Lorene::Gravastar Class Reference
[Stars and black holes]

Class for perfect fluid rotating gravastar. More...

#include <gravastar.h>

Inheritance diagram for Lorene::Gravastar:
Lorene::Star_rot Lorene::Star

List of all members.

Public Member Functions

 Gravastar (Map &mp_i, int nzet_i, const Eos &eos_i, const double rho_core_i)
 Standard constructor.
 Gravastar (const Gravastar &)
 Copy constructor.
 Gravastar (Map &mp_i, const Eos &eos_i, FILE *fich)
 Constructor from a file (see sauve(FILE*) ).
 ~Gravastar ()
 Destructor.
void operator= (const Gravastar &)
 Assignment to another Gravastar.
void equation_of_state ()
 Allows to computes the proper baryon and energy density, as well as pressure from the enthalpy, in the gravastar's crust only (in the core, p=-rho=cst).
void equilibrium (double omega0, double fact_omega, int nzadapt, const Tbl &ent_limit, const Itbl &icontrol, const Tbl &control, Tbl &diff, Param *=0x0)
 Computes an equilibrium configuration.
bool is_relativistic () const
 Returns true for a relativistic star, false for a Newtonian one.
virtual double get_omega_c () const
 Returns the central value of the rotation angular velocity ([f_unit] ).
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_tnphi () const
 Returns the component $\tilde N^\varphi = N^\varphi r\sin\theta$ of the shift vector.
const Scalarget_uuu () const
 Returns the norm of u_euler.
const Scalarget_nuf () const
 Returns the part of the Metric potential $\nu = \ln N$ = logn generated by the matter terms.
const Scalarget_nuq () const
 Returns the Part of the Metric potential $\nu = \ln N$ = logn generated by the quadratic terms.
const Scalarget_dzeta () const
 Returns the Metric potential $\zeta = \ln(AN)$.
const Scalarget_tggg () const
 Returns the Metric potential $\tilde G = (NB-1) r\sin\theta$.
const Vectorget_w_shift () const
 Returns the vector $W^i$ used in the decomposition of shift , following Shibata's prescription [Prog.
const Scalarget_khi_shift () const
 Returns the scalar $\chi$ used in the decomposition of shift following Shibata's prescription [Prog.
const Sym_tensorget_tkij () const
 Returns the tensor ${\tilde K_{ij}}$ related to the extrinsic curvature tensor by ${\tilde K_{ij}} = B^{-2} K_{ij}$.
const Scalarget_ak_car () const
 Returns the scalar $A^2 K_{ij} K^{ij}$.
virtual void sauve (FILE *) const
 Save in a file.
virtual void display_poly (ostream &) const
 Display in polytropic units.
virtual const Itbll_surf () const
 Description of the stellar surface: returns a 2-D Itbl containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$.
virtual double mass_b () const
 Baryon mass.
virtual double mass_g () const
 Gravitational mass.
virtual double angu_mom () const
 Angular momentum.
virtual double tsw () const
 Ratio T/W.
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 r_circ () const
 Circumferential radius.
virtual double aplat () const
 Flatening r_pole/r_eq.
virtual double area () const
 Integrated surface area in ${\rm km}^2$.
virtual double mean_radius () const
 Mean star radius from the area $ r_{\rm mean} = \sqrt{\mathcal{A}} / 4\pi$.
virtual double z_eqf () const
 Forward redshift factor at equator.
virtual double z_eqb () const
 Backward redshift factor at equator.
virtual double z_pole () const
 Redshift factor at North pole.
virtual double mom_quad () const
 Quadrupole moment.
virtual const Tblsurf_grav () const
 Surface gravity (table along the theta direction).
virtual double r_isco (ostream *ost=0x0) const
 Circumferential radius of the innermost stable circular orbit (ISCO).
virtual double f_isco () const
 Orbital frequency at the innermost stable circular orbit (ISCO).
virtual double espec_isco () const
 Energy of a particle on the ISCO.
virtual double lspec_isco () const
 Angular momentum of a particle on the ISCO.
virtual double f_eq () const
 Orbital frequency at the equator.
virtual void hydro_euler ()
 Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame.
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 .
void extrinsic_curvature ()
 Computes tkij and ak_car from shift , nnn and b_car .
virtual void equilibrium (double ent_c, double omega0, double fact_omega, int nzadapt, const Tbl &ent_limit, const Itbl &icontrol, const Tbl &control, double mbar_wanted, double aexp_mass, Tbl &diff, Param *=0x0)
 Computes an equilibrium configuration.
Mapset_mp ()
 Read/write of the mapping.
void set_enthalpy (const Scalar &)
 Assignment of the enthalpy field.
virtual void equilibrium_spher (double ent_c, double precis=1.e-14, const Tbl *pent_limit=0x0)
 Computes a spherical static configuration.
const Mapget_mp () const
 Returns the mapping.
int get_nzet () const
 Returns the number of domains occupied by the star.
const Eosget_eos () const
 Returns the equation of state.
const Scalarget_ent () const
 Returns the enthalpy field.
const Scalarget_nbar () const
 Returns the proper baryon density.
const Scalarget_ener () const
 Returns the proper total energy density.
const Scalarget_press () const
 Returns the fluid pressure.
const Scalarget_ener_euler () const
 Returns the total energy density with respect to the Eulerian observer.
const Scalarget_s_euler () const
 Returns the trace of the stress tensor in the Eulerian frame.
const Scalarget_gam_euler () const
 Returns the Lorentz factor between the fluid and Eulerian observers.
const Vectorget_u_euler () const
 Returns the fluid 3-velocity with respect to the Eulerian observer.
const Tensorget_stress_euler () const
 Returns the spatial part of the stress-energy tensor with respect to the Eulerian observer.
const Scalarget_logn () const
 Returns the logarithm of the lapse N.
const Scalarget_nn () const
 Returns the lapse function N.
const Vectorget_beta () const
 Returns the shift vector $\beta^i$.
const Scalarget_lnq () const
const Metricget_gamma () const
 Returns the 3-metric $\gamma$.
double ray_eq () const
 Coordinate radius at $\phi=0$, $\theta=\pi/2$ [r_unit].
double ray_eq_pis2 () const
 Coordinate radius at $\phi=\pi/2$, $\theta=\pi/2$ [r_unit].
double ray_eq_pi () const
 Coordinate radius at $\phi=\pi$, $\theta=\pi/2$ [r_unit].
double ray_eq_3pis2 () const
 Coordinate radius at $\phi=3\pi/2$, $\theta=\pi/2$ [r_unit].
double ray_pole () const
 Coordinate radius at $\theta=0$ [r_unit].
const Tblxi_surf () const
 Description of the stellar surface: returns a 2-D Tbl containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$.

Static Public Member Functions

static double lambda_grv2 (const Scalar &sou_m, const Scalar &sou_q)
 Computes the coefficient $\lambda$ which ensures that the GRV2 virial identity is satisfied.

