LORENE
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Base class for axisymmetric stationary compact stars in Quasi-Isotropic coordinates (under development). More...
#include <compobj.h>
Public Member Functions | |
Star_QI (Map &mp_i) | |
Standard constructor. | |
Star_QI (const Star_QI &) | |
Copy constructor. | |
Star_QI (Map &mp_i, FILE *fich) | |
Constructor from a file (see sauve(FILE*) ). | |
virtual | ~Star_QI () |
Destructor. | |
void | operator= (const Star_QI &) |
Assignment to another Star_QI . | |
const Scalar & | get_logn () const |
Returns the logarithm of the lapse N. | |
const Scalar & | get_tnphi () const |
Returns the component ![]() | |
const Scalar & | get_nuf () const |
Returns the part of the Metric potential ![]() logn generated by the matter terms. | |
const Scalar & | get_nuq () const |
Returns the Part of the Metric potential ![]() logn generated by the quadratic terms. | |
const Scalar & | get_dzeta () const |
Returns the Metric potential ![]() | |
const Scalar & | get_tggg () const |
Returns the Metric potential ![]() | |
const Vector & | get_w_shift () const |
Returns the vector ![]() shift , following Shibata's prescription [Prog. | |
const Scalar & | get_khi_shift () const |
Returns the scalar ![]() shift following Shibata's prescription [Prog. | |
virtual void | sauve (FILE *) const |
Save in a file. | |
virtual double | mass_g () const |
Gravitational mass. | |
virtual double | angu_mom () const |
Angular momentum. | |
virtual double | grv2 () const |
Error on the virial identity GRV2. | |
virtual double | grv3 (ostream *ost=0x0) const |
Error on the virial identity GRV3. | |
virtual double | mom_quad () const |
Quadrupole moment. | |
void | update_metric () |
Computes metric coefficients from known potentials. | |
void | fait_shift () |
Computes shift from w_shift and khi_shift according to Shibata's prescription [Prog. | |
void | fait_nphi () |
Computes tnphi and nphi from the Cartesian components of the shift, stored in shift . | |
const Scalar & | get_bbb () const |
Returns the metric factor B. | |
const Scalar & | get_a_car () const |
Returns the square of the metric factor A. | |
const Scalar & | get_b_car () const |
Returns the square of the metric factor B. | |
const Scalar & | get_nphi () const |
Returns the metric coefficient ![]() | |
const Scalar & | get_ak_car () const |
Returns the scalar ![]() | |
void | gyoto_data (const char *file_name) const |
Save in a file for GYOTO. | |
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 | extrinsic_curvature () |
Computes the extrinsic curvature and ak_car from nphi , nn and b_car . | |
Map & | set_mp () |
Read/write of the mapping. | |
const Map & | get_mp () const |
Returns the mapping. | |
const Scalar & | get_nn () const |
Returns the lapse function N . | |
const Vector & | get_beta () const |
Returns the shift vector ![]() | |
const Metric & | get_gamma () const |
Returns the 3-metric ![]() | |
const Scalar & | get_ener_euler () const |
Returns the total energy density E in the Eulerian frame. | |
const Vector & | get_mom_euler () const |
Returns the total 3-momentum density ![]() | |
const Sym_tensor & | get_stress_euler () const |
Returns the stress tensor ![]() | |
const Sym_tensor & | get_kk () const |
Returns the extrinsic curvature tensor ![]() | |
virtual double | adm_mass () const |
ADM mass (computed as a surface integral at spatial infinity) | |
Static Public Member Functions | |
static double | lambda_grv2 (const Scalar &sou_m, const Scalar &sou_q) |
Computes the coefficient ![]() | |
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 | |
Scalar | logn |
Logarithm of the lapse N . | |
Scalar | tnphi |
Component ![]() | |
Scalar | nuf |
Part of the Metric potential ![]() logn generated by the matter terms. | |
Scalar | nuq |
Part of the Metric potential ![]() logn generated by the quadratic terms. | |
Scalar | dzeta |
Metric potential ![]() | |
Scalar | tggg |
Metric potential ![]() | |
