Class for relativistic differentially rotating stars in Dirac gauge and maximal slicing. More...

#include <star_rot_dirac_diff.h>

Inheritance diagram for Lorene::Star_rot_Dirac_diff:

Public Member Functions
	Star_rot_Dirac_diff (Map &mp_i, int nzet_i, const Eos &eos_i, double(frot_i)(double, const Tbl &), double(primfrot_i)(double, const Tbl &), const Tbl &par_frot_i)
	Standard constructor. More...

	Star_rot_Dirac_diff (const Star_rot_Dirac_diff &)
	Copy constructor. More...

	Star_rot_Dirac_diff (Map &mp_i, const Eos &eos_i, FILE fich, double(frot_i)(double, const Tbl &), double(*primfrot_i)(double, const Tbl &))
	Constructor from a file (see `sauve(FILE*)` ). More...

virtual	~Star_rot_Dirac_diff ()
	Destructor. More...

void	operator= (const Star_rot_Dirac_diff &)
	Assignment to another `Star_rot_Dirac_diff`. More...

const Scalar &	get_omega_field () const
	Returns the angular velocity field $\Omega$ . More...

virtual double	get_omega_c () const
	Returns the central value of the rotation angular velocity ([f_unit] ) More...

virtual void	sauve (FILE *) const
	Save in a file. More...

virtual double	tsw () const
	Ratio T/W. More...

virtual void	hydro_euler ()
	Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame. More...

void	fait_omega_field (double omeg_min, double omeg_max, double precis, int nitermax)
	Computes $\Omega(r,\theta)$ (member `omega_field` ). More...

void	fait_prim_field ()
	Computes the member `prim_field` from `omega_field` . More...

double	funct_omega (double omeg) const
	Evaluates $F(\Omega)$ , where F is the function defining the rotation profile. More...

double	prim_funct_omega (double omeg) const
	Evaluates the primitive of $F(\Omega)$ , where F is the function defining the rotation profile. More...

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)
	Computes an equilibrium configuration. More...

int	get_relat () const
	Returns the relativity parameter. More...

bool	is_relativistic () const
	Checks whether the star is computed using a relativistic theory. More...

int	spectral_filter_order () const
	Returns the filtering order. More...

double	get_omega () const
	Returns the rotation angular velocity $\Omega$ . More...

const Scalar &	get_psi4 () const
	Returns the conformal factor $\Psi^4$ . More...

const Scalar &	get_psi2 () const
	Returns $\Psi^2$ . More...

const Scalar &	get_qqq () const
	Returns $Q=\Psi^2 N$ . More...

const Scalar &	get_ln_psi () const
	Returns $ln(\Psi)$ . More...

const Vector &	get_j_euler () const
	Returns the momentum density 3-vector with respect to the Eulerian observer. More...

const Scalar &	get_v2 () const
	Returns $\gamma_{ij}v^i v^j$ . More...

const Metric	get_tgamma () const
	Returns the conformal metric $\tilde{\gamma}_{ij}$ . More...

const Sym_tensor	get_aa () const
	Returns $A^{ij}$ . More...

const Sym_tensor	get_taa () const
	Returns $\tilde{A}_{ij}$ . More...

const Scalar	get_aa_quad () const
	Returns $\tilde{A}_{ij} A^{ij}$ . More...

const Sym_tensor_trans	get_hh () const
	Returns $h^{ij}$ . More...

virtual double	mass_b () const
	Baryonic mass. More...

virtual double	mass_g () const
	Gravitational mass. More...

virtual double	angu_mom () const
	Angular momentum. More...

virtual double	grv2 () const
	Error on the virial identity GRV2. More...

virtual double	grv3 () const
	Error on the virial identity GRV3. More...

virtual double	aplat () const
	Flattening r_pole/r_eq. More...

virtual double	r_circ () const
	Circumferential equatorial radius. More...

virtual double	rp_circ () const
	Circumferential polar radius. More...

virtual double	ellipt () const
	Ellipticity e. More...

void	update_metric ()
	Computes metric quantities from known potentials. More...

void	solve_logn_f (Scalar &ln_f_new) const
	Solution of the two scalar Poisson equations for rotating stars in Dirac gauge. More...

void	solve_logn_q (Scalar &ln_q_new) const
	Solution of the two scalar Poisson equations for rotating stars in Dirac gauge. More...

void	solve_qqq (Scalar &q_new) const
	Solution of the two scalar Poisson equations for rotating stars in Dirac gauge. More...

void	solve_shift (Vector &shift_new) const
	Solution of the shift equation for rotating stars in Dirac gauge. More...

void	solve_hij (Sym_tensor_trans &hij_new) const
	Solution of the tensor Poisson equation for rotating stars in Dirac gauge. More...

Map &	set_mp ()
	Read/write of the mapping. More...

void	set_enthalpy (const Scalar &)
	Assignment of the enthalpy field. More...

void	equation_of_state ()
	Computes the proper baryon and energy density, as well as pressure from the enthalpy. More...

virtual void	equilibrium_spher (double ent_c, double precis=1.e-14, const Tbl *pent_limit=0x0)
	Computes a spherical static configuration. More...

const Map &	get_mp () const
	Returns the mapping. More...

int	get_nzet () const
	Returns the number of domains occupied by the star. More...

const Eos &	get_eos () const
	Returns the equation of state. More...

const Scalar &	get_ent () const
	Returns the enthalpy field. More...

const Scalar &	get_nbar () const
	Returns the proper baryon density. More...

const Scalar &	get_ener () const
	Returns the proper total energy density. More...

const Scalar &	get_press () const
	Returns the fluid pressure. More...

const Scalar &	get_ener_euler () const
	Returns the total energy density with respect to the Eulerian observer. More...

const Scalar &	get_s_euler () const
	Returns the trace of the stress tensor in the Eulerian frame. More...

const Scalar &	get_gam_euler () const
	Returns the Lorentz factor between the fluid and Eulerian observers. More...

const Vector &	get_u_euler () const
	Returns the fluid 3-velocity with respect to the Eulerian observer. More...

const Tensor &	get_stress_euler () const
	Returns the spatial part of the stress-energy tensor with respect to the Eulerian observer. More...

const Scalar &	get_logn () const
	Returns the logarithm of the lapse N. More...

const Scalar &	get_nn () const
	Returns the lapse function N. More...

const Vector &	get_beta () const
	Returns the shift vector $\beta^i$ . More...

const Scalar &	get_lnq () const

const Metric &	get_gamma () const
	Returns the 3-metric $\gamma$ . More...

double	ray_eq () const
	Coordinate radius at $\phi=0$ , $\theta=\pi/2$ [r_unit]. More...

double	ray_eq_pis2 () const
	Coordinate radius at $\phi=\pi/2$ , $\theta=\pi/2$ [r_unit]. More...

double	ray_eq_pi () const
	Coordinate radius at $\phi=\pi$ , $\theta=\pi/2$ [r_unit]. More...

double	ray_eq_3pis2 () const
	Coordinate radius at $\phi=3\pi/2$ , $\theta=\pi/2$ [r_unit]. More...

double	ray_pole () const
	Coordinate radius at $\theta=0$ [r_unit]. More...

virtual const Itbl &	l_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 $(\theta', \phi')$ . More...

const Tbl &	xi_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 $(\theta', \phi')$ . More...

