163 mutable double* p_epsilon_A_minus_one ;
323 double area()
const ;
391 virtual void sauve(FILE *)
const ;
398ostream& operator<<(ostream& ,
const Spheroid& ) ;
436 bool check_expansion(
double thres = 1.e-7)
const ;
Class describing an apparent horizon.
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.
const Scalar & l_non_affinity(const Scalar &bb, const Scalar &lapse)
non-affinity (or surface gravity) with respect to the outgoing null vector field
App_hor(const Mg3d &grid_angu, double radius)
Standard constructor.
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.
void operator=(const App_hor &)
Assignment to another App_hor.
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 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.
App_hor(const App_hor &)
Copy constructor.
const Sym_tensor & lie_derive_shear(const Scalar &bb, const Scalar &lapse)
Lie derivative of shear tensor with respect to the evolution vector field.
virtual ~App_hor()
Destructor.
App_hor(FILE *)
Constructor from a file (see sauve(FILE*) )
Metric for tensor calculation.
Tensor field of valence 0 (or component of a tensorial field).
Spheroidal 2-surfaces embedded in a time-slice of the 3+1 formalism.
Sym_tensor & set_hh()
Sets the symmetric tensor .
Tensor derive_cov2dflat(const Tensor &uu) const
Computes the round covariant derivative on the spheroid.
virtual ~Spheroid()
Destructor.
const Scalar & sqrt_q() const
Computes the normal vector field to the 2-surface.
Tensor proj
The 3-d projector on the 2-surface (contravariant-covariant form).
Metric & set_qab()
Sets the modified metric (non degenerated) .
Sym_tensor qq
The 3-d covariant degenerated 2-metric on the surface.
const Scalar & theta_minus() const
Computes the ingoing null expansion .
const Tensor & get_proj() const
returns the 3-d projector on 2-surface
const Scalar & get_ggg() const
Returns the normalization scalar G.
virtual void sauve(FILE *) const
Save in a file.
const Metric & get_qab() const
Returns the metric .
Vector & set_ll()
Sets the vector .
Vector ll
Normal-tangent component of the extrinsic curvature of the 3-slice.
Scalar & set_ggg()
Sets the normalization factor G.
double * p_multipole_angu
Angular momentum multipole for the spheroid.
const Tensor & get_jac2d() const
returns the 2-d jacobian of coordinate transformation
double * p_mass
Mass defined from angular momentum.
Scalar trk
Trace K of the extrinsic curvature of the 3-slice.
Scalar * p_theta_plus
Classical Penrose parameter, difference wrt one.
Scalar ggg
Normalization function for the ingoing null vector k.
void operator=(const Spheroid &)
Assignment to another Spheroid.
Scalar & set_hsurf()
Sets the field h_surf.
double epsilon_A_minus_one() const
Computation of the refined Penrose parameter for axisymmetric spacetimes, and its difference wrt one.
void set_der_0x0() const
Sets to 0x0 all the pointers on derived quantities.
Scalar & set_fff()
Sets the normalization factor F.
const Tensor & delta() const
Computes the delta coefficients for covariant derivative.
double multipole_angu(const int order) const
Computes the angular multipole of a given order for the spheroid, assumed to be spherical.
bool issphere
Flag to know whether the horizon is geometrically round or distorted.
Tensor jac2d
The jacobian of the adaptation of coordinates (contravariant/covariant representation)
const Vector & get_ll() const
Returns the vector .
Scalar & set_trk()
Sets the trace K on the 2-surface.
friend ostream & operator<<(ostream &, const Spheroid &)
Display.
double mass() const
Computes the mass as defined from the calculus of angular momentum, done with respect to a divergence...
Sym_tensor jj
Tangent components of the extrinsic curvature of the 3-slice.
double * p_area
The area of the 2-surface.
const Scalar & get_fff() const
Returns the normalization scalar F.
Scalar fff
Normalization function for the outgoing null vector l.
double area() const
Computes the area of the 2-surface.
Sym_tensor & set_qq()
Sets the degenerated metric .
double multipole_mass(const int order) const
Computes the mass multipole of a given order for the spheroid, assumed to be spherical.
const Sym_tensor & get_jj() const
Returns the symmetric tensor .
Scalar h_surf
The location of the 2-surface as r = h_surf .
Vector & set_ss()
Sets the vector .
Sym_tensor hh
The ricci scalar on the 2-surface.
const Scalar & get_trk() const
Returns the trace K on the 2-surface.
double * p_epsilon_P_minus_one
Refined Penrose parameter, difference wrt one.
const Vector & get_ss() const
Returns the vector .
Spheroid(FILE *)
Constructor from a file (see sauve(FILE*) )
Scalar * p_sqrt_q
Surface element .
Vector ss
The adapted normal vector field to spheroid in the 3-slice.
const Scalar & get_hsurf() const
Returns the field h_surf.
Scalar & set_ricci()
Sets the 2-Ricci scalar .
const Sym_tensor & get_hh() const
Returns the symmetric tensor .
void update_from_tslice(const Metric &gamij, const Sym_tensor &Kij)
Updates from the 3-slice data.
virtual void del_deriv() const
Deletes all the derived quantities.
const Scalar & get_ricci() const
Returns the 2-ricci scalar .
Tensor & set_proj()
Sets the projector .
const Sym_tensor & shear() const
Computes the shear of the 2-surface .
Scalar * p_theta_minus
Null ingoing expansion.
double angu_mom() const
Computes the angular momentum with respect to a divergence-free vector field tangent to the 2-surface...
Sym_tensor & set_jj()
Sets the symmetric tensor .
const Sym_tensor & get_qq() const
returns the 3-d degenerate 2-metric
Vector ephi
The conformal Killing vector field on the 2-surface (set to by default to the axial vector associated...
const Vector & get_ephi() const
Returns the conformal Killing symmetry vector on the 2-surface.
double * p_multipole_mass
Mass multipole for the spheroid.
void set_ephi(const Scalar &)
Assigns the conformal Killing vector field to phi.
double * p_angu_mom
The angular momentum.
Tensor derive_cov2d(const Tensor &uu) const
Computes the total covariant derivative on the spheroid.
Scalar ricci
Induced metric on the 2-surface .
bool get_issphere() const
Returns the flag saying whether or not the horizon is geometrically round.
Sym_tensor * p_shear
The shear tensor.
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 .
bool set_issphere()
Sets the boolean linked to geometrical shape of the horizon.
Class intended to describe valence-2 symmetric tensors.
Tensor field of valence 1.