Vector | w_shift |
Vector ![]() shift , following Shibata's prescription [Prog. | |
Scalar | khi_shift |
Scalar ![]() shift , following Shibata's prescription [Prog. | |
Scalar | ssjm1_nuf |
Effective source at the previous step for the resolution of the Poisson equation for nuf by means of Map_et::poisson . | |
Scalar | ssjm1_nuq |
Effective source at the previous step for the resolution of the Poisson equation for nuq by means of Map_et::poisson . | |
Scalar | ssjm1_dzeta |
Effective source at the previous step for the resolution of the Poisson equation for dzeta . | |
Scalar | ssjm1_tggg |
Effective source at the previous step for the resolution of the Poisson equation for tggg . | |
Scalar | ssjm1_khi |
Effective source at the previous step for the resolution of the Poisson equation for the scalar ![]() Map_et::poisson . | |
Vector | ssjm1_wshift |
Effective source at the previous step for the resolution of the vector Poisson equation for ![]() | |
double * | p_grv2 |
Error on the virial identity GRV2. | |
double * | p_grv3 |
Error on the virial identity GRV3. | |
double * | p_mom_quad |
Quadrupole moment | |
double * | p_mass_g |
Gravitational mass (ADM mass as a volume integral) | |
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 ![]() | |
Scalar | ak_car |
Scalar ![]() | |
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. | |
Map & | mp |
Mapping describing the coordinate system (r,theta,phi) | |
Scalar | nn |
Lapse function N . | |
Vector | beta |
Shift vector ![]() | |
Metric | gamma |
3-metric ![]() | |
Scalar | ener_euler |
Total energy density E in the Eulerian frame. | |
Vector | mom_euler |
Total 3-momentum density ![]() | |
Sym_tensor | stress_euler |
Stress tensor ![]() | |
Sym_tensor | kk |
Extrinsic curvature tensor ![]() | |
double * | p_adm_mass |
ADM mass. | |
Base class for axisymmetric stationary compact stars in Quasi-Isotropic coordinates (under development).
()
The time slice
Lorene::Star_QI::Star_QI | ( | Map & | mp_i | ) |
Standard constructor.
mp_i | Mapping on which the star is contructed |
Definition at line 68 of file star_QI.C.
References Lorene::Compobj::beta, dzeta, khi_shift, logn, nuf, nuq, set_der_0x0(), Lorene::Tensor::set_etat_zero(), ssjm1_dzeta, ssjm1_khi, ssjm1_nuf, ssjm1_nuq, ssjm1_tggg, ssjm1_wshift, tggg, tnphi, and w_shift.
Constructor from a file (see sauve(FILE*)
).
mp_i | Mapping on which the star is constructed |
fich | input file (must have been created by the function Star_QI::sauve ) |
Definition at line 137 of file star_QI.C.
References dzeta, fait_nphi(), fait_shift(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_mg(), khi_shift, logn, Lorene::Compobj::mp, nuf, nuq, set_der_0x0(), ssjm1_dzeta, ssjm1_khi, ssjm1_nuf, ssjm1_nuq, ssjm1_tggg, ssjm1_wshift, tggg, update_metric(), and w_shift.
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ADM mass (computed as a surface integral at spatial infinity)
Definition at line 310 of file compobj.C.
References Lorene::Metric::cov(), Lorene::Tensor::derive_con(), Lorene::Tensor_sym::derive_con(), Lorene::Vector::flux(), Lorene::Compobj::gamma, Lorene::Tensor::get_triad(), Lorene::Compobj::mp, Lorene::Compobj::p_adm_mass, Lorene::Tensor::trace(), and Lorene::Tensor::up().
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Angular momentum.
Reimplemented from Lorene::Compobj_QI.
Definition at line 96 of file star_QI_global.C.
References Lorene::Compobj_QI::a_car, Lorene::Compobj_QI::b_car, Lorene::Compobj_QI::bbb, Lorene::Map::get_bvect_spher(), Lorene::Scalar::get_spectral_va(), Lorene::Tensor::get_triad(), Lorene::Scalar::integrale(), Lorene::Compobj::mom_euler, Lorene::Compobj::mp, Lorene::Scalar::mult_r(), Lorene::Compobj_QI::p_angu_mom, and Lorene::Scalar::set_spectral_va().
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Deletes all the derived quantities.
Reimplemented from Lorene::Compobj_QI.
Reimplemented in Lorene::Boson_star.
Definition at line 222 of file star_QI.C.
