Lorene::AltBH_QI Class Reference
[Stationary compact objects (under development)]

Alternative black hole spacetime in Quasi-Isotropic coordinates (***under development***). More...

#include <compobj.h>

Inheritance diagram for Lorene::AltBH_QI:
Lorene::Compobj_QI Lorene::Compobj

List of all members.

Public Member Functions

 AltBH_QI (Map &mp_i, const char *file_name, double a_spin_i)
 Standard constructor.
 AltBH_QI (const AltBH_QI &)
 Copy constructor.
 AltBH_QI (Map &mp_i, FILE *fich)
 Constructor from a file (see sauve(FILE*) ).
virtual ~AltBH_QI ()
 Destructor.
void operator= (const AltBH_QI &)
 Assignment to another AltBH_QI.
const Scalarget_krphi () const
 Returns K_{(r)(phi)}/sin(theta).
virtual void sauve (FILE *) const
 Save in a file.
virtual void extrinsic_curvature ()
 Computation of the extrinsic curvature.
const Scalarget_bbb () const
 Returns the metric factor B.
const Scalarget_a_car () const
 Returns the square of the metric factor A.
const Scalarget_b_car () const
 Returns the square of the metric factor B.
const Scalarget_nphi () const
 Returns the metric coefficient $N^\varphi$.
const Scalarget_ak_car () const
 Returns the scalar $A^2 K_{ij} K^{ij}$.
void gyoto_data (const char *file_name) const
 Save in a file for GYOTO.
virtual double angu_mom () const
 Angular momentum.
virtual double r_isco (int lmin, ostream *ost=0x0) const
 Coordinate r of the innermost stable circular orbit (ISCO).
virtual double f_isco (int lmin) const
 Orbital frequency at the innermost stable circular orbit (ISCO).
virtual double espec_isco (int lmin) const
 Energy of a particle at the ISCO.
virtual double lspec_isco (int lmin) const
 Angular momentum of a particle at the ISCO.
virtual double r_mb (int lmin, ostream *ost=0x0) const
 Coordinate r of the marginally bound circular orbit (R_mb).
virtual void update_metric ()
 Updates the 3-metric $\gamma_{ij}$ from A and B and the shift vector $\beta^i$ from $N^\phi$.
Mapset_mp ()
 Read/write of the mapping.
const Mapget_mp () const
 Returns the mapping.
const Scalarget_nn () const
 Returns the lapse function N .
const Vectorget_beta () const
 Returns the shift vector $\beta^i$.
const Metricget_gamma () const
 Returns the 3-metric $\gamma_{ij}$.
const Scalarget_ener_euler () const
 Returns the total energy density E in the Eulerian frame.
const Vectorget_mom_euler () const
 Returns the total 3-momentum density $P^i$ in the Eulerian frame.
const Sym_tensorget_stress_euler () const
 Returns the stress tensor $S_{ij}$ with respect to the Eulerian observer.
const Sym_tensorget_kk () const
 Returns the extrinsic curvature tensor $K_{ij}$.
virtual double adm_mass () const
 ADM mass (computed as a surface integral at spatial infinity).

Protected Member Functions

virtual void del_deriv () const
 Deletes all the derived quantities.
virtual void set_der_0x0 () const
 Sets to 0x0 all the pointers on derived quantities.
virtual ostream & operator>> (ostream &) const
 Operator >> (virtual function called by the operator <<).

Protected Attributes

char description1 [256]
 String describing the model.
char description2 [256]
 String describing the model.
double a_spin
 Spin parameter of the model.
Scalar krphi
 K_{(r)(phi)} read in the file.
Scalar a_car
 Square of the metric factor A.
Scalar bbb
 Metric factor B.
Scalar b_car
 Square of the metric factor B.
Scalar nphi
 Metric coefficient $N^\varphi$.
Scalar ak_car
 Scalar $A^2 K_{ij} K^{ij}$.
double * p_angu_mom
 Angular momentum.
double * p_r_isco
 Coordinate r of the ISCO.
double * p_f_isco
 Orbital frequency of the ISCO.
double * p_espec_isco
 Specific energy of a particle at the ISCO.
double * p_lspec_isco
 Specific angular momentum of a particle at the ISCO.
double * p_r_mb
 Coordinate r of the marginally bound orbit.
Mapmp
 Mapping describing the coordinate system (r,theta,phi).
Scalar nn
 Lapse function N .
Vector beta
 Shift vector $\beta^i$.
Metric gamma
 3-metric $\gamma_{ij}$
Scalar ener_euler
 Total energy density E in the Eulerian frame.
Vector mom_euler
 Total 3-momentum density $P^i$ in the Eulerian frame.
Sym_tensor stress_euler
 Stress tensor $S_{ij}$ with respect to the Eulerian observer.
Sym_tensor kk
 Extrinsic curvature tensor $K_{ij}$.
double * p_adm_mass
 ADM mass.