Protected Member Functions
virtual ostream &	operator>> (ostream &) const
	Operator >> (virtual function called by the operator <<). More...

virtual void	del_deriv () const
	Deletes all the derived quantities. More...

void	set_der_0x0 () const
	Sets to `0x0` all the pointers on derived quantities. More...

virtual void	del_hydro_euler ()
	Sets to `ETATNONDEF` (undefined state) the hydrodynamical quantities relative to the Eulerian observer. More...

Protected Attributes
double(*	frot )(double, const Tbl &)
	Function $F(\Omega)$ defining the rotation profile. More...

double(*	primfrot )(double, const Tbl &)
	Primitive of the function $F(\Omega)$ , which vanishes at the stellar center. More...

Tbl	par_frot
	Parameters of the function $F(\Omega)$ . More...

Scalar	omega_field
	Field $\Omega(r,\theta)$ . More...

double	omega_min
	Minimum value of $\Omega$ . More...

double	omega_max
	Maximum value of $\Omega$ . More...

Scalar	prim_field
	Field $\int_{\Omega_{\rm c}}^\Omega F(\Omega') \, d\Omega'$ . More...

int	relat_type
	Relativistic flag. More...

int	spectral_filter
	Spectral exponential filtering order. More...

double	omega
	Rotation angular velocity ([f_unit] ) More...

Scalar	psi4
	Conformal factor $\Psi^4$ . More...

Scalar	psi2
	$\Psi^2$ More...

Scalar	qqq
	$Q = \Psi^2 N$ More...

Scalar	ln_psi
	$ln(\Psi)$ More...

Vector	j_euler
	Momentum density 3-vector with respect to the Eulerian observer. More...

Scalar	v2
	$\gamma_{ij}v^i v^j$ More...

const Metric_flat &	flat
	flat metric $f_{ij}$ (spherical components) More...

Metric	tgamma
	$\tilde{\gamma}_{ij}$ More...

Sym_tensor	aa
	$A^{ij}$ More...

Sym_tensor	taa
	$\tilde{A}_{ij}$ More...

Scalar	aa_quad
	$\tilde{A}_{ij} A^{ij}$ More...

Sym_tensor_trans	hh
	$h^{ij}$ is defined by $\tilde{\gamma}^{ij}=f^{ij}+h^{ij}$ . More...

double *	p_angu_mom
	Angular momentum. More...

double *	p_grv2
	Error on the virial identity GRV2. More...

double *	p_grv3
	Error on the virial identity GRV3. More...

double *	p_tsw
	Ratio T/W. More...

double *	p_r_circ
	Circumferential equatorial radius. More...

double *	p_rp_circ
	Circumferential polar radius. More...

Map &	mp
	Mapping associated with the star. More...

int	nzet
	Number of domains of `*mp` occupied by the star. More...

const Eos &	eos
	Equation of state of the stellar matter. More...

Scalar	ent
	Log-enthalpy. More...

Scalar	nbar
	Baryon density in the fluid frame. More...

Scalar	ener
	Total energy density in the fluid frame. More...

Scalar	press
	Fluid pressure. More...

Scalar	ener_euler
	Total energy density in the Eulerian frame. More...

Scalar	s_euler
	Trace of the stress scalar in the Eulerian frame. More...

Scalar	gam_euler
	Lorentz factor between the fluid and Eulerian observers. More...

Vector	u_euler
	Fluid 3-velocity with respect to the Eulerian observer. More...

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

Scalar	logn
	Logarithm of the lapse N . More...

Scalar	nn
	Lapse function N . More...

Vector	beta
	Shift vector. More...

Scalar	lnq

Metric	gamma
	3-metric More...

double *	p_ray_eq
	Coordinate radius at $\phi=0$ , $\theta=\pi/2$ . More...

double *	p_ray_eq_pis2
	Coordinate radius at $\phi=\pi/2$ , $\theta=\pi/2$ . More...

double *	p_ray_eq_pi
	Coordinate radius at $\phi=\pi$ , $\theta=\pi/2$ . More...

double *	p_ray_eq_3pis2
	Coordinate radius at $\phi=3\pi/2$ , $\theta=\pi/2$ . More...

double *	p_ray_pole
	Coordinate radius at $\theta=0$ . More...

Itbl *	p_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 $(\theta', \phi')$ . More...

Tbl *	p_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 $(\theta', \phi')$ . More...

double *	p_mass_b
	Baryon mass. More...

double *	p_mass_g
	Gravitational mass. More...

Friends
ostream &	operator<< (ostream &, const Star &)
	Display. More...

Detailed Description

Class for relativistic differentially rotating stars in Dirac gauge and maximal slicing.

(*** Under development ***)()

Definition at line 49 of file star_rot_dirac_diff.h.

Constructor & Destructor Documentation

◆ Star_rot_Dirac_diff() [1/3]

Lorene::Star_rot_Dirac_diff::Star_rot_Dirac_diff	(	Map &	mp_i,
		int	nzet_i,
		const Eos &	eos_i,
		double(*)(double, const Tbl &)	frot_i,
		double(*)(double, const Tbl &)	primfrot_i,
		const Tbl &	par_frot_i
	)

Standard constructor.

Parameters

mp_i	Mapping on which the star will be defined
nzet_i	Number of domains occupied by the star
relat	should be `true` for a relativistic star, `false` for a Newtonian one
eos_i	Equation of state of the stellar matter
frot_i	Function $F(\Omega)$ defining the rotation profile.
primfrot_i	Primitive of $F(\Omega)$ which vanishes at the stellar center
par_frot_i	Parameters of functions `frot_i` and `primfrot_i` , `par_frot_i(0)` being the central value of $\Omega$ .

Definition at line 53 of file star_rot_dirac_diff.C.

References omega_field, omega_max, omega_min, and prim_field.

◆ Star_rot_Dirac_diff() [2/3]

Lorene::Star_rot_Dirac_diff::Star_rot_Dirac_diff ( const Star_rot_Dirac_diff & star )

Copy constructor.

Definition at line 76 of file star_rot_dirac_diff.C.

◆ Star_rot_Dirac_diff() [3/3]

Lorene::Star_rot_Dirac_diff::Star_rot_Dirac_diff	(	Map &	mp_i,
		const Eos &	eos_i,
		FILE *	fich,
		double(*)(double, const Tbl &)	frot_i,
		double(*)(double, const Tbl &)	primfrot_i
	)

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

Parameters

mp_i	Mapping on which the star will be defined
eos_i	Equation of state of the stellar matter
fich	input file (must have been created by the function `sauve` )
frot_i	Function $F(\Omega)$ defining the rotation profile.
primfrot_i	Primitive of $F(\Omega)$ which vanishes at the stellar center

Definition at line 90 of file star_rot_dirac_diff.C.