References Lorene::Compobj_QI::del_deriv(), p_grv2, p_grv3, p_mass_g, p_mom_quad, and set_der_0x0().
Energy of a particle at the ISCO.
Definition at line 320 of file compobj_QI_global.C.
References Lorene::Compobj_QI::p_espec_isco, and Lorene::Compobj_QI::r_isco().
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Computes the extrinsic curvature and ak_car
from nphi
, nn
and b_car
.
Reimplemented from Lorene::Compobj.
Reimplemented in Lorene::AltBH_QI.
Definition at line 339 of file compobj_QI.C.
References Lorene::Compobj_QI::ak_car, Lorene::Compobj_QI::b_car, Lorene::Compobj_QI::del_deriv(), Lorene::Scalar::dsdr(), Lorene::Scalar::dsdt(), Lorene::Compobj::extrinsic_curvature(), Lorene::Map::get_mg(), Lorene::Scalar::inc_dzpuis(), Lorene::Compobj::kk, Lorene::Compobj::mp, Lorene::Scalar::mult_rsint(), Lorene::Scalar::mult_sint(), Lorene::Compobj::nn, Lorene::Compobj_QI::nphi, and Lorene::Tensor::set().
Orbital frequency at the innermost stable circular orbit (ISCO).
Definition at line 286 of file compobj_QI_global.C.
References Lorene::Compobj_QI::p_f_isco, and Lorene::Compobj_QI::r_isco().
void Lorene::Star_QI::fait_nphi | ( | ) |
Computes tnphi
and nphi
from the Cartesian components of the shift, stored in shift
.
Definition at line 386 of file star_QI.C.
References Lorene::Compobj::beta, Lorene::Map::comp_p_from_cartesian(), Lorene::Scalar::div_rsint(), Lorene::Compobj::mp, Lorene::Compobj_QI::nphi, and tnphi.
void Lorene::Star_QI::fait_shift | ( | ) |
Computes shift
from w_shift
and khi_shift
according to Shibata's prescription [Prog.
Theor. Phys. 101 , 1199 (1999)] :
Definition at line 340 of file star_QI.C.
References Lorene::Compobj::beta, Lorene::contract(), Lorene::Map::cosp, Lorene::Map::cost, Lorene::Tensor::dec_dzpuis(), Lorene::Scalar::derive_con(), Lorene::Tensor::derive_con(), Lorene::Scalar::domain(), Lorene::Map::flat_met_cart(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), khi_shift, Lorene::Compobj::mp, Lorene::Vector::set(), Lorene::Scalar::set_domain(), Lorene::Scalar::set_dzpuis(), Lorene::Map::sinp, Lorene::Map::sint, Lorene::Vector::std_spectral_base(), w_shift, Lorene::Map::x, Lorene::Map::y, and Lorene::Map::z.
Returns the square of the metric factor A.
Definition at line 378 of file compobj.h.
References Lorene::Compobj_QI::a_car.
Returns the scalar
For axisymmetric stars, this quantity is related to the derivatives of
In particular it is related to the quantities
Definition at line 404 of file compobj.h.
References Lorene::Compobj_QI::ak_car.
Returns the square of the metric factor B.
Definition at line 381 of file compobj.h.
References Lorene::Compobj_QI::b_car.
Returns the metric factor B.
Definition at line 375 of file compobj.h.
References Lorene::Compobj_QI::bbb.
Returns the shift vector
Definition at line 213 of file compobj.h.
References Lorene::Compobj::beta.
Returns the total energy density E in the Eulerian frame.
Definition at line 219 of file compobj.h.
References Lorene::Compobj::ener_euler.
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Returns the extrinsic curvature tensor
Definition at line 228 of file compobj.h.
References Lorene::Compobj::kk.
Returns the total 3-momentum density
Definition at line 222 of file compobj.h.
References Lorene::Compobj::mom_euler.
Returns the lapse function N .
Definition at line 210 of file compobj.h.
References Lorene::Compobj::nn.
Returns the metric coefficient
Definition at line 384 of file compobj.h.
References Lorene::Compobj_QI::nphi.
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Returns the stress tensor
Definition at line 225 of file compobj.h.
References Lorene::Compobj::stress_euler.
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Error on the virial identity GRV2.
This indicator is only valid for relativistic computations.