Protected Member Functions

virtual ostream & operator>> (ostream &) const
 Operator >> (virtual function called by the operator <<).
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 void del_hydro_euler ()
 Sets to ETATNONDEF (undefined state) the hydrodynamical quantities relative to the Eulerian observer.
virtual void partial_display (ostream &) const
 Printing of some informations, excluding all global quantities.

Protected Attributes

double rho_core
 Energy density in gravastar's core.
bool relativistic
 Indicator of relativity: true for a relativistic star, false for a Newtonian one.
double unsurc2
 $1/c^2$ : unsurc2=1 for a relativistic star, 0 for a Newtonian one.
double omega
 Rotation angular velocity ([f_unit] ).
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 tnphi
 Component $\tilde N^\varphi = N^\varphi r\sin\theta$ of the shift vector.
Scalar uuu
 Norm of u_euler.
Scalar nuf
 Part of the Metric potential $\nu = \ln N$ = logn generated by the matter terms.
Scalar nuq
 Part of the Metric potential $\nu = \ln N$ = logn generated by the quadratic terms.
Scalar dzeta
 Metric potential $\zeta = \ln(AN)$.
Scalar tggg
 Metric potential $\tilde G = (NB-1) r\sin\theta$.
Vector w_shift
 Vector $W^i$ used in the decomposition of shift , following Shibata's prescription [Prog.
Scalar khi_shift
 Scalar $\chi$ used in the decomposition of shift , following Shibata's prescription [Prog.
Sym_tensor tkij
 Tensor ${\tilde K_{ij}}$ related to the extrinsic curvature tensor by ${\tilde K_{ij}} = B^{-2} K_{ij}$.
Scalar ak_car
 Scalar $A^2 K_{ij} K^{ij}$.
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 $\chi$ by means of Map_et::poisson .
Vector ssjm1_wshift
 Effective source at the previous step for the resolution of the vector Poisson equation for $W^i$.
double * p_angu_mom
 Angular momentum.
double * p_tsw
 Ratio T/W.
double * p_grv2
 Error on the virial identity GRV2.
double * p_grv3
 Error on the virial identity GRV3.
double * p_r_circ
 Circumferential radius.
double * p_aplat
 Flatening r_pole/r_eq.
double * p_area
 Integrated surface area.
double * p_z_eqf
 Forward redshift factor at equator.
double * p_z_eqb
 Backward redshift factor at equator.
double * p_z_pole
 Redshift factor at North pole.
double * p_mom_quad
 Quadrupole moment.
double * p_r_isco
 Circumferential radius of the ISCO.
double * p_f_isco
 Orbital frequency of the ISCO.
double * p_espec_isco
 Specific energy of a particle on the ISCO.
double * p_lspec_isco
 Specific angular momentum of a particle on the ISCO.
double * p_f_eq
 Orbital frequency at the equator.
Tblp_surf_grav
 Surface gravity (along the theta direction).
Mapmp
 Mapping associated with the star.
int nzet
 Number of domains of *mp occupied by the star.
const Eoseos
 Equation of state of the stellar matter.
Scalar ent
 Log-enthalpy.
Scalar nbar
 Baryon density in the fluid frame.
Scalar ener
 Total energy density in the fluid frame.
Scalar press
 Fluid pressure.
Scalar ener_euler
 Total energy density in the Eulerian frame.
Scalar s_euler
 Trace of the stress scalar in the Eulerian frame.
Scalar gam_euler
 Lorentz factor between the fluid and Eulerian observers.
Vector u_euler
 Fluid 3-velocity with respect to the Eulerian observer.
Sym_tensor stress_euler
 Spatial part of the stress-energy tensor with respect to the Eulerian observer.
Scalar logn
 Logarithm of the lapse N .
Scalar nn
 Lapse function N .
Vector beta
 Shift vector.
Scalar lnq
Metric gamma
 3-metric
double * p_ray_eq
 Coordinate radius at $\phi=0$, $\theta=\pi/2$.
double * p_ray_eq_pis2
 Coordinate radius at $\phi=\pi/2$, $\theta=\pi/2$.
double * p_ray_eq_pi
 Coordinate radius at $\phi=\pi$, $\theta=\pi/2$.
double * p_ray_eq_3pis2
 Coordinate radius at $\phi=3\pi/2$, $\theta=\pi/2$.
double * p_ray_pole
 Coordinate radius at $\theta=0$.
Itblp_l_surf
 Description of the stellar surface: 2-D Itbl containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$.
Tblp_xi_surf
 Description of the stellar surface: 2-D Tbl containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$.
double * p_mass_b
 Baryon mass.
double * p_mass_g
 Gravitational mass.

Friends

class Star
ostream & operator<< (ostream &, const Star &)
 Display.

Detailed Description

Class for perfect fluid rotating gravastar.

()

Definition at line 49 of file gravastar.h.


Constructor & Destructor Documentation

Lorene::Gravastar::Gravastar ( Map mp_i,
int  nzet_i,
const Eos eos_i,
const double  rho_core_i 
)

Standard constructor.

Parameters:
mp_i Mapping on which the gravastar is contructed
nzet_i Number of domains occupied by the gravastar
eos_i Equation of state of the crust matter
rho_core_i Energy density in gravastar's core (constant, =-p_core) NB:pas de choix pour l'EOS en fait : a virer??

Definition at line 51 of file gravastar.C.

Lorene::Gravastar::Gravastar ( const Gravastar  ) 

Copy constructor.

Lorene::Gravastar::Gravastar ( Map mp_i,
const Eos eos_i,
FILE *  fich 
)

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

Parameters:
mp_i Mapping on which the gravastar is constructed
eos_i Equation of state of the crust matter
fich input file (must have been created by the function Gravastar::sauve )
Lorene::Gravastar::~Gravastar (  ) 

Destructor.

Definition at line 59 of file gravastar.C.

References Lorene::Star_rot::del_deriv().


Member Function Documentation

double Lorene::Star_rot::angu_mom (  )  const [virtual, inherited]
double Lorene::Star_rot::aplat (  )  const [virtual, inherited]

Flatening r_pole/r_eq.

Definition at line 435 of file star_rot_global.C.

References Lorene::Star_rot::p_aplat, Lorene::Star::ray_eq(), and Lorene::Star::ray_pole().

double Lorene::Star_rot::area (  )  const [virtual, inherited]
void Lorene::Star_rot::del_deriv (  )  const [protected, virtual, inherited]
void Lorene::Star_rot::del_hydro_euler (  )  [protected, virtual, inherited]

Sets to ETATNONDEF (undefined state) the hydrodynamical quantities relative to the Eulerian observer.

Reimplemented from Lorene::Star.

Definition at line 353 of file star_rot.C.