References fait_prim_field(), Lorene::fread_be(), Lorene::Map::get_mg(), Lorene::Star::mp, omega_field, omega_max, and omega_min.

◆ ~Star_rot_Dirac_diff()

Lorene::Star_rot_Dirac_diff::~Star_rot_Dirac_diff ( )

virtual

Destructor.

Definition at line 116 of file star_rot_dirac_diff.C.

Member Function Documentation

◆ angu_mom()

double Lorene::Star_rot_Dirac::angu_mom ( ) const

virtualinherited

Angular momentum.

Definition at line 146 of file strot_dirac_global.C.

References Lorene::contract(), Lorene::Metric::cov(), Lorene::Metric::determinant(), Lorene::Star::gamma, Lorene::Map::get_bvect_spher(), Lorene::Scalar::integrale(), Lorene::Star_rot_Dirac::j_euler, Lorene::Star::mp, Lorene::Star_rot_Dirac::p_angu_mom, Lorene::Vector::set(), Lorene::Scalar::set_etat_zero(), Lorene::sqrt(), and Lorene::Scalar::std_spectral_base().

◆ aplat()

double Lorene::Star_rot_Dirac::aplat ( ) const

virtualinherited

Flattening r_pole/r_eq.

Definition at line 421 of file strot_dirac_global.C.

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

◆ del_deriv()

void Lorene::Star_rot_Dirac::del_deriv ( ) const

protectedvirtualinherited

Deletes all the derived quantities.

Reimplemented from Lorene::Star.

Definition at line 235 of file star_rot_dirac.C.

References Lorene::Star::del_deriv(), Lorene::Star_rot_Dirac::p_angu_mom, Lorene::Star_rot_Dirac::p_grv2, Lorene::Star_rot_Dirac::p_grv3, Lorene::Star_rot_Dirac::p_r_circ, Lorene::Star_rot_Dirac::p_rp_circ, Lorene::Star_rot_Dirac::p_tsw, and Lorene::Star_rot_Dirac::set_der_0x0().

◆ del_hydro_euler()

void Lorene::Star_rot_Dirac::del_hydro_euler ( )

protectedvirtualinherited

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

Reimplemented from Lorene::Star.

Definition at line 263 of file star_rot_dirac.C.

References Lorene::Star_rot_Dirac::del_deriv(), Lorene::Star::del_hydro_euler(), Lorene::Star_rot_Dirac::j_euler, Lorene::Scalar::set_etat_nondef(), Lorene::Tensor::set_etat_nondef(), and Lorene::Star_rot_Dirac::v2.

◆ ellipt()

double Lorene::Star_rot_Dirac::ellipt ( ) const

virtualinherited

Ellipticity e.

Defined as $e = \sqrt{1 - \left( \frac{R^c_e}{R^c_p} \right)^2}$ , where $R^c_e$ and $R^c_p$ are, respectively, the equatorial and polar circumferential radius, given by r_circ() and rp_circ().

Definition at line 431 of file strot_dirac_global.C.

References Lorene::Star_rot_Dirac::r_circ(), Lorene::Star_rot_Dirac::rp_circ(), and Lorene::sqrt().

◆ equation_of_state()

void Lorene::Star::equation_of_state ( )

inherited

Computes the proper baryon and energy density, as well as pressure from the enthalpy.

Definition at line 465 of file star.C.

References Lorene::Param::add_int(), Lorene::Scalar::allocate_all(), Lorene::Star::del_deriv(), Lorene::Star::ener, Lorene::Eos::ener_ent(), Lorene::Star::ent, Lorene::Star::eos, Lorene::Mg3d::get_grille3d(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Star::mp, Lorene::Star::nbar, Lorene::Eos::nbar_ent(), Lorene::Star::nzet, Lorene::Star::press, Lorene::Eos::press_ent(), Lorene::Mtbl::set(), Lorene::Scalar::set_domain(), Lorene::Mtbl::set_etat_qcq(), Lorene::Tbl::set_etat_qcq(), Lorene::Scalar::set_etat_qcq(), Lorene::Scalar::std_spectral_base(), Lorene::Mtbl::t, and Lorene::Grille3d::x.

◆ equilibrium()

void Lorene::Star_rot_Dirac_diff::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
	)

virtual

Computes an equilibrium configuration.

Parameters

ent_c	[input] Central enthalpy
omega0	[input] Requested central angular velocity (if `fact_omega=1`. )
fact_omega	[input] 1.01 = search for the Keplerian frequency, = 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 central 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 47 of file strot_dirac_diff_equil.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_t(), and Lorene::Star::mp.

◆ equilibrium_spher()

void Lorene::Star::equilibrium_spher	(	double	ent_c,
		double	precis = `1.e-14`,
		const Tbl *	pent_limit = `0x0`
	)

virtualinherited

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_af::get_alpha(), Lorene::Map_et::get_alpha(), Lorene::Map_af::get_beta(), Lorene::Map_et::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::Tensor::set_etat_zero(), Lorene::sqrt(), Lorene::Scalar::std_spectral_base(), Lorene::Star::u_euler, Lorene::Scalar::val_grid_point(), and Lorene::Map::val_r().

◆ fait_omega_field()

void Lorene::Star_rot_Dirac_diff::fait_omega_field	(	double	omeg_min,
		double	omeg_max,
		double	precis,
		int	nitermax
	)

Computes $\Omega(r,\theta)$ (member omega_field ).

The computation amounts to solving the equation

$F(\Omega) - {\gamma_{\varphi \varphi} (\beta^\varphi + \Omega) \over N^2 - \gamma_{\varphi \varphi}(\beta^\varphi + \Omega)^2} = 0$

for $\Omega$ .

Parameters

omeg_min	[input] Lower bound of the interval for searching omega
omeg_max	[input] Higher bound of the interval for searching omega
precis	[input] Required precision in the determination of the zero by the secant method
nitermax	[input] Maximum number of iterations in the secant method to compute the zero.

Definition at line 52 of file strot_dirac_diff_faitomeg.C.

References Lorene::Param::add_int(), Lorene::Param::add_scalar(), Lorene::Param::add_star(), Lorene::Scalar::annule(), Lorene::Star::beta, Lorene::Metric::cov(), Lorene::Scalar::div_rsint(), Lorene::Star::gamma, Lorene::Scalar::get_etat(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Star::mp, Lorene::Scalar::mult_rsint(), omega_field, Lorene::Star_rot_Dirac::psi4, and Lorene::Star_rot_Dirac::qqq.

◆ fait_prim_field()

void Lorene::Star_rot_Dirac_diff::fait_prim_field ( )

Computes the member prim_field from omega_field .

Definition at line 176 of file strot_dirac_diff_faitomeg.C.

References Lorene::Scalar::allocate_all(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Star::mp, Lorene::Star::nzet, omega_field, par_frot, prim_field, primfrot, Lorene::Tbl::set(), Lorene::Scalar::set_domain(), Lorene::Scalar::std_spectral_base(), and Lorene::Scalar::val_grid_point().