Friends

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

Detailed Description

Alternative black hole spacetime in Quasi-Isotropic coordinates (***under development***).

()

The metric is expressed in Quasi-Isotropic (QI) coordinates :

\[ ds^2 = - N^2 dt^2 + A^2 (dr^2 + r^2 d\theta^2) + B^2 r^2 \sin^2\theta (d\varphi - N^\varphi dt)^2 \]

Definition at line 920 of file compobj.h.


Constructor & Destructor Documentation

Lorene::AltBH_QI::AltBH_QI ( Map mp_i,
const char *  file_name,
double  a_spin_i 
)
Lorene::AltBH_QI::AltBH_QI ( const AltBH_QI other  ) 

Copy constructor.

Definition at line 172 of file altBH_QI.C.

References set_der_0x0().

Lorene::AltBH_QI::AltBH_QI ( Map mp_i,
FILE *  fich 
)

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

Parameters:
mp_i Mapping on which the star is constructed
fich input file (must have been created by the function AltBH_QI::sauve )

Definition at line 183 of file altBH_QI.C.

References set_der_0x0().

Lorene::AltBH_QI::~AltBH_QI (  )  [virtual]

Destructor.

Definition at line 199 of file altBH_QI.C.

References del_deriv().


Member Function Documentation

double Lorene::Compobj::adm_mass (  )  const [virtual, inherited]
double Lorene::Compobj_QI::angu_mom (  )  const [virtual, inherited]

Angular momentum.

Reimplemented in Lorene::Star_QI.

Definition at line 93 of file compobj_QI_global.C.

References Lorene::Compobj_QI::p_angu_mom.

void Lorene::AltBH_QI::del_deriv (  )  const [protected, virtual]

Deletes all the derived quantities.

Reimplemented from Lorene::Compobj_QI.

Definition at line 210 of file altBH_QI.C.

References set_der_0x0().

double Lorene::Compobj_QI::espec_isco ( int  lmin  )  const [virtual, inherited]

Energy of a particle at the ISCO.

Definition at line 323 of file compobj_QI_global.C.

References Lorene::Compobj_QI::p_espec_isco, and Lorene::Compobj_QI::r_isco().

void Lorene::AltBH_QI::extrinsic_curvature (  )  [virtual]
double Lorene::Compobj_QI::f_isco ( int  lmin  )  const [virtual, inherited]

Orbital frequency at the innermost stable circular orbit (ISCO).

Definition at line 289 of file compobj_QI_global.C.

References Lorene::Compobj_QI::p_f_isco, and Lorene::Compobj_QI::r_isco().

const Scalar& Lorene::Compobj_QI::get_a_car (  )  const [inline, inherited]

Returns the square of the metric factor A.

Definition at line 381 of file compobj.h.

References Lorene::Compobj_QI::a_car.

const Scalar& Lorene::Compobj_QI::get_ak_car (  )  const [inline, inherited]

Returns the scalar $A^2 K_{ij} K^{ij}$.

For axisymmetric stars, this quantity is related to the derivatives of $N^\varphi$ by

\[ A^2 K_{ij} K^{ij} = {B^2 \over 2 N^2} \, r^2\sin^2\theta \, \left[ \left( {\partial N^\varphi \over \partial r} \right) ^2 + {1\over r^2} \left( {\partial N^\varphi \over \partial \theta} \right) ^2 \right] \ . \]

In particular it is related to the quantities $k_1$ and $k_2$ introduced by Eqs. (3.7) and (3.8) of Bonazzola et al. Astron. Astrophys. 278 , 421 (1993) by

\[ A^2 K_{ij} K^{ij} = 2 A^2 (k_1^2 + k_2^2) \ . \]

Definition at line 407 of file compobj.h.

References Lorene::Compobj_QI::ak_car.

const Scalar& Lorene::Compobj_QI::get_b_car (  )  const [inline, inherited]

Returns the square of the metric factor B.

Definition at line 384 of file compobj.h.

References Lorene::Compobj_QI::b_car.

const Scalar& Lorene::Compobj_QI::get_bbb (  )  const [inline, inherited]

Returns the metric factor B.

Definition at line 378 of file compobj.h.

References Lorene::Compobj_QI::bbb.

const Vector& Lorene::Compobj::get_beta (  )  const [inline, inherited]

Returns the shift vector $\beta^i$.

Definition at line 216 of file compobj.h.

References Lorene::Compobj::beta.

const Scalar& Lorene::Compobj::get_ener_euler (  )  const [inline, inherited]

Returns the total energy density E in the Eulerian frame.