References Lorene::Star_rot::del_deriv().

void Lorene::Star_rot::display_poly ( ostream &  ost  )  const [virtual, inherited]
void Lorene::Gravastar::equation_of_state (  ) 
void Lorene::Star_rot::equilibrium ( double  ent_c,
double  omega0,
double  fact_omega,
int  nzadapt,
const Tbl ent_limit,
const Itbl icontrol,
const Tbl control,
double  mbar_wanted,
double  aexp_mass,
Tbl diff,
Param = 0x0 
) [virtual, inherited]

Computes an equilibrium configuration.

Parameters:
ent_c [input] Central enthalpy
omega0 [input] Requested angular velocity (if fact_omega=1. )
fact_omega [input] 1.01 = search for the Keplerian frequency, 1. = otherwise.
nzadapt [input] Number of (inner) domains where the mapping adaptation to an iso-enthalpy surface should be performed
ent_limit [input] 1-D Tbl of dimension nzet which defines the enthalpy at the outer boundary of each domain
icontrol [input] Set of integer parameters (stored as a 1-D Itbl of size 8) to control the iteration:

  • icontrol(0) = mer_max : maximum number of steps
  • icontrol(1) = mer_rot : step at which the rotation is switched on
  • icontrol(2) = mer_change_omega : step at which the rotation velocity is changed to reach the final one
  • icontrol(3) = mer_fix_omega : step at which the final rotation velocity must have been reached
  • icontrol(4) = mer_mass : the absolute value of mer_mass is the step from which the baryon mass is forced to converge, by varying the central enthalpy (mer_mass>0 ) or the angular velocity (mer_mass<0 )
  • icontrol(5) = mermax_poisson : maximum number of steps in Map_et::poisson
  • icontrol(6) = mer_triax : step at which the 3-D perturbation is switched on
  • icontrol(7) = delta_mer_kep : number of steps after mer_fix_omega when omega starts to be increased by fact_omega to search for the Keplerian velocity
control [input] Set of parameters (stored as a 1-D Tbl of size 7) to control the iteration:

  • control(0) = precis : threshold on the enthalpy relative change for ending the computation
  • control(1) = omega_ini : initial angular velocity, switched on only if mer_rot<0 , otherwise 0 is used
  • control(2) = relax : relaxation factor in the main iteration
  • control(3) = relax_poisson : relaxation factor in Map_et::poisson
  • control(4) = thres_adapt : threshold on dH/dr for freezing the adaptation of the mapping
  • control(5) = ampli_triax : relative amplitude of the 3-D perturbation
  • control(6) = precis_adapt : precision for Map_et::adapt
mbar_wanted [input] Requested baryon mass (effective only if mer_mass > mer_max )
aexp_mass [input] Exponent for the increase factor of the central enthalpy to converge to the requested baryon mass
diff [output] 1-D Tbl of size 7 for the storage of some error indicators :

  • diff(0) : Relative change in the enthalpy field between two successive steps
  • diff(1) : Relative error in the resolution of the Poisson equation for nuf
  • diff(2) : Relative error in the resolution of the Poisson equation for nuq
  • diff(3) : Relative error in the resolution of the Poisson equation for dzeta
  • diff(4) : Relative error in the resolution of the Poisson equation for tggg
  • diff(5) : Relative error in the resolution of the equation for shift (x comp.)
  • diff(6) : Relative error in the resolution of the equation for shift (y comp.)

Definition at line 74 of file star_rot_equil.C.

References Lorene::Star_rot::a_car, Lorene::abs(), Lorene::Map::adapt(), Lorene::Param::add_cmp_mod(), Lorene::Param::add_double(), Lorene::Param::add_double_mod(), Lorene::Param::add_int(), Lorene::Param::add_int_mod(), Lorene::Param::add_tbl(), Lorene::Param::add_tenseur_mod(), Lorene::Star_rot::ak_car, Lorene::Tensor::annule_domain(), Lorene::Star_rot::bbb, Lorene::Star::beta, Lorene::Valeur::c_cf, Lorene::Vector::change_triad(), Lorene::Map::cmp_zero(), Lorene::Valeur::coef(), Lorene::contract(), Lorene::cos(), Lorene::Scalar::derive_con(), Lorene::Scalar::derive_cov(), Lorene::diffrel(), Lorene::Scalar::dsdr(), Lorene::Star_rot::dzeta, Lorene::Star::ener_euler, Lorene::Star::ent, Lorene::Star::equation_of_state(), Lorene::Star_rot::fait_nphi(), Lorene::Map::flat_met_cart(), Lorene::Map::flat_met_spher(), Lorene::Star::gam_euler, Lorene::Map::get_bvect_cart(), Lorene::Map::get_mg(), 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_t(), Lorene::Star_rot::grv2(), Lorene::Map_et::homothetie(), Lorene::Star_rot::hydro_euler(), Lorene::Star_rot::khi_shift, Lorene::log(), Lorene::log10(), Lorene::Star::logn, Lorene::Star_rot::mass_b(), Lorene::Star_rot::mass_g(), Lorene::Star::mp, Lorene::Scalar::mult_rsint(), Lorene::Star::nbar, Lorene::Star::nn, Lorene::Star_rot::nphi, Lorene::Star_rot::nuf, Lorene::Star_rot::nuq, Lorene::Star::nzet, Lorene::Star_rot::omega, Lorene::Star_rot::partial_display(), Lorene::Map::phi, Lorene::Scalar::poisson(), Lorene::Map::poisson2d(), Lorene::pow(), Lorene::Star::press, Lorene::Star::ray_eq(), Lorene::Star::ray_pole(), Lorene::Map::reevaluate(), Lorene::Star_rot::relativistic, Lorene::Star::s_euler, Lorene::Vector::set(), Lorene::Tenseur::set(), Lorene::Tbl::set(), Lorene::Scalar::set_dzpuis(), Lorene::Tenseur::set_etat_qcq(), Lorene::Tbl::set_etat_qcq(), Lorene::Map::sint, Lorene::sqrt(), Lorene::Star_rot::ssjm1_khi, Lorene::Star_rot::ssjm1_nuf, Lorene::Star_rot::ssjm1_nuq, Lorene::Star_rot::ssjm1_tggg, Lorene::Star_rot::ssjm1_wshift, Lorene::Scalar::std_spectral_base(), Lorene::Scalar::test_poisson(), Lorene::Star_rot::tggg, Lorene::Star_rot::tkij, Lorene::Star::u_euler, Lorene::Tensor::up(), Lorene::Star_rot::update_metric(), Lorene::Star_rot::uuu, Lorene::Scalar::val_grid_point(), and Lorene::Star_rot::w_shift.

void Lorene::Gravastar::equilibrium ( double  omega0,
double  fact_omega,
int  nzadapt,
const Tbl ent_limit,
const Itbl icontrol,
const Tbl control,
Tbl diff,
Param = 0x0 
)

Computes an equilibrium configuration.