◆ funct_omega()

double Lorene::Star_rot_Dirac_diff::funct_omega ( double omeg ) const

Evaluates $F(\Omega)$ , where F is the function defining the rotation profile.

This function is linked to the components of the fluid 4-velocity by

$F(\Omega) = u^t u_\varphi \ .$

funct_omega calls frot with the parameters par_frot .

Parameters

omeg	[input] value of $\Omega$

Returns: value of $F(\Omega)$

Definition at line 250 of file star_rot_dirac_diff.C.

References frot, and par_frot.

◆ get_aa()

const Sym_tensor Lorene::Star_rot_Dirac::get_aa ( ) const

inlineinherited

Returns $A^{ij}$ .

Definition at line 245 of file star_rot_dirac.h.

References Lorene::Star_rot_Dirac::aa.

◆ get_aa_quad()

const Scalar Lorene::Star_rot_Dirac::get_aa_quad ( ) const

inlineinherited

Returns $\tilde{A}_{ij} A^{ij}$ .

Definition at line 255 of file star_rot_dirac.h.

References Lorene::Star_rot_Dirac::aa_quad.

◆ get_beta()

const Vector& Lorene::Star::get_beta ( ) const

inlineinherited

Returns the shift vector $\beta^i$ .

Definition at line 402 of file star.h.

References Lorene::Star::beta.

◆ get_ener()

const Scalar& Lorene::Star::get_ener ( ) const

inlineinherited

Returns the proper total energy density.

Definition at line 370 of file star.h.

References Lorene::Star::ener.

◆ get_ener_euler()

const Scalar& Lorene::Star::get_ener_euler ( ) const

inlineinherited

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

Definition at line 376 of file star.h.

References Lorene::Star::ener_euler.

◆ get_ent()

const Scalar& Lorene::Star::get_ent ( ) const

inlineinherited

Returns the enthalpy field.

Definition at line 364 of file star.h.

References Lorene::Star::ent.

◆ get_eos()

const Eos& Lorene::Star::get_eos ( ) const

inlineinherited

Returns the equation of state.

Definition at line 361 of file star.h.

References Lorene::Star::eos.

◆ get_gam_euler()

const Scalar& Lorene::Star::get_gam_euler ( ) const

inlineinherited

Returns the Lorentz factor between the fluid and Eulerian observers.

Definition at line 382 of file star.h.

References Lorene::Star::gam_euler.

◆ get_gamma()

const Metric& Lorene::Star::get_gamma ( ) const

inlineinherited

Returns the 3-metric $\gamma$ .

Definition at line 409 of file star.h.

References Lorene::Star::gamma.

◆ get_hh()

const Sym_tensor_trans Lorene::Star_rot_Dirac::get_hh ( ) const

inlineinherited

Returns $h^{ij}$ .

Definition at line 260 of file star_rot_dirac.h.

References Lorene::Star_rot_Dirac::hh.

◆ get_j_euler()

const Vector& Lorene::Star_rot_Dirac::get_j_euler ( ) const

inlineinherited

Returns the momentum density 3-vector with respect to the Eulerian observer.

Definition at line 227 of file star_rot_dirac.h.

References Lorene::Star_rot_Dirac::j_euler.

◆ get_ln_psi()

const Scalar& Lorene::Star_rot_Dirac::get_ln_psi ( ) const

inlineinherited

Returns $ln(\Psi)$ .

Definition at line 217 of file star_rot_dirac.h.

References Lorene::Star_rot_Dirac::ln_psi.

◆ get_logn()

const Scalar& Lorene::Star::get_logn ( ) const

inlineinherited

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.

◆ get_mp()

const Map& Lorene::Star::get_mp ( ) const

inlineinherited

Returns the mapping.

Definition at line 355 of file star.h.

References Lorene::Star::mp.

◆ get_nbar()

const Scalar& Lorene::Star::get_nbar ( ) const

inlineinherited

Returns the proper baryon density.

Definition at line 367 of file star.h.

References Lorene::Star::nbar.

◆ get_nn()

const Scalar& Lorene::Star::get_nn ( ) const

inlineinherited

Returns the lapse function N.

Definition at line 399 of file star.h.

References Lorene::Star::nn.

◆ get_nzet()

int Lorene::Star::get_nzet ( ) const

inlineinherited

Returns the number of domains occupied by the star.

Definition at line 358 of file star.h.

References Lorene::Star::nzet.

◆ get_omega()

double Lorene::Star_rot_Dirac::get_omega ( ) const

inlineinherited

Returns the rotation angular velocity $\Omega$ .

Definition at line 196 of file star_rot_dirac.h.

References Lorene::Star_rot_Dirac::omega.

◆ get_omega_c()

double Lorene::Star_rot_Dirac_diff::get_omega_c ( ) const

virtual

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

Definition at line 262 of file star_rot_dirac_diff.C.

References omega_field, and Lorene::Scalar::val_grid_point().

◆ get_omega_field()

const Scalar& Lorene::Star_rot_Dirac_diff::get_omega_field ( ) const

inline

Returns the angular velocity field $\Omega$ .

Definition at line 149 of file star_rot_dirac_diff.h.

References omega_field.

◆ get_press()

const Scalar& Lorene::Star::get_press ( ) const

inlineinherited

Returns the fluid pressure.

Definition at line 373 of file star.h.

References Lorene::Star::press.

◆ get_psi2()

const Scalar& Lorene::Star_rot_Dirac::get_psi2 ( ) const

inlineinherited

Returns $\Psi^2$ .

Definition at line 207 of file star_rot_dirac.h.

References Lorene::Star_rot_Dirac::psi2.

◆ get_psi4()

const Scalar& Lorene::Star_rot_Dirac::get_psi4 ( ) const

inlineinherited

Returns the conformal factor $\Psi^4$ .

Definition at line 202 of file star_rot_dirac.h.

References Lorene::Star_rot_Dirac::psi4.

◆ get_qqq()

const Scalar& Lorene::Star_rot_Dirac::get_qqq ( ) const

inlineinherited

Returns $Q=\Psi^2 N$ .

Definition at line 212 of file star_rot_dirac.h.

References Lorene::Star_rot_Dirac::qqq.

◆ get_relat()

int Lorene::Star_rot_Dirac::get_relat ( ) const

inlineinherited

Returns the relativity parameter.

Definition at line 185 of file star_rot_dirac.h.

References Lorene::Star_rot_Dirac::relat_type.

◆ get_s_euler()

const Scalar& Lorene::Star::get_s_euler ( ) const

inlineinherited

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

Definition at line 379 of file star.h.

References Lorene::Star::s_euler.

◆ get_stress_euler()

const Tensor& Lorene::Star::get_stress_euler ( ) const

inlineinherited

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.

◆ get_taa()

const Sym_tensor Lorene::Star_rot_Dirac::get_taa ( ) const

inlineinherited

Returns $\tilde{A}_{ij}$ .

Definition at line 250 of file star_rot_dirac.h.

References Lorene::Star_rot_Dirac::taa.

