheroid::ll [protected, inherited]

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

$ L_a $ (covariant representation)

Definition at line 125 of file spheroid.h.

double* Spheroid::p_angu_mom [mutable, protected, inherited]

The angular momentum.

Definition at line 155 of file spheroid.h.

double* Spheroid::p_area [mutable, protected, inherited]

The area of the 2-surface.

Definition at line 154 of file spheroid.h.

double* Spheroid::p_epsilon_P_minus_one [mutable, protected, inherited]

Refined Penrose parameter, difference wrt one.

Definition at line 160 of file spheroid.h.

double* Spheroid::p_mass [mutable, protected, inherited]

Mass defined from angular momentum.

Definition at line 156 of file spheroid.h.

double* Spheroid::p_multipole_angu [mutable, protected, inherited]

Angular momentum multipole for the spheroid.

Definition at line 158 of file spheroid.h.

double* Spheroid::p_multipole_mass [mutable, protected, inherited]

Mass multipole for the spheroid.

Definition at line 157 of file spheroid.h.

Sym_tensor* Spheroid::p_shear [mutable, protected, inherited]

The shear tensor.

Definition at line 163 of file spheroid.h.

Scalar* Spheroid::p_sqrt_q [mutable, protected, inherited]

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

Definition at line 153 of file spheroid.h.

Scalar* Spheroid::p_theta_minus [mutable, protected, inherited]

Null ingoing expansion.

Definition at line 162 of file spheroid.h.

Scalar* Spheroid::p_theta_plus [mutable, protected, inherited]

Classical Penrose parameter, difference wrt one.

Null outgoing expansion

Definition at line 161 of file spheroid.h.

Tensor Spheroid::proj [protected, inherited]

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

Definition at line 96 of file spheroid.h.

Sym_tensor Spheroid::qq [protected, inherited]

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

Definition at line 100 of file spheroid.h.

Scalar Spheroid::ricci [protected, inherited]

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

Definition at line 113 of file spheroid.h.

Vector Spheroid::ss [protected, inherited]

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

Definition at line 104 of file spheroid.h.

Scalar Spheroid::trk [protected, inherited]

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

Definition at line 120 of file spheroid.h.

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