Parameters:
omega0 [input] Requested angular velocity (if fact_omega=1. )
fact_omega [input] 1.01 = search for the Keplerian frequency, 1. = otherwise.
nzadapt [input] Number of (inner) domains where the mapping adaptation to an iso-enthalpy surface should be performed
ent_limit [input] 1-D Tbl of dimension nzet which defines the enthalpy at the outer boundary of each domain
icontrol [input] Set of integer parameters (stored as a 1-D Itbl of size 8) to control the iteration:

  • icontrol(0) = mer_max : maximum number of steps
  • icontrol(1) = mer_rot : step at which the rotation is switched on
  • icontrol(2) = mer_change_omega : step at which the rotation velocity is changed to reach the final one
  • icontrol(3) = mer_fix_omega : step at which the final rotation velocity must have been reached
  • icontrol(4) = mer_mass : the absolute value of mer_mass is the step from which the baryon mass is forced to converge, by varying the central enthalpy (mer_mass>0 ) or the angular velocity (mer_mass<0 )
  • icontrol(5) = mermax_poisson : maximum number of steps in Map_et::poisson
  • icontrol(6) = mer_triax : step at which the 3-D perturbation is switched on
  • icontrol(7) = delta_mer_kep : number of steps after mer_fix_omega when omega starts to be increased by fact_omega to search for the Keplerian velocity
control [input] Set of parameters (stored as a 1-D Tbl of size 7) to control the iteration:

  • control(0) = precis : threshold on the enthalpy relative change for ending the computation
  • control(1) = omega_ini : initial angular velocity, switched on only if mer_rot<0 , otherwise 0 is used
  • control(2) = relax : relaxation factor in the main iteration
  • control(3) = relax_poisson : relaxation factor in Map_et::poisson
  • control(4) = thres_adapt : threshold on dH/dr for freezing the adaptation of the mapping
  • control(5) = ampli_triax : relative amplitude of the 3-D perturbation
  • control(6) = precis_adapt : precision for Map_et::adapt
diff [output] 1-D Tbl of size 7 for the storage of some error indicators :

  • diff(0) : Relative change in the enthalpy field between two successive steps
  • diff(1) : Relative error in the resolution of the Poisson equation for nuf
  • diff(2) : Relative error in the resolution of the Poisson equation for nuq
  • diff(3) : Relative error in the resolution of the Poisson equation for dzeta
  • diff(4) : Relative error in the resolution of the Poisson equation for tggg
  • diff(5) : Relative error in the resolution of the equation for shift (x comp.)
  • diff(6) : Relative error in the resolution of the equation for shift (y comp.)

Definition at line 47 of file gravastar_equil.C.

References Lorene::Star_rot::a_car, Lorene::Map::adapt(), Lorene::Param::add_cmp_mod(), Lorene::Param::add_double(), Lorene::Param::add_double_mod(), Lorene::Param::add_int(), Lorene::Param::add_int_mod(), Lorene::Param::add_tbl(), Lorene::Param::add_tenseur_mod(), Lorene::Star_rot::ak_car, Lorene::Tensor::annule_domain(), Lorene::Star_rot::bbb, Lorene::Star::beta, Lorene::Vector::change_triad(), Lorene::Map::cmp_zero(), Lorene::contract(), Lorene::Scalar::derive_con(), Lorene::Scalar::derive_cov(), des_profile(), Lorene::diffrel(), Lorene::Scalar::dsdr(), Lorene::Star_rot::dzeta, Lorene::Star::ener_euler, Lorene::Star::ent, equation_of_state(), Lorene::Star_rot::fait_nphi(), Lorene::Map::flat_met_cart(), Lorene::Map::flat_met_spher(), Lorene::Star::gam_euler, Lorene::Map::get_bvect_cart(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_t(), Lorene::Star_rot::grv2(), Lorene::Map_et::homothetie(), Lorene::Star_rot::hydro_euler(), Lorene::Star_rot::khi_shift, Lorene::log(), Lorene::log10(), Lorene::Star::logn, Lorene::Star::mp, Lorene::Scalar::mult_rsint(), Lorene::Star::nbar, Lorene::Star::nn, Lorene::Star_rot::nphi, Lorene::Star_rot::nuf, Lorene::Star_rot::nuq, Lorene::Star::nzet, Lorene::Star_rot::omega, Lorene::Star_rot::partial_display(), Lorene::Scalar::poisson(), Lorene::Map::poisson2d(), Lorene::Star::press, Lorene::Star::ray_eq(), Lorene::Star::ray_pole(), Lorene::Map::reevaluate(), Lorene::Star_rot::relativistic, Lorene::Star::s_euler, Lorene::Vector::set(), Lorene::Tenseur::set(), Lorene::Tbl::set(), Lorene::Scalar::set_dzpuis(), Lorene::Tenseur::set_etat_qcq(), Lorene::Tbl::set_etat_qcq(), Lorene::sqrt(), Lorene::Star_rot::ssjm1_khi, Lorene::Star_rot::ssjm1_nuf, Lorene::Star_rot::ssjm1_nuq, Lorene::Star_rot::ssjm1_tggg, Lorene::Star_rot::ssjm1_wshift, Lorene::Scalar::std_spectral_base(), Lorene::Scalar::test_poisson(), Lorene::Star_rot::tggg, Lorene::Star_rot::tkij, Lorene::Star::u_euler, Lorene::Tensor::up(), Lorene::Star_rot::update_metric(), Lorene::Star_rot::uuu, Lorene::Scalar::val_grid_point(), and Lorene::Star_rot::w_shift.

void Lorene::Star::equilibrium_spher ( double  ent_c,
double  precis = 1.e-14,
const Tbl pent_limit = 0x0 
) [virtual, inherited]

Computes a spherical static configuration.

Parameters:
ent_c [input] central value of the enthalpy
precis [input] threshold in the relative difference between the enthalpy fields of two consecutive steps to stop the iterative procedure (default value: 1.e-14)
ent_limit [input] : array of enthalpy values to be set at the boundaries between the domains; if set to 0x0 (default), the initial values will be kept.

Definition at line 101 of file star_equil_spher.C.