◆ get_tgamma()

const Metric Lorene::Star_rot_Dirac::get_tgamma ( ) const

inlineinherited

Returns the conformal metric $\tilde{\gamma}_{ij}$ .

Definition at line 240 of file star_rot_dirac.h.

References Lorene::Star_rot_Dirac::tgamma.

◆ get_u_euler()

const Vector& Lorene::Star::get_u_euler ( ) const

inlineinherited

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

Definition at line 385 of file star.h.

References Lorene::Star::u_euler.

◆ get_v2()

const Scalar& Lorene::Star_rot_Dirac::get_v2 ( ) const

inlineinherited

Returns $\gamma_{ij}v^i v^j$ .

Definition at line 232 of file star_rot_dirac.h.

References Lorene::Star_rot_Dirac::v2.

◆ grv2()

double Lorene::Star_rot_Dirac::grv2 ( ) const

virtualinherited

Error on the virial identity GRV2.

Definition at line 207 of file strot_dirac_global.C.

References Lorene::Star_rot_Dirac::aa, Lorene::Metric::con(), Lorene::Metric::cov(), Lorene::Scalar::div_r_dzpuis(), Lorene::Scalar::dsdr(), Lorene::Scalar::dsdt(), Lorene::Star::ener_euler, Lorene::Star::gamma, Lorene::Star::logn, Lorene::Star_rot_Dirac::p_grv2, Lorene::Star::press, Lorene::sqrt(), Lorene::Scalar::std_spectral_base(), Lorene::Star_rot_Dirac::taa, and Lorene::Star_rot_Dirac::v2.

◆ grv3()

double Lorene::Star_rot_Dirac::grv3 ( ) const

virtualinherited

Error on the virial identity GRV3.

Definition at line 276 of file strot_dirac_global.C.

References Lorene::Star_rot_Dirac::aa_quad, Lorene::Metric::con(), Lorene::Metric::connect(), Lorene::contract(), Lorene::Scalar::derive_con(), Lorene::Scalar::derive_cov(), Lorene::Metric::determinant(), Lorene::Star::gamma, Lorene::Connection::get_delta(), Lorene::Scalar::integrale(), Lorene::Star::logn, Lorene::Star_rot_Dirac::p_grv3, Lorene::Star::s_euler, Lorene::sqrt(), and Lorene::Scalar::std_spectral_base().

◆ hydro_euler()

void Lorene::Star_rot_Dirac_diff::hydro_euler ( )

virtual

Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame.

The calculation is performed starting from the quantities omega_field , ent , ener , press , and a_car ,
which are supposed to be up to date.
From these, the following fields are updated: gam_euler , u_euler , ener_euler , s_euler .

Reimplemented from Lorene::Star_rot_Dirac.

Definition at line 44 of file strot_dirac_diff_hydro.C.

References Lorene::Star::beta, Lorene::Metric::con(), Lorene::contract(), Lorene::Metric::cov(), Lorene::Star_rot_Dirac::del_deriv(), Lorene::Star::ener, Lorene::Star::ener_euler, Lorene::Star::gam_euler, Lorene::Star::gamma, Lorene::Star_rot_Dirac::j_euler, Lorene::Scalar::mult_rsint(), Lorene::Star::nn, omega_field, Lorene::Star::press, Lorene::Star::s_euler, Lorene::Vector::set(), Lorene::Scalar::set_etat_zero(), Lorene::sqrt(), Lorene::Vector::std_spectral_base(), Lorene::Tensor::std_spectral_base(), Lorene::Scalar::std_spectral_base(), Lorene::Star::stress_euler, Lorene::Star::u_euler, and Lorene::Star_rot_Dirac::v2.

◆ is_relativistic()

bool Lorene::Star_rot_Dirac::is_relativistic ( ) const

inlineinherited

Checks whether the star is computed using a relativistic theory.

Definition at line 188 of file star_rot_dirac.h.

References Lorene::Star_rot_Dirac::relat_type.

◆ l_surf()

const Itbl & Lorene::Star::l_surf ( ) const

virtualinherited

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 in Lorene::Star_rot.

Definition at line 66 of file star_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.

◆ mass_b()

double Lorene::Star_rot_Dirac::mass_b ( ) const

virtualinherited

Baryonic mass.

Implements Lorene::Star.

Definition at line 97 of file strot_dirac_global.C.

References Lorene::Metric::determinant(), Lorene::Star::gam_euler, Lorene::Star::gamma, Lorene::Scalar::integrale(), Lorene::Star::nbar, Lorene::Star::p_mass_b, Lorene::sqrt(), and Lorene::Scalar::std_spectral_base().

◆ mass_g()

double Lorene::Star_rot_Dirac::mass_g ( ) const

virtualinherited

Gravitational mass.

Implements Lorene::Star.

Definition at line 120 of file strot_dirac_global.C.

References Lorene::Star::beta, Lorene::contract(), Lorene::Metric::cov(), Lorene::Metric::determinant(), Lorene::Star::ener_euler, Lorene::Star::gamma, Lorene::Scalar::integrale(), Lorene::Star_rot_Dirac::j_euler, Lorene::Star::nn, Lorene::Star::p_mass_g, Lorene::Star::s_euler, Lorene::sqrt(), and Lorene::Scalar::std_spectral_base().

◆ operator=()

void Lorene::Star_rot_Dirac_diff::operator= ( const Star_rot_Dirac_diff & star )

Assignment to another Star_rot_Dirac_diff.

Definition at line 126 of file star_rot_dirac_diff.C.

References frot, omega_field, omega_max, omega_min, Lorene::Star_rot_Dirac::operator=(), par_frot, prim_field, and primfrot.

◆ operator>>()

ostream & Lorene::Star_rot_Dirac_diff::operator>> ( ostream & ost ) const

protectedvirtual

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

Reimplemented from Lorene::Star_rot_Dirac.

Definition at line 170 of file star_rot_dirac_diff.C.

◆ prim_funct_omega()

double Lorene::Star_rot_Dirac_diff::prim_funct_omega ( double omeg ) const

Evaluates the primitive of $F(\Omega)$ , where F is the function defining the rotation profile.

Parameters

omeg	[input] value of $\Omega$

Returns: value of $\int_{\Omega_{\rm c}}^\Omega F(\Omega') \, d\Omega'$

Definition at line 256 of file star_rot_dirac_diff.C.

References par_frot, and primfrot.

◆ r_circ()

double Lorene::Star_rot_Dirac::r_circ ( ) const

virtualinherited

Circumferential equatorial radius.

Definition at line 334 of file strot_dirac_global.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_type_t(), Lorene::Star::mp, Lorene::Star::nzet, and Lorene::Star_rot_Dirac::p_r_circ.

◆ ray_eq()

double Lorene::Star::ray_eq ( ) const

inherited

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

Definition at line 111 of file star_global.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_p(), Lorene::Mg3d::get_type_t(), Lorene::Star::mp, and Lorene::Star::p_ray_eq.