Definition at line 222 of file compobj.h.

References Lorene::Compobj::ener_euler.

const Metric& Lorene::Compobj::get_gamma (  )  const [inline, inherited]

Returns the 3-metric $\gamma_{ij}$.

Definition at line 219 of file compobj.h.

References Lorene::Compobj::gamma.

const Sym_tensor& Lorene::Compobj::get_kk (  )  const [inline, inherited]

Returns the extrinsic curvature tensor $K_{ij}$.

Definition at line 231 of file compobj.h.

References Lorene::Compobj::kk.

const Scalar& Lorene::AltBH_QI::get_krphi (  )  const [inline]

Returns K_{(r)(phi)}/sin(theta).

Definition at line 982 of file compobj.h.

References krphi.

const Vector& Lorene::Compobj::get_mom_euler (  )  const [inline, inherited]

Returns the total 3-momentum density $P^i$ in the Eulerian frame.

Definition at line 225 of file compobj.h.

References Lorene::Compobj::mom_euler.

const Map& Lorene::Compobj::get_mp (  )  const [inline, inherited]

Returns the mapping.

Definition at line 210 of file compobj.h.

References Lorene::Compobj::mp.

const Scalar& Lorene::Compobj::get_nn (  )  const [inline, inherited]

Returns the lapse function N .

Definition at line 213 of file compobj.h.

References Lorene::Compobj::nn.

const Scalar& Lorene::Compobj_QI::get_nphi (  )  const [inline, inherited]

Returns the metric coefficient $N^\varphi$.

Definition at line 387 of file compobj.h.

References Lorene::Compobj_QI::nphi.

const Sym_tensor& Lorene::Compobj::get_stress_euler (  )  const [inline, inherited]

Returns the stress tensor $S_{ij}$ with respect to the Eulerian observer.

Definition at line 228 of file compobj.h.

References Lorene::Compobj::stress_euler.

void Lorene::Compobj_QI::gyoto_data ( const char *  file_name  )  const [inherited]
double Lorene::Compobj_QI::lspec_isco ( int  lmin  )  const [virtual, inherited]

Angular momentum of a particle at the ISCO.

Definition at line 306 of file compobj_QI_global.C.

References Lorene::Compobj_QI::p_lspec_isco, and Lorene::Compobj_QI::r_isco().

void Lorene::AltBH_QI::operator= ( const AltBH_QI other  ) 

Assignment to another AltBH_QI.

Reimplemented from Lorene::Compobj_QI.

Definition at line 229 of file altBH_QI.C.

References del_deriv().

ostream & Lorene::AltBH_QI::operator>> ( ostream &  ost  )  const [protected, virtual]

Operator >> (virtual function called by the operator <<).

Reimplemented from Lorene::Compobj_QI.

Definition at line 251 of file altBH_QI.C.

References description1, and description2.

double Lorene::Compobj_QI::r_isco ( int  lmin,
ostream *  ost = 0x0 
) const [virtual, inherited]

Coordinate r of the innermost stable circular orbit (ISCO).

Parameters:
lmin index of the innermost domain in which the ISCO is searched: the ISCO is searched inwards from the last but one domain to the domain of index lmin.
ost output stream to give details of the computation; if set to 0x0 [default value], no details will be given.

Definition at line 111 of file compobj_QI_global.C.

References Lorene::Param::add_int(), Lorene::Param::add_scalar(), Lorene::Tensor::annule_domain(), Lorene::Compobj_QI::bbb, Lorene::Scalar::dsdr(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Scalar::get_spectral_va(), Lorene::Compobj::mp, Lorene::Compobj::nn, Lorene::Compobj_QI::nphi, Lorene::Compobj_QI::p_espec_isco, Lorene::Compobj_QI::p_f_isco, Lorene::Compobj_QI::p_lspec_isco, Lorene::Compobj_QI::p_r_isco, Lorene::Map::r, Lorene::sqrt(), Lorene::Scalar::std_spectral_base(), Lorene::Valeur::val_point(), Lorene::Map::val_r(), and Lorene::zerosec().

double Lorene::Compobj_QI::r_mb ( int  lmin,
ostream *  ost = 0x0 
) const [virtual, inherited]
void Lorene::AltBH_QI::sauve ( FILE *   )  const [virtual]

Save in a file.

Reimplemented from Lorene::Compobj_QI.

Definition at line 243 of file altBH_QI.C.

void Lorene::AltBH_QI::set_der_0x0 (  )  const [protected, virtual]

Sets to 0x0 all the pointers on derived quantities.

Reimplemented from Lorene::Compobj_QI.

Definition at line 219 of file altBH_QI.C.