References Lorene::Star_rot::a_car, Lorene::Map_et::adapt(), Lorene::Param::add_double(), Lorene::Param::add_int(), Lorene::Param::add_int_mod(), Lorene::Param::add_tbl(), Lorene::Scalar::annule(), Lorene::Star_rot::b_car, Lorene::Star_rot::bbb, Lorene::diffrel(), Lorene::Scalar::dsdr(), Lorene::Map_af::dsdr(), Lorene::Star_rot::dzeta, Lorene::Star::ener, Lorene::Star::ener_euler, Lorene::Star::ent, Lorene::Star::equation_of_state(), Lorene::exp(), Lorene::Star::gam_euler, Lorene::Star::gamma, Lorene::Map_et::get_alpha(), Lorene::Map_af::get_alpha(), Lorene::Map_et::get_beta(), Lorene::Map_af::get_beta(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Map_af::homothetie(), Lorene::Scalar::integrale(), Lorene::Star::logn, Lorene::Star::mass_b(), Lorene::Star::mass_g(), Lorene::Star::mp, Lorene::Star::nn, Lorene::norme(), Lorene::Star::nzet, Lorene::Map_af::poisson(), Lorene::Star::press, Lorene::Star::s_euler, Lorene::Vector::set(), Lorene::Map_af::set_alpha(), Lorene::Map_af::set_beta(), Lorene::Scalar::set_dzpuis(), Lorene::Cmp::set_etat_qcq(), Lorene::Scalar::set_etat_zero(), Lorene::sqrt(), Lorene::Scalar::std_spectral_base(), Lorene::Star::u_euler, Lorene::Scalar::val_grid_point(), and Lorene::Map::val_r().

double Lorene::Star_rot::espec_isco (  )  const [virtual, inherited]

Energy of a particle on the ISCO.

Definition at line 292 of file star_rot_isco.C.

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

void Lorene::Star_rot::extrinsic_curvature (  )  [inherited]
double Lorene::Star_rot::f_eq (  )  const [virtual, inherited]

Orbital frequency at the equator.

Definition at line 310 of file star_rot_isco.C.

References Lorene::Star_rot::p_f_eq, and Lorene::Star_rot::r_isco().

double Lorene::Star_rot::f_isco (  )  const [virtual, inherited]

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

Definition at line 258 of file star_rot_isco.C.

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

void Lorene::Star_rot::fait_nphi (  )  [inherited]

Computes tnphi and nphi from the Cartesian components of the shift, stored in shift .

Definition at line 756 of file star_rot.C.

References Lorene::Star::beta, Lorene::Map::comp_p_from_cartesian(), Lorene::Scalar::div_rsint(), Lorene::Star::mp, Lorene::Star_rot::nphi, and Lorene::Star_rot::tnphi.

void Lorene::Star_rot::fait_shift (  )  [inherited]
const Scalar& Lorene::Star_rot::get_a_car (  )  const [inline, inherited]

Returns the square of the metric factor A.

Definition at line 326 of file star_rot.h.

References Lorene::Star_rot::a_car.

const Scalar& Lorene::Star_rot::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 410 of file star_rot.h.

References Lorene::Star_rot::ak_car.

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

Returns the square of the metric factor B.

Definition at line 329 of file star_rot.h.

References Lorene::Star_rot::b_car.

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

Returns the metric factor B.

Definition at line 323 of file star_rot.h.

References Lorene::Star_rot::bbb.

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

Returns the shift vector $\beta^i$.

Definition at line 402 of file star.h.

References Lorene::Star::beta.

const Scalar& Lorene::Star_rot::get_dzeta (  )  const [inline, inherited]

Returns the Metric potential $\zeta = \ln(AN)$.

Definition at line 353 of file star_rot.h.

References Lorene::Star_rot::dzeta.

const Scalar& Lorene::Star::get_ener (  )  const [inline, inherited]

Returns the proper total energy density.

Definition at line 370 of file star.h.

References Lorene::Star::ener.

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

Returns the total energy density with respect to the Eulerian observer.

Definition at line 376 of file star.h.

References Lorene::Star::ener_euler.

const Scalar& Lorene::Star::get_ent (  )  const [inline, inherited]

Returns the enthalpy field.

Definition at line 364 of file star.h.

References Lorene::Star::ent.

const Eos& Lorene::Star::get_eos (  )  const [inline, inherited]

Returns the equation of state.

Definition at line 361 of file star.h.

References Lorene::Star::eos.

const Scalar& Lorene::Star::get_gam_euler (  )  const [inline, inherited]

Returns the Lorentz factor between the fluid and Eulerian observers.

Definition at line 382 of file star.h.

References Lorene::Star::gam_euler.

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

Returns the 3-metric $\gamma$.

Definition at line 409 of file star.h.

References Lorene::Star::gamma.

const Scalar& Lorene::Star_rot::get_khi_shift (  )  const [inline, inherited]

Returns the scalar $\chi$ used in the decomposition of shift following Shibata's prescription [Prog.

Theor. Phys. 101 , 1199 (1999)] :

\[ N^i = {7\over 8} W^i - {1\over 8} \left(\nabla^i\chi+\nabla^iW^kx_k\right) \]

NB: w_shift contains the components of $W^i$ with respect to the Cartesian triad associated with the mapping mp .

Definition at line 384 of file star_rot.h.

References Lorene::Star_rot::khi_shift.

const Scalar& Lorene::Star::get_logn (  )  const [inline, inherited]

Returns the logarithm of the lapse N.

In the Newtonian case, this is the Newtonian gravitational potential (in units of $c^2$).

Definition at line 396 of file star.h.

References Lorene::Star::logn.

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

Returns the mapping.

Definition at line 355 of file star.h.

References Lorene::Star::mp.

const Scalar& Lorene::Star::get_nbar (  )  const [inline, inherited]

Returns the proper baryon density.

Definition at line 367 of file star.h.

References Lorene::Star::nbar.

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

Returns the lapse function N.

Definition at line 399 of file star.h.

References Lorene::Star::nn.

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

Returns the metric coefficient $N^\varphi$.

Definition at line 332 of file star_rot.h.

References Lorene::Star_rot::nphi.

const Scalar& Lorene::Star_rot::get_nuf (  )  const [inline, inherited]

Returns the part of the Metric potential $\nu = \ln N$ = logn generated by the matter terms.

Definition at line 345 of file star_rot.h.

References Lorene::Star_rot::nuf.

const Scalar& Lorene::Star_rot::get_nuq (  )  const [inline, inherited]

Returns the Part of the Metric potential $\nu = \ln N$ = logn generated by the quadratic terms.

Definition at line 350 of file star_rot.h.

References Lorene::Star_rot::nuq.

int Lorene::Star::get_nzet (  )  const [inline, inherited]

Returns the number of domains occupied by the star.

Definition at line 358 of file star.h.

References Lorene::Star::nzet.

double Lorene::Star_rot::get_omega_c (  )  const [virtual, inherited]

Returns the central value of the rotation angular velocity ([f_unit] ).

Definition at line 648 of file star_rot.C.

References Lorene::Star_rot::omega.

const Scalar& Lorene::Star::get_press (  )  const [inline, inherited]

Returns the fluid pressure.

Definition at line 373 of file star.h.

References Lorene::Star::press.

const Scalar& Lorene::Star::get_s_euler (  )  const [inline, inherited]

Returns the trace of the stress tensor in the Eulerian frame.

Definition at line 379 of file star.h.

References Lorene::Star::s_euler.

const Tensor& Lorene::Star::get_stress_euler (  )  const [inline, inherited]

Returns the spatial part of the stress-energy tensor with respect to the Eulerian observer.

Definition at line 390 of file star.h.