◆ ray_eq_3pis2()

double Lorene::Star::ray_eq_3pis2 ( ) const

inherited

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

Definition at line 236 of file star_global.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_p(), Lorene::Mg3d::get_type_t(), Lorene::Star::mp, and Lorene::Star::p_ray_eq_3pis2.

◆ ray_eq_pi()

double Lorene::Star::ray_eq_pi ( ) const

inherited

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

Definition at line 189 of file star_global.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_p(), Lorene::Mg3d::get_type_t(), Lorene::Star::mp, and Lorene::Star::p_ray_eq_pi.

◆ ray_eq_pis2()

double Lorene::Star::ray_eq_pis2 ( ) const

inherited

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

Definition at line 141 of file star_global.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_p(), Lorene::Mg3d::get_type_t(), Lorene::Star::mp, and Lorene::Star::p_ray_eq_pis2.

◆ ray_pole()

double Lorene::Star::ray_pole ( ) const

inherited

Coordinate radius at $\theta=0$ [r_unit].

Definition at line 281 of file star_global.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_type_t(), Lorene::Star::mp, and Lorene::Star::p_ray_pole.

◆ rp_circ()

double Lorene::Star_rot_Dirac::rp_circ ( ) const

virtualinherited

◆ sauve()

void Lorene::Star_rot_Dirac_diff::sauve ( FILE * fich ) const

virtual

Save in a file.

Reimplemented from Lorene::Star_rot_Dirac.

Definition at line 151 of file star_rot_dirac_diff.C.

References Lorene::fwrite_be(), omega_field, omega_max, omega_min, par_frot, Lorene::Star::sauve(), Lorene::Tbl::sauve(), and Lorene::Scalar::sauve().

◆ set_der_0x0()

void Lorene::Star_rot_Dirac::set_der_0x0 ( ) const

protectedvirtualinherited

Sets to 0x0 all the pointers on derived quantities.

Reimplemented from Lorene::Star.

Definition at line 251 of file star_rot_dirac.C.

References Lorene::Star_rot_Dirac::p_angu_mom, Lorene::Star_rot_Dirac::p_grv2, Lorene::Star_rot_Dirac::p_grv3, Lorene::Star_rot_Dirac::p_r_circ, Lorene::Star_rot_Dirac::p_rp_circ, and Lorene::Star_rot_Dirac::p_tsw.

◆ set_enthalpy()

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().

◆ set_mp()

Map& Lorene::Star::set_mp ( )

inlineinherited

Read/write of the mapping.

Definition at line 322 of file star.h.

References Lorene::Star::mp.

◆ solve_hij()

void Lorene::Star_rot_Dirac::solve_hij ( Sym_tensor_trans & hij_new ) const

inherited

Solution of the tensor Poisson equation for rotating stars in Dirac gauge.

Definition at line 81 of file strot_dirac_solvehij.C.

References Lorene::Star_rot_Dirac::aa, Lorene::Star::beta, Lorene::Metric::con(), Lorene::contract(), Lorene::Metric::cov(), Lorene::Scalar::derive_con(), Lorene::Tensor_sym::derive_con(), Lorene::Tensor::derive_cov(), Lorene::Scalar::derive_cov(), Lorene::Tensor_sym::derive_cov(), Lorene::Sym_tensor::derive_lie(), Lorene::Scalar::derive_lie(), Lorene::Vector::divergence(), Lorene::Map::flat_met_spher(), Lorene::Map::get_bvect_spher(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Star_rot_Dirac::hh, Lorene::Tensor::inc_dzpuis(), Lorene::Scalar::inc_dzpuis(), Lorene::Star_rot_Dirac::ln_psi, Lorene::Star::mp, Lorene::Star::nn, Lorene::Vector::ope_killing_conf(), Lorene::Sym_tensor_trans::poisson(), Lorene::Star_rot_Dirac::psi2, Lorene::Star_rot_Dirac::psi4, Lorene::Star_rot_Dirac::qqq, Lorene::Star::s_euler, Lorene::Tensor::set(), Lorene::Scalar::set_dzpuis(), Lorene::Scalar::set_etat_zero(), Lorene::Star::stress_euler, Lorene::Star_rot_Dirac::tgamma, and Lorene::Tensor::trace().

◆ solve_logn_f()

void Lorene::Star_rot_Dirac::solve_logn_f ( Scalar & ln_f_new ) const

inherited

Solution of the two scalar Poisson equations for rotating stars in Dirac gauge.

Definition at line 65 of file strot_dirac_solvenq.C.

References Lorene::Star::ener_euler, Lorene::Scalar::poisson(), Lorene::Star_rot_Dirac::psi4, and Lorene::Star::s_euler.

◆ solve_logn_q()

void Lorene::Star_rot_Dirac::solve_logn_q ( Scalar & ln_q_new ) const

inherited

Solution of the two scalar Poisson equations for rotating stars in Dirac gauge.

Definition at line 79 of file strot_dirac_solvenq.C.

References Lorene::Star_rot_Dirac::aa_quad, Lorene::contract(), Lorene::Scalar::derive_con(), Lorene::Tensor::derive_cov(), Lorene::Scalar::derive_cov(), Lorene::Map::flat_met_spher(), Lorene::Map::get_bvect_spher(), Lorene::Star_rot_Dirac::hh, Lorene::Tensor::inc_dzpuis(), Lorene::Star_rot_Dirac::ln_psi, Lorene::Star::logn, Lorene::Star::mp, Lorene::Scalar::poisson(), Lorene::Star_rot_Dirac::psi4, Lorene::Star_rot_Dirac::tgamma, and Lorene::Tensor::up_down().

◆ solve_qqq()

void Lorene::Star_rot_Dirac::solve_qqq ( Scalar & q_new ) const

inherited

Solution of the two scalar Poisson equations for rotating stars in Dirac gauge.

Definition at line 108 of file strot_dirac_solvenq.C.

References Lorene::Star_rot_Dirac::aa_quad, Lorene::contract(), Lorene::Metric::cov(), Lorene::Scalar::derive_con(), Lorene::Tensor::derive_cov(), Lorene::Scalar::derive_cov(), Lorene::Tensor_sym::derive_cov(), Lorene::Map::flat_met_spher(), Lorene::Scalar::get_etat(), Lorene::Star_rot_Dirac::hh, Lorene::Tenseur::inc_dzpuis(), Lorene::Star_rot_Dirac::ln_psi, Lorene::Star::mp, Lorene::Star::nn, Lorene::Scalar::poisson(), Lorene::Star_rot_Dirac::psi2, Lorene::Star_rot_Dirac::psi4, Lorene::Star_rot_Dirac::qqq, Lorene::Star::s_euler, and Lorene::Star_rot_Dirac::tgamma.

◆ solve_shift()

void Lorene::Star_rot_Dirac::solve_shift ( Vector & shift_new ) const

inherited

Solution of the shift equation for rotating stars in Dirac gauge.

Definition at line 57 of file strot_dirac_solveshift.C.