Map& Lorene::Compobj::set_mp (  )  [inline, inherited]

Read/write of the mapping.

Definition at line 203 of file compobj.h.

References Lorene::Compobj::mp.

void Lorene::Compobj_QI::update_metric (  )  [virtual, inherited]

Friends And Related Function Documentation

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

Display.


Member Data Documentation

Scalar Lorene::Compobj_QI::a_car [protected, inherited]

Square of the metric factor A.

Definition at line 290 of file compobj.h.

double Lorene::AltBH_QI::a_spin [protected]

Spin parameter of the model.

Definition at line 928 of file compobj.h.

Scalar Lorene::Compobj_QI::ak_car [protected, inherited]

Scalar $A^2 K_{ij} K^{ij}$.

For axisymmetric stars, this quantity is related to the derivatives of $N^\varphi$ by

\[ A^2 K_{ij} K^{ij} = {B^2 \over 2 N^2} \, r^2\sin^2\theta \, \left[ \left( {\partial N^\varphi \over \partial r} \right) ^2 + {1\over r^2} \left( {\partial N^\varphi \over \partial \theta} \right) ^2 \right] \ . \]

In particular it is related to the quantities $k_1$ and $k_2$ introduced by Eqs.~(3.7) and (3.8) of Bonazzola et al. Astron. Astrophys. 278 , 421 (1993) by

\[ A^2 K_{ij} K^{ij} = 2 A^2 (k_1^2 + k_2^2) \ . \]

Definition at line 318 of file compobj.h.

Scalar Lorene::Compobj_QI::b_car [protected, inherited]

Square of the metric factor B.

Definition at line 296 of file compobj.h.

Scalar Lorene::Compobj_QI::bbb [protected, inherited]

Metric factor B.

Definition at line 293 of file compobj.h.

Vector Lorene::Compobj::beta [protected, inherited]

Shift vector $\beta^i$.

Definition at line 141 of file compobj.h.

char Lorene::AltBH_QI::description1[256] [protected]

String describing the model.

Definition at line 926 of file compobj.h.

char Lorene::AltBH_QI::description2[256] [protected]

String describing the model.

Definition at line 927 of file compobj.h.

Scalar Lorene::Compobj::ener_euler [protected, inherited]

Total energy density E in the Eulerian frame.

Definition at line 147 of file compobj.h.

Metric Lorene::Compobj::gamma [protected, inherited]

3-metric $\gamma_{ij}$

Definition at line 144 of file compobj.h.

Sym_tensor Lorene::Compobj::kk [protected, inherited]

Extrinsic curvature tensor $K_{ij}$.

Definition at line 156 of file compobj.h.

K_{(r)(phi)} read in the file.

Definition at line 930 of file compobj.h.

Vector Lorene::Compobj::mom_euler [protected, inherited]

Total 3-momentum density $P^i$ in the Eulerian frame.

Definition at line 150 of file compobj.h.

Map& Lorene::Compobj::mp [protected, inherited]

Mapping describing the coordinate system (r,theta,phi).

Definition at line 135 of file compobj.h.

Scalar Lorene::Compobj::nn [protected, inherited]

Lapse function N .

Definition at line 138 of file compobj.h.

Scalar Lorene::Compobj_QI::nphi [protected, inherited]

Metric coefficient $N^\varphi$.

Definition at line 299 of file compobj.h.

double* Lorene::Compobj::p_adm_mass [mutable, protected, inherited]

ADM mass.

Definition at line 161 of file compobj.h.

double* Lorene::Compobj_QI::p_angu_mom [mutable, protected, inherited]

Angular momentum.

Definition at line 324 of file compobj.h.

double* Lorene::Compobj_QI::p_espec_isco [mutable, protected, inherited]

Specific energy of a particle at the ISCO.

Definition at line 328 of file compobj.h.

double* Lorene::Compobj_QI::p_f_isco [mutable, protected, inherited]

Orbital frequency of the ISCO.

Definition at line 326 of file compobj.h.

double* Lorene::Compobj_QI::p_lspec_isco [mutable, protected, inherited]

Specific angular momentum of a particle at the ISCO.

Definition at line 330 of file compobj.h.

double* Lorene::Compobj_QI::p_r_isco [mutable, protected, inherited]

Coordinate r of the ISCO.

Definition at line 325 of file compobj.h.

double* Lorene::Compobj_QI::p_r_mb [mutable, protected, inherited]

Coordinate r of the marginally bound orbit.

Definition at line 331 of file compobj.h.

Sym_tensor Lorene::Compobj::stress_euler [protected, inherited]

Stress tensor $S_{ij}$ with respect to the Eulerian observer.

Definition at line 153 of file compobj.h.


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

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