Definition at line 123 of file star_QI_global.C.
References Lorene::Compobj_QI::a_car, Lorene::Compobj_QI::ak_car, Lorene::Compobj_QI::b_car, Lorene::Scalar::derive_cov(), Lorene::Map::flat_met_spher(), Lorene::Map::get_bvect_spher(), Lorene::Tensor::get_triad(), lambda_grv2(), logn, Lorene::Compobj::mp, p_grv2, and Lorene::Compobj::stress_euler.
Error on the virial identity GRV3.
The error is computed as the integral defined by Eq. (43) of [Gourgoulhon and Bonazzola, Class. Quantum Grav. 11, 443 (1994)] divided by the integral of the matter terms.
ost | output stream to give details of the computation; if set to 0x0 [default value], no details will be given. |
Definition at line 148 of file star_QI_global.C.
References Lorene::Compobj_QI::a_car, Lorene::Compobj_QI::ak_car, Lorene::Compobj_QI::bbb, Lorene::Scalar::derive_cov(), Lorene::Scalar::dsdr(), dzeta, Lorene::Map::flat_met_spher(), Lorene::Compobj::gamma, Lorene::Scalar::get_dzpuis(), Lorene::Scalar::get_etat(), Lorene::Scalar::integrale(), Lorene::log(), logn, Lorene::Compobj::mp, Lorene::Valeur::mult_ct(), p_grv3, Lorene::Scalar::set_dzpuis(), Lorene::Scalar::set_spectral_va(), Lorene::Scalar::srdsdt(), Lorene::Valeur::ssint(), Lorene::Scalar::std_spectral_base(), Lorene::Compobj::stress_euler, Lorene::Valeur::sx(), Lorene::Tensor::trace(), and Lorene::Map_radial::xsr.
Save in a file for GYOTO.
Definition at line 232 of file compobj_QI.C.
References Lorene::Compobj::beta, Lorene::Metric::con(), Lorene::Metric::cov(), Lorene::fwrite_be(), Lorene::Compobj::gamma, Lorene::Map::get_mg(), Lorene::Compobj::kk, Lorene::Compobj::mp, Lorene::Compobj::nn, Lorene::Compobj_QI::r_isco(), Lorene::Compobj_QI::r_mb(), Lorene::Map::sauve(), Lorene::Scalar::sauve(), Lorene::Tensor::sauve(), Lorene::Tensor_sym::sauve(), and Lorene::Mg3d::sauve().
Computes the coefficient
in order that the total source does not contain any monopolar term, i.e. in order that
where
Then, by construction, the new source
sou_m | [input] matter source term ![]() |
sou_q | [input] quadratic source term ![]() |
Definition at line 321 of file star_QI_global.C.
References Lorene::Valeur::c, Lorene::Scalar::check_dzpuis(), Lorene::Valeur::coef_i(), Lorene::Map_radial::dxdr, Lorene::Map_af::get_alpha(), Lorene::Map_af::get_beta(), Lorene::Scalar::get_etat(), Lorene::Tbl::get_etat(), Lorene::Valeur::get_etat(), Lorene::Mg3d::get_grille3d(), Lorene::Map::get_mg(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Scalar::get_spectral_va(), Lorene::Mg3d::get_type_r(), Lorene::Map_af::set_alpha(), Lorene::Map_af::set_beta(), Lorene::Mtbl::t, Lorene::Tbl::t, Lorene::Map::val_r(), Lorene::Grille3d::x, and Lorene::Map_radial::xsr.
Angular momentum of a particle at the ISCO.
Definition at line 303 of file compobj_QI_global.C.
References Lorene::Compobj_QI::p_lspec_isco, and Lorene::Compobj_QI::r_isco().
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Gravitational mass.
Definition at line 64 of file star_QI_global.C.
References Lorene::Compobj_QI::a_car, Lorene::Compobj_QI::b_car, Lorene::Compobj_QI::bbb, Lorene::Compobj::ener_euler, Lorene::Compobj::gamma, Lorene::Scalar::integrale(), Lorene::Compobj::mom_euler, Lorene::Compobj::nn, p_mass_g, Lorene::Scalar::std_spectral_base(), Lorene::Compobj::stress_euler, tnphi, and Lorene::Tensor::trace().
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Quadrupole moment.