References Lorene::Star_rot_Dirac::aa, Lorene::Star::beta, Lorene::Metric::connect(), Lorene::contract(), Lorene::Tensor::derive_cov(), Lorene::Scalar::derive_cov(), Lorene::Vector::div_free(), Lorene::Vector::divergence(), Lorene::Map::flat_met_spher(), Lorene::Connection::get_delta(), Lorene::Star_rot_Dirac::hh, Lorene::Tensor::inc_dzpuis(), Lorene::Star_rot_Dirac::j_euler, Lorene::Star_rot_Dirac::ln_psi, Lorene::Star::mp, Lorene::Star::nn, Lorene::Vector_divfree::poisson(), Lorene::Star_rot_Dirac::psi4, Lorene::Vector::set(), Lorene::Scalar::set_dzpuis(), and Lorene::Star_rot_Dirac::tgamma.

◆ spectral_filter_order()

int Lorene::Star_rot_Dirac::spectral_filter_order ( ) const

inlineinherited

Returns the filtering order.

Definition at line 191 of file star_rot_dirac.h.

References Lorene::Star_rot_Dirac::spectral_filter.

◆ tsw()

double Lorene::Star_rot_Dirac_diff::tsw ( ) const

virtual

◆ update_metric()

void Lorene::Star_rot_Dirac::update_metric ( )

inherited

Computes metric quantities from known potentials.

The calculation is performed starting from qqq, logn, shift, hh, which are supposed to be up to date. From these, the following fields are updated: nnn, psi4, psi2, ln_psi, tgamma, aa, taa, and aa_quad.

Definition at line 65 of file strot_dirac_upmetr.C.

◆ xi_surf()

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.

Friends And Related Function Documentation

◆ operator<<

ostream& operator<<	(	ostream &	ost,
		const Star &	et
	)

friend

Display.

Definition at line 415 of file star.C.

Member Data Documentation

◆ aa

Sym_tensor Lorene::Star_rot_Dirac::aa

protectedinherited

$A^{ij}$

Definition at line 97 of file star_rot_dirac.h.

◆ aa_quad

Scalar Lorene::Star_rot_Dirac::aa_quad

protectedinherited

$\tilde{A}_{ij} A^{ij}$

Definition at line 99 of file star_rot_dirac.h.

◆ beta

Vector Lorene::Star::beta

protectedinherited

Shift vector.

Definition at line 228 of file star.h.

◆ ener

Scalar Lorene::Star::ener

protectedinherited

Total energy density in the fluid frame.

Definition at line 193 of file star.h.

◆ ener_euler

Scalar Lorene::Star::ener_euler

protectedinherited

Total energy density in the Eulerian frame.

Definition at line 198 of file star.h.

◆ ent

Scalar Lorene::Star::ent

protectedinherited

Log-enthalpy.

Definition at line 190 of file star.h.

◆ eos

const Eos& Lorene::Star::eos

protectedinherited

Equation of state of the stellar matter.

Definition at line 185 of file star.h.

◆ flat

const Metric_flat& Lorene::Star_rot_Dirac::flat

protectedinherited

flat metric $f_{ij}$ (spherical components)

Definition at line 94 of file star_rot_dirac.h.

◆ frot

double(* Lorene::Star_rot_Dirac_diff::frot) (double, const Tbl &)

protected

Function $F(\Omega)$ defining the rotation profile.

This function is linked to the components of the fluid 4-velocity by

$F(\Omega) = u^t u_\varphi \ .$

The first argument of frot must be $\Omega$ ; the second argument contains the parameters, the first of which being necessarily the central value of $\Omega$ .

Definition at line 64 of file star_rot_dirac_diff.h.

◆ gam_euler

Scalar Lorene::Star::gam_euler

protectedinherited

Lorentz factor between the fluid and Eulerian observers.

Definition at line 204 of file star.h.

◆ gamma

Metric Lorene::Star::gamma

protectedinherited

3-metric

Definition at line 235 of file star.h.

◆ hh

Sym_tensor_trans Lorene::Star_rot_Dirac::hh

protectedinherited

$h^{ij}$ is defined by $\tilde{\gamma}^{ij}=f^{ij}+h^{ij}$ .

We impose the Dirac gauge $D_j h^{ij}$ explicitly by defining $h^{ij}$ to be a symmetric transverse tensor.

Definition at line 106 of file star_rot_dirac.h.

◆ j_euler

Vector Lorene::Star_rot_Dirac::j_euler

protectedinherited

Momentum density 3-vector with respect to the Eulerian observer.

Definition at line 87 of file star_rot_dirac.h.

◆ ln_psi

Scalar Lorene::Star_rot_Dirac::ln_psi

protectedinherited

$ln(\Psi)$

Definition at line 77 of file star_rot_dirac.h.

◆ logn

Scalar Lorene::Star::logn

protectedinherited

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.

◆ mp

Map& Lorene::Star::mp

protectedinherited

Mapping associated with the star.

Definition at line 180 of file star.h.

◆ nbar

Scalar Lorene::Star::nbar

protectedinherited

Baryon density in the fluid frame.

Definition at line 192 of file star.h.

◆ nn

Scalar Lorene::Star::nn

protectedinherited

Lapse function N .

Definition at line 225 of file star.h.

◆ nzet

int Lorene::Star::nzet

protectedinherited

Number of domains of *mp occupied by the star.

Definition at line 183 of file star.h.

◆ omega

double Lorene::Star_rot_Dirac::omega

protectedinherited

Rotation angular velocity ([f_unit] )

Definition at line 69 of file star_rot_dirac.h.

◆ omega_field

Scalar Lorene::Star_rot_Dirac_diff::omega_field

protected

Field $\Omega(r,\theta)$ .

Definition at line 84 of file star_rot_dirac_diff.h.

◆ omega_max

double Lorene::Star_rot_Dirac_diff::omega_max

protected

Maximum value of $\Omega$ .

Definition at line 87 of file star_rot_dirac_diff.h.

◆ omega_min

double Lorene::Star_rot_Dirac_diff::omega_min

protected

Minimum value of $\Omega$ .

Definition at line 86 of file star_rot_dirac_diff.h.

◆ p_angu_mom

double* Lorene::Star_rot_Dirac::p_angu_mom

mutableprotectedinherited

Angular momentum.

Definition at line 116 of file star_rot_dirac.h.

◆ p_grv2

double* Lorene::Star_rot_Dirac::p_grv2

mutableprotectedinherited

Error on the virial identity GRV2.

Definition at line 117 of file star_rot_dirac.h.

◆ p_grv3

double* Lorene::Star_rot_Dirac::p_grv3

mutableprotectedinherited

Error on the virial identity GRV3.

Definition at line 118 of file star_rot_dirac.h.

◆ p_l_surf

Itbl* Lorene::Star::p_l_surf

mutableprotectedinherited

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.

◆ p_mass_b

double* Lorene::Star::p_mass_b

mutableprotectedinherited

Baryon mass.

Definition at line 268 of file star.h.

◆ p_mass_g

double* Lorene::Star::p_mass_g

mutableprotectedinherited

Gravitational mass.

Definition at line 269 of file star.h.