References Lorene::Star::stress_euler.

const Scalar& Lorene::Star_rot::get_tggg (  )  const [inline, inherited]

Returns the Metric potential $\tilde G = (NB-1) r\sin\theta$.

Definition at line 356 of file star_rot.h.

References Lorene::Star_rot::tggg.

const Sym_tensor& Lorene::Star_rot::get_tkij (  )  const [inline, inherited]

Returns the tensor ${\tilde K_{ij}}$ related to the extrinsic curvature tensor by ${\tilde K_{ij}} = B^{-2} K_{ij}$.

tkij contains the Cartesian components of ${\tilde K_{ij}}$.

Definition at line 391 of file star_rot.h.

References Lorene::Star_rot::tkij.

const Scalar& Lorene::Star_rot::get_tnphi (  )  const [inline, inherited]

Returns the component $\tilde N^\varphi = N^\varphi r\sin\theta$ of the shift vector.

Definition at line 337 of file star_rot.h.

References Lorene::Star_rot::tnphi.

const Vector& Lorene::Star::get_u_euler (  )  const [inline, inherited]

Returns the fluid 3-velocity with respect to the Eulerian observer.

Definition at line 385 of file star.h.

References Lorene::Star::u_euler.

const Scalar& Lorene::Star_rot::get_uuu (  )  const [inline, inherited]

Returns the norm of u_euler.

Definition at line 340 of file star_rot.h.

References Lorene::Star_rot::uuu.

const Vector& Lorene::Star_rot::get_w_shift (  )  const [inline, inherited]

Returns the vector $W^i$ used in the decomposition of shift , following Shibata's prescription [Prog.

Theor. Phys. 101 , 1199 (1999)] :

\[ N^i = {7\over 8} W^i - {1\over 8} \left(\nabla^i\chi+\nabla^iW^kx_k\right) \]

NB: w_shift contains the components of $W^i$ with respect to the Cartesian triad associated with the mapping mp .

Definition at line 370 of file star_rot.h.

References Lorene::Star_rot::w_shift.

double Lorene::Star_rot::grv2 (  )  const [virtual, inherited]
double Lorene::Star_rot::grv3 ( ostream *  ost = 0x0  )  const [virtual, inherited]
void Lorene::Star_rot::hydro_euler (  )  [virtual, inherited]
bool Lorene::Star_rot::is_relativistic (  )  const [inline, inherited]

Returns true for a relativistic star, false for a Newtonian one.

Definition at line 315 of file star_rot.h.

References Lorene::Star_rot::relativistic.

const Itbl & Lorene::Star_rot::l_surf (  )  const [virtual, inherited]

Description of the stellar surface: returns a 2-D Itbl containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$.

The stellar surface is defined as the location where the enthalpy (member ent ) vanishes.

Reimplemented from Lorene::Star.

Definition at line 77 of file star_rot_global.C.

References Lorene::Star::ent, Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Scalar::get_spectral_va(), Lorene::Star::mp, Lorene::Star::nzet, Lorene::Star::p_l_surf, and Lorene::Star::p_xi_surf.

double Lorene::Star_rot::lambda_grv2 ( const Scalar sou_m,
const Scalar sou_q 
) [static, inherited]

Computes the coefficient $\lambda$ which ensures that the GRV2 virial identity is satisfied.

$\lambda$ is the coefficient by which one must multiply the quadratic source term $\sigma_q$ of the 2-D Poisson equation

\[ \Delta_2 u = \sigma_m + \sigma_q \]

in order that the total source does not contain any monopolar term, i.e. in order that

\[ \int_0^{2\pi} \int_0^{+\infty} \sigma(r, \theta) \, r \, dr \, d\theta = 0 \ , \]

where $\sigma = \sigma_m + \sigma_q$. $\lambda$ is computed according to the formula

\[ \lambda = - { \int_0^{2\pi} \int_0^{+\infty} \sigma_m(r, \theta) \, r \, dr \, d\theta \over \int_0^{2\pi} \int_0^{+\infty} \sigma_q(r, \theta) \, r \, dr \, d\theta } \ . \]

Then, by construction, the new source $\sigma' = \sigma_m + \lambda \sigma_q$ has a vanishing monopolar term.

Parameters:
sou_m [input] matter source term $\sigma_m$
sou_q [input] quadratic source term $\sigma_q$
Returns:
value of $\lambda$

Definition at line 69 of file star_rot_lambda_grv2.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_dzpuis(), Lorene::Valeur::get_etat(), Lorene::Scalar::get_etat(), Lorene::Tbl::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::Scalar::set_dzpuis(), Lorene::Scalar::std_spectral_base(), Lorene::Tbl::t, Lorene::Mtbl::t, Lorene::Map::val_r(), Lorene::Grille3d::x, and Lorene::Map_radial::xsr.

double Lorene::Star_rot::lspec_isco (  )  const [virtual, inherited]

Angular momentum of a particle on the ISCO.

Definition at line 275 of file star_rot_isco.C.

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

double Lorene::Star_rot::mass_b (  )  const [virtual, inherited]
double Lorene::Star_rot::mass_g (  )  const [virtual, inherited]
double Lorene::Star_rot::mean_radius (  )  const [virtual, inherited]

Mean star radius from the area $ r_{\rm mean} = \sqrt{\mathcal{A}} / 4\pi$.

Definition at line 425 of file star_rot_global.C.

References Lorene::Star_rot::area(), and Lorene::sqrt().

double Lorene::Star_rot::mom_quad (  )  const [virtual, inherited]

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 ${\bar I}_{zz}$ of the MTW (1973) reduced quadrupole moment ${\bar I}_{ij}$ by: $Q = -3/2 {\bar I}_{zz}$. Note that Q is the negative of the quadrupole moment defined by Laarakkers and Poisson, Astrophys. J. 512 , 282 (1999).

Definition at line 530 of file star_rot_global.C.

References Lorene::Star_rot::a_car, Lorene::Star_rot::ak_car, Lorene::Star_rot::bbb, Lorene::Scalar::check_dzpuis(), Lorene::Scalar::derive_cov(), Lorene::Star::ener_euler, Lorene::Map::flat_met_spher(), Lorene::Scalar::get_etat(), Lorene::Scalar::inc_dzpuis(), Lorene::Scalar::integrale(), Lorene::log(), Lorene::Star::logn, Lorene::Star::mp, Lorene::Valeur::mult_ct(), Lorene::Scalar::mult_r(), Lorene::Star::nbar, Lorene::Star_rot::p_mom_quad, Lorene::Star_rot::relativistic, Lorene::Star::s_euler, Lorene::Scalar::set_spectral_va(), and Lorene::Scalar::std_spectral_base().

void Lorene::Gravastar::operator= ( const Gravastar  ) 

Assignment to another Gravastar.