The quadrupole moment Q is defined according to Eq. (7) of [Salgado, Bonazzola, Gourgoulhon and Haensel, Astron. Astrophys. 291 , 155 (1994)]. At the Newtonian limit it is related to the component
Definition at line 250 of file star_QI_global.C.
References Lorene::Compobj_QI::a_car, Lorene::Compobj_QI::ak_car, Lorene::Compobj_QI::bbb, Lorene::Scalar::check_dzpuis(), Lorene::Scalar::derive_cov(), Lorene::Compobj::ener_euler, Lorene::Map::flat_met_spher(), Lorene::Compobj::gamma, Lorene::Scalar::get_etat(), Lorene::Scalar::inc_dzpuis(), Lorene::Scalar::integrale(), Lorene::log(), logn, Lorene::Compobj::mp, Lorene::Valeur::mult_ct(), Lorene::Scalar::mult_r(), p_mom_quad, Lorene::Scalar::set_spectral_va(), Lorene::Scalar::std_spectral_base(), Lorene::Compobj::stress_euler, and Lorene::Tensor::trace().
Assignment to another Star_QI
.
Definition at line 250 of file star_QI.C.
References del_deriv(), dzeta, khi_shift, logn, nuf, nuq, Lorene::Compobj_QI::operator=(), ssjm1_dzeta, ssjm1_khi, ssjm1_nuf, ssjm1_nuq, ssjm1_tggg, ssjm1_wshift, tggg, tnphi, and w_shift.
Operator >> (virtual function called by the operator <<).
Reimplemented from Lorene::Compobj_QI.
Reimplemented in Lorene::Boson_star.
Definition at line 300 of file star_QI.C.
References angu_mom(), dzeta, grv2(), grv3(), logn, mass_g(), mom_quad(), nuf, nuq, Lorene::Compobj_QI::operator>>(), Lorene::pow(), and Lorene::Scalar::val_grid_point().
Coordinate r of the innermost stable circular orbit (ISCO).
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 108 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().
Coordinate r of the marginally bound circular orbit (R_mb).
Definition at line 341 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_r_mb, Lorene::Map::r, Lorene::Compobj_QI::r_isco(), Lorene::sqrt(), Lorene::Scalar::std_spectral_base(), Lorene::Valeur::val_point(), Lorene::Map::val_r(), and Lorene::zerosec().
Save in a file.
Reimplemented from Lorene::Compobj_QI.
Reimplemented in Lorene::Boson_star.
Definition at line 279 of file star_QI.C.
References dzeta, khi_shift, nuf, nuq, Lorene::Scalar::sauve(), Lorene::Tensor::sauve(), ssjm1_dzeta, ssjm1_khi, ssjm1_nuf, ssjm1_nuq, ssjm1_tggg, ssjm1_wshift, tggg, and w_shift.
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Sets to 0x0
all the pointers on derived quantities.
Reimplemented in Lorene::Boson_star.
Definition at line 235 of file star_QI.C.
References p_grv2, p_grv3, p_mass_g, and p_mom_quad.
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Read/write of the mapping.
Definition at line 200 of file compobj.h.
References Lorene::Compobj::mp.
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Computes metric coefficients from known potentials.
The calculation is performed starting from the quantities logn
, dzeta
, tggg
and shift
, which are supposed to be up to date.
From these, the following fields are updated: nnn
, a_car
, bbb
and b_car
, as well as the 3-metric gamma
.
Reimplemented from Lorene::Compobj_QI.
Definition at line 410 of file star_QI.C.
References Lorene::Compobj_QI::a_car, Lorene::Compobj_QI::b_car, Lorene::Compobj_QI::bbb, del_deriv(), Lorene::Scalar::div_rsint(), dzeta, Lorene::exp(), logn, Lorene::Compobj::nn, Lorene::Scalar::std_spectral_base(), tggg, and Lorene::Compobj_QI::update_metric().
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Effective source at the previous step for the resolution of the Poisson equation for the scalar Map_et::poisson
.
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Effective source at the previous step for the resolution of the Poisson equation for nuf
by means of Map_et::poisson
.
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Effective source at the previous step for the resolution of the Poisson equation for nuq
by means of Map_et::poisson
.
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Effective source at the previous step for the resolution of the vector Poisson equation for
mp
)
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