◆ p_r_circ

double* Lorene::Star_rot_Dirac::p_r_circ

mutableprotectedinherited

Circumferential equatorial radius.

Definition at line 120 of file star_rot_dirac.h.

◆ p_ray_eq

double* Lorene::Star::p_ray_eq

mutableprotectedinherited

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

Definition at line 242 of file star.h.

◆ p_ray_eq_3pis2

double* Lorene::Star::p_ray_eq_3pis2

mutableprotectedinherited

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

Definition at line 251 of file star.h.

◆ p_ray_eq_pi

double* Lorene::Star::p_ray_eq_pi

mutableprotectedinherited

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

Definition at line 248 of file star.h.

◆ p_ray_eq_pis2

double* Lorene::Star::p_ray_eq_pis2

mutableprotectedinherited

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

Definition at line 245 of file star.h.

◆ p_ray_pole

double* Lorene::Star::p_ray_pole

mutableprotectedinherited

Coordinate radius at $\theta=0$ .

Definition at line 254 of file star.h.

◆ p_rp_circ

double* Lorene::Star_rot_Dirac::p_rp_circ

mutableprotectedinherited

Circumferential polar radius.

Definition at line 121 of file star_rot_dirac.h.

◆ p_tsw

double* Lorene::Star_rot_Dirac::p_tsw

mutableprotectedinherited

Ratio T/W.

Definition at line 119 of file star_rot_dirac.h.

◆ p_xi_surf

Tbl* Lorene::Star::p_xi_surf

mutableprotectedinherited

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.

◆ par_frot

Tbl Lorene::Star_rot_Dirac_diff::par_frot

protected

Parameters of the function $F(\Omega)$ .

To be used as the second argument of functions frot and primfrot . The parameter par_frot(0) must always be the central angular velocity.

Definition at line 81 of file star_rot_dirac_diff.h.

◆ press

Scalar Lorene::Star::press

protectedinherited

Fluid pressure.

Definition at line 194 of file star.h.

◆ prim_field

Scalar Lorene::Star_rot_Dirac_diff::prim_field

protected

Field $\int_{\Omega_{\rm c}}^\Omega F(\Omega') \, d\Omega'$ .

Definition at line 90 of file star_rot_dirac_diff.h.

◆ primfrot

double(* Lorene::Star_rot_Dirac_diff::primfrot) (double, const Tbl &)

protected

Primitive of the function $F(\Omega)$ , which vanishes at the stellar center.

The first argument of primfrot must be $\Omega$ ; the second argument contains the parameters, the first of which being necessarily the central value of $\Omega$ .

Definition at line 72 of file star_rot_dirac_diff.h.

◆ psi2

Scalar Lorene::Star_rot_Dirac::psi2

protectedinherited

$\Psi^2$

Definition at line 75 of file star_rot_dirac.h.

◆ psi4

Scalar Lorene::Star_rot_Dirac::psi4

protectedinherited

Conformal factor $\Psi^4$ .

Definition at line 74 of file star_rot_dirac.h.

◆ qqq

Scalar Lorene::Star_rot_Dirac::qqq

protectedinherited

$Q = \Psi^2 N$

Definition at line 76 of file star_rot_dirac.h.

◆ relat_type

int Lorene::Star_rot_Dirac::relat_type

protectedinherited

Relativistic flag.

0 : Newtonian theory (not implemented) 1 : full General Relativity, maximal slicing and Dirac's Gauge 2 : Conformal Flatness Condition (CFC) 3 : CFC with $\hat{A}^{ij}_{TT} = 0$ (see Cordero-Carrion et al. 2009).

Definition at line 59 of file star_rot_dirac.h.

◆ s_euler

Scalar Lorene::Star::s_euler

protectedinherited

Trace of the stress scalar in the Eulerian frame.

Definition at line 201 of file star.h.

◆ spectral_filter

int Lorene::Star_rot_Dirac::spectral_filter

protectedinherited

Spectral exponential filtering order.

If 0, no filtering is done (see also Scalar::exponential_filter_r). Filtering is performed only in shells containing matter, i.e. for domain numbers l such that $0 < l <$ nzet .

Definition at line 67 of file star_rot_dirac.h.

◆ stress_euler

Sym_tensor Lorene::Star::stress_euler

protectedinherited

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

Definition at line 212 of file star.h.

◆ taa

Sym_tensor Lorene::Star_rot_Dirac::taa

protectedinherited

$\tilde{A}_{ij}$

Definition at line 98 of file star_rot_dirac.h.

◆ tgamma

Metric Lorene::Star_rot_Dirac::tgamma

protectedinherited

$\tilde{\gamma}_{ij}$

Definition at line 96 of file star_rot_dirac.h.

◆ u_euler

Vector Lorene::Star::u_euler

protectedinherited

Fluid 3-velocity with respect to the Eulerian observer.

Definition at line 207 of file star.h.

◆ v2

Scalar Lorene::Star_rot_Dirac::v2

protectedinherited

$\gamma_{ij}v^i v^j$

Definition at line 88 of file star_rot_dirac.h.

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

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Star_rot_Dirac_diff() [1/3]

◆ Star_rot_Dirac_diff() [2/3]

◆ Star_rot_Dirac_diff() [3/3]

◆ ~Star_rot_Dirac_diff()

Member Function Documentation

◆ angu_mom()

◆ aplat()

◆ del_deriv()

◆ del_hydro_euler()

◆ ellipt()

◆ equation_of_state()

◆ equilibrium()

◆ equilibrium_spher()

◆ fait_omega_field()

◆ fait_prim_field()

◆ funct_omega()

◆ get_aa()

◆ get_aa_quad()

◆ get_beta()

◆ get_ener()

◆ get_ener_euler()

◆ get_ent()

◆ get_eos()

◆ get_gam_euler()

◆ get_gamma()

◆ get_hh()

◆ get_j_euler()

◆ get_ln_psi()

◆ get_logn()

◆ get_mp()

◆ get_nbar()

◆ get_nn()

◆ get_nzet()

◆ get_omega()

◆ get_omega_c()

◆ get_omega_field()

◆ get_press()

◆ get_psi2()

◆ get_psi4()

◆ get_qqq()

◆ get_relat()

◆ get_s_euler()

◆ get_stress_euler()

◆ get_taa()

◆ get_tgamma()

◆ get_u_euler()

◆ get_v2()

◆ grv2()

◆ grv3()

◆ hydro_euler()

◆ is_relativistic()

◆ l_surf()

◆ mass_b()

◆ mass_g()

◆ operator=()

◆ operator>>()

◆ prim_funct_omega()

◆ r_circ()

◆ ray_eq()

◆ ray_eq_3pis2()

◆ ray_eq_pi()

◆ ray_eq_pis2()

◆ ray_pole()

◆ rp_circ()

◆ sauve()

◆ set_der_0x0()

◆ set_enthalpy()

◆ set_mp()

◆ solve_hij()

◆ solve_logn_f()

◆ solve_logn_q()

◆ solve_qqq()

◆ solve_shift()

◆ spectral_filter_order()