Reimplemented from Lorene::Star_rot.

ostream & Lorene::Gravastar::operator>> ( ostream &  ost  )  const [protected, virtual]
void Lorene::Star_rot::partial_display ( ostream &  ost  )  const [protected, virtual, inherited]
double Lorene::Star_rot::r_circ (  )  const [virtual, inherited]
double Lorene::Star_rot::r_isco ( ostream *  ost = 0x0  )  const [virtual, inherited]
double Lorene::Star::ray_eq (  )  const [inherited]
double Lorene::Star::ray_eq_3pis2 (  )  const [inherited]
double Lorene::Star::ray_eq_pi (  )  const [inherited]
double Lorene::Star::ray_eq_pis2 (  )  const [inherited]
double Lorene::Star::ray_pole (  )  const [inherited]
void Lorene::Star_rot::sauve ( FILE *  fich  )  const [virtual, inherited]
void Lorene::Star_rot::set_der_0x0 (  )  const [protected, virtual, inherited]
void Lorene::Star::set_enthalpy ( const Scalar ent_i  )  [inherited]

Assignment of the enthalpy field.

Definition at line 382 of file star.C.

References Lorene::Star::del_deriv(), Lorene::Star::ent, and Lorene::Star::equation_of_state().

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

Read/write of the mapping.

Definition at line 322 of file star.h.

References Lorene::Star::mp.

const Tbl & Lorene::Star_rot::surf_grav (  )  const [virtual, inherited]
double Lorene::Star_rot::tsw (  )  const [virtual, inherited]
void Lorene::Star_rot::update_metric (  )  [inherited]

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.

Definition at line 54 of file star_rot_upmetr.C.

References Lorene::Star_rot::a_car, Lorene::Star_rot::b_car, Lorene::Star_rot::bbb, Lorene::Star_rot::del_deriv(), Lorene::Scalar::div_rsint(), Lorene::Star_rot::dzeta, Lorene::exp(), Lorene::Star_rot::extrinsic_curvature(), Lorene::Star::gamma, Lorene::Map::get_bvect_spher(), Lorene::Star::logn, Lorene::Star::mp, Lorene::Star::nn, Lorene::Tensor::set(), Lorene::Scalar::std_spectral_base(), Lorene::Star_rot::tggg, and Lorene::Star_rot::unsurc2.

const Tbl & Lorene::Star::xi_surf (  )  const [inherited]

Description of the stellar surface: returns a 2-D Tbl containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$.

The stellar surface is defined as the location where the enthalpy (member ent) vanishes.

Definition at line 92 of file star_global.C.

References Lorene::Star::l_surf(), Lorene::Star::p_l_surf, and Lorene::Star::p_xi_surf.

double Lorene::Star_rot::z_eqb (  )  const [virtual, inherited]
double Lorene::Star_rot::z_eqf (  )  const [virtual, inherited]
double Lorene::Star_rot::z_pole (  )  const [virtual, inherited]

Redshift factor at North pole.

Definition at line 511 of file star_rot_global.C.

References Lorene::Star::nn, Lorene::Star_rot::p_z_pole, Lorene::Star::ray_pole(), and Lorene::Scalar::val_point().


Friends And Related Function Documentation

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

Display.


Member Data Documentation

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

Square of the metric factor A.

Definition at line 110 of file star_rot.h.

Scalar Lorene::Star_rot::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 192 of file star_rot.h.

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

Square of the metric factor B.

Definition at line 116 of file star_rot.h.

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

Metric factor B.

Definition at line 113 of file star_rot.h.

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

Shift vector.

Definition at line 228 of file star.h.

Scalar Lorene::Star_rot::dzeta [protected, inherited]

Metric potential $\zeta = \ln(AN)$.

Definition at line 140 of file star_rot.h.

Scalar Lorene::Star::ener [protected, inherited]

Total energy density in the fluid frame.

Definition at line 193 of file star.h.

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

Total energy density in the Eulerian frame.

Definition at line 198 of file star.h.

Scalar Lorene::Star::ent [protected, inherited]

Log-enthalpy.

Definition at line 190 of file star.h.

const Eos& Lorene::Star::eos [protected, inherited]

Equation of state of the stellar matter.

Definition at line 185 of file star.h.

Scalar Lorene::Star::gam_euler [protected, inherited]

Lorentz factor between the fluid and Eulerian observers.

Definition at line 204 of file star.h.

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

3-metric

Definition at line 235 of file star.h.

Scalar Lorene::Star_rot::khi_shift [protected, inherited]

Scalar $\chi$ used in the decomposition of shift , following Shibata's prescription [Prog.

Theor. Phys. 101 , 1199 (1999)] :

\[ N^i = {7\over 8} W^i - {1\over 8} \left(\nabla^i\chi+\nabla^iW^kx_k\right) \]

Definition at line 166 of file star_rot.h.

Scalar Lorene::Star::logn [protected, inherited]

Logarithm of the lapse N .

In the Newtonian case, this is the Newtonian gravitational potential (in units of $c^2$).

Definition at line 222 of file star.h.

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

Mapping associated with the star.

Definition at line 180 of file star.h.

Scalar Lorene::Star::nbar [protected, inherited]

Baryon density in the fluid frame.

Definition at line 192 of file star.h.

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

Lapse function N .

Definition at line 225 of file star.h.

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

Metric coefficient $N^\varphi$.

Definition at line 119 of file star_rot.h.

Scalar Lorene::Star_rot::nuf [protected, inherited]

Part of the Metric potential $\nu = \ln N$ = logn generated by the matter terms.

Definition at line 132 of file star_rot.h.

Scalar Lorene::Star_rot::nuq [protected, inherited]

Part of the Metric potential $\nu = \ln N$ = logn generated by the quadratic terms.

Definition at line 137 of file star_rot.h.

int Lorene::Star::nzet [protected, inherited]

Number of domains of *mp occupied by the star.

Definition at line 183 of file star.h.

double Lorene::Star_rot::omega [protected, inherited]

Rotation angular velocity ([f_unit] ).

Definition at line 107 of file star_rot.h.

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

Angular momentum.

Definition at line 238 of file star_rot.h.

double* Lorene::Star_rot::p_aplat [mutable, protected, inherited]

Flatening r_pole/r_eq.

Definition at line 243 of file star_rot.h.

double* Lorene::Star_rot::p_area [mutable, protected, inherited]

Integrated surface area.

Definition at line 244 of file star_rot.h.

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

Specific energy of a particle on the ISCO.

Definition at line 252 of file star_rot.h.

double* Lorene::Star_rot::p_f_eq [mutable, protected, inherited]

Orbital frequency at the equator.

Definition at line 255 of file star_rot.h.

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

Orbital frequency of the ISCO.

Definition at line 250 of file star_rot.h.

double* Lorene::Star_rot::p_grv2 [mutable, protected, inherited]

Error on the virial identity GRV2.

Definition at line 240 of file star_rot.h.

double* Lorene::Star_rot::p_grv3 [mutable, protected, inherited]

Error on the virial identity GRV3.

Definition at line 241 of file star_rot.h.

Itbl* Lorene::Star::p_l_surf [mutable, protected, inherited]

Description of the stellar surface: 2-D Itbl containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$.

Definition at line 260 of file star.h.

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

Specific angular momentum of a particle on the ISCO.

Definition at line 254 of file star_rot.h.

double* Lorene::Star::p_mass_b [mutable, protected, inherited]

Baryon mass.

Definition at line 268 of file star.h.

double* Lorene::Star::p_mass_g [mutable, protected, inherited]

Gravitational mass.

Definition at line 269 of file star.h.

double* Lorene::Star_rot::p_mom_quad [mutable, protected, inherited]

Quadrupole moment.

Definition at line 248 of file star_rot.h.

double* Lorene::Star_rot::p_r_circ [mutable, protected, inherited]

Circumferential radius.

Definition at line 242 of file star_rot.h.

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

Circumferential radius of the ISCO.

Definition at line 249 of file star_rot.h.

double* Lorene::Star::p_ray_eq [mutable, protected, inherited]

Coordinate radius at $\phi=0$, $\theta=\pi/2$.

Definition at line 242 of file star.h.

double* Lorene::Star::p_ray_eq_3pis2 [mutable, protected, inherited]

Coordinate radius at $\phi=3\pi/2$, $\theta=\pi/2$.

Definition at line 251 of file star.h.

double* Lorene::Star::p_ray_eq_pi [mutable, protected, inherited]

Coordinate radius at $\phi=\pi$, $\theta=\pi/2$.

Definition at line 248 of file star.h.

double* Lorene::Star::p_ray_eq_pis2 [mutable, protected, inherited]

Coordinate radius at $\phi=\pi/2$, $\theta=\pi/2$.

Definition at line 245 of file star.h.

double* Lorene::Star::p_ray_pole [mutable, protected, inherited]

Coordinate radius at $\theta=0$.

Definition at line 254 of file star.h.

Tbl* Lorene::Star_rot::p_surf_grav [mutable, protected, inherited]

Surface gravity (along the theta direction).

Definition at line 256 of file star_rot.h.

double* Lorene::Star_rot::p_tsw [mutable, protected, inherited]

Ratio T/W.

Definition at line 239 of file star_rot.h.

Tbl* Lorene::Star::p_xi_surf [mutable, protected, inherited]

Description of the stellar surface: 2-D Tbl containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$.

Definition at line 266 of file star.h.

double* Lorene::Star_rot::p_z_eqb [mutable, protected, inherited]

Backward redshift factor at equator.

Definition at line 246 of file star_rot.h.

double* Lorene::Star_rot::p_z_eqf [mutable, protected, inherited]

Forward redshift factor at equator.

Definition at line 245 of file star_rot.h.

double* Lorene::Star_rot::p_z_pole [mutable, protected, inherited]

Redshift factor at North pole.

Definition at line 247 of file star_rot.h.

Scalar Lorene::Star::press [protected, inherited]

Fluid pressure.

Definition at line 194 of file star.h.

bool Lorene::Star_rot::relativistic [protected, inherited]

Indicator of relativity: true for a relativistic star, false for a Newtonian one.

Definition at line 100 of file star_rot.h.

double Lorene::Gravastar::rho_core [protected]

Energy density in gravastar's core.

Definition at line 57 of file gravastar.h.

Scalar Lorene::Star::s_euler [protected, inherited]

Trace of the stress scalar in the Eulerian frame.

Definition at line 201 of file star.h.

Scalar Lorene::Star_rot::ssjm1_dzeta [protected, inherited]

Effective source at the previous step for the resolution of the Poisson equation for dzeta .

Definition at line 209 of file star_rot.h.

Scalar Lorene::Star_rot::ssjm1_khi [protected, inherited]

Effective source at the previous step for the resolution of the Poisson equation for the scalar $\chi$ by means of Map_et::poisson .

$\chi$ is an intermediate quantity for the resolution of the elliptic equation for the shift vector $N^i$

Definition at line 222 of file star_rot.h.

Scalar Lorene::Star_rot::ssjm1_nuf [protected, inherited]

Effective source at the previous step for the resolution of the Poisson equation for nuf by means of Map_et::poisson .

Definition at line 198 of file star_rot.h.

Scalar Lorene::Star_rot::ssjm1_nuq [protected, inherited]

Effective source at the previous step for the resolution of the Poisson equation for nuq by means of Map_et::poisson .

Definition at line 204 of file star_rot.h.

Scalar Lorene::Star_rot::ssjm1_tggg [protected, inherited]

Effective source at the previous step for the resolution of the Poisson equation for tggg .

Definition at line 214 of file star_rot.h.

Vector Lorene::Star_rot::ssjm1_wshift [protected, inherited]

Effective source at the previous step for the resolution of the vector Poisson equation for $W^i$.

$W^i$ is an intermediate quantity for the resolution of the elliptic equation for the shift vector $N^i$ (Components with respect to the Cartesian triad associated with the mapping mp )

Definition at line 231 of file star_rot.h.

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

Spatial part of the stress-energy tensor with respect to the Eulerian observer.

Definition at line 212 of file star.h.

Scalar Lorene::Star_rot::tggg [protected, inherited]

Metric potential $\tilde G = (NB-1) r\sin\theta$.

Definition at line 143 of file star_rot.h.

Sym_tensor Lorene::Star_rot::tkij [protected, inherited]

Tensor ${\tilde K_{ij}}$ related to the extrinsic curvature tensor by ${\tilde K_{ij}} = B^{-2} K_{ij}$.

tkij contains the Cartesian components of ${\tilde K_{ij}}$.

Definition at line 173 of file star_rot.h.

Scalar Lorene::Star_rot::tnphi [protected, inherited]

Component $\tilde N^\varphi = N^\varphi r\sin\theta$ of the shift vector.

Definition at line 124 of file star_rot.h.

Vector Lorene::Star::u_euler [protected, inherited]

Fluid 3-velocity with respect to the Eulerian observer.

Definition at line 207 of file star.h.

double Lorene::Star_rot::unsurc2 [protected, inherited]

$1/c^2$ : unsurc2=1 for a relativistic star, 0 for a Newtonian one.

Definition at line 105 of file star_rot.h.

Scalar Lorene::Star_rot::uuu [protected, inherited]

Norm of u_euler.

Definition at line 127 of file star_rot.h.

Vector Lorene::Star_rot::w_shift [protected, inherited]

Vector $W^i$ used in the decomposition of shift , following Shibata's prescription [Prog.

Theor. Phys. 101 , 1199 (1999)] :

\[ N^i = {7\over 8} W^i - {1\over 8} \left(\nabla^i\chi+\nabla^iW^kx_k\right) \]

NB: w_shift contains the components of $W^i$ with respect to the Cartesian triad associated with the mapping mp .

Definition at line 156 of file star_rot.h.


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

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