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* Definition of Lorene class Isol_hole
*
*/
/*
* Copyright (c) 2009 Nicolas Vasset
*/
#ifndef __ISOLHOLE_H_
#define __ISOLHOLE_H_
// Headers Lorene
#include "tensor.h"
#include "metric.h"
#include "spheroid.h"
#include "excision_surf.h"
#include "excision_hor.h"
class Eos ;
//---------------------------//
// Class Isol_hole //
//---------------------------//
namespace Lorene {
/** Class to compute quasistationary single black hole spacetimes in vacuum.
* It takes as arguments:
* - A Mapping \c mp
* - A rotation rate \f$ \Omega\f$ of the horizon in the \f$ \varphi \f$
* direction, assumed to be the direction of the rotational symmetry.
* - A Scalar NoK, storing the boundary value to be verified either for the
* lapse or the surface gravity at the excised boundary (which is a MOTS in
* the philosophy of this class). Whether it corresponds to the lapse or the
* surface gravity is controlled by the boolean NorKappa. (Warning: setting a
* boundary on Kappa is not implemented yet).
* - A boolean isCF, to determine whether or not one adopts the conformally
* flat approximation in the spacetime construction. Set to FALSE by default.
*
* The main goal of this class is the computation of metric data from those
* parameters, as well as some global quantities related to the physical
* characteristics of the spacetime. Those metric data are given on a
* spacelike 3-slice, assuming a global timelike Killing field and using
* adapted coordinates.
*/
class Isol_hole {
// Data :
// -----
protected:
const Map& mp ; ///< Mapping associated with the star
double Omega ; /** Rotation rate of the horizon in the azimuthal
*direction.
*/
bool NorKappa ; /** Indicates if the boundary value for the lapse
* or the surface gravity is used.
*/
Scalar boundNoK ; /** Stores the boundary value of the lapse or surface
* gravity.
*/
bool isCF ; ///< Indicates if the CF approximation is used.
// Metric data
// -----------------
/// Lapse function
Scalar lapse ;
// Conformal factor
Scalar conf_fact;
/// Shift vector
Vector shift ;
/** Deviation tensor( non-flat part of the conformal 3-metric on
* the slice; see Bonazzola et al. (2004)).
*/
Sym_tensor hij ;
/** Rescaled tracefree extrinsic curvature tensor: see Cordero et al.( * 2009).
*/
Sym_tensor hatA ;
// Derived data :
// ------------
protected:
/// Computation of the spheroid associated with the black hole horizon
mutable Spheroid* p_hor ;
/// Computation of the ADM mass of the BH spacetime.
mutable double* p_adm_mass ;
/** Computation of the Komar angular momentum w.r.t. assumed
*rotational symmetry
*/
mutable double* p_komar_angmom ;
/**Computation of the Virial residual, as difference at infinity
*between the ADM mass and the Komar integral associated to the mass.
*/
mutable double* p_virial_residue ;
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor.
*
* @param mp_i Mapping on which the black hole slice will be defined
* @param Omega_i rotation rate of the horizon
* @param NorKappa_i FALSE: use of boundary value for the lapse
* TRUE use of boundary value for the surface gravity
* (Warning! not implemented yet!)
* @param NoK_i value either for the lapse or surface gravity.
* @param isCF_i FALSE: Full GR 3+1 equations to be verified
* TRUE: IWM approximation used in determination of the
* spacetime geometry;
*/
Isol_hole(const Map& mp_i, double Omega_i, bool NorKappa_i, Scalar NoK_i, bool isCF_i = false) ;
Isol_hole(const Isol_hole& ) ; ///< Copy constructor
/** Constructor from a file (see \c sauve(FILE* )).
*
* @param mp_i Mapping on which the star will be defined
* @param Omega_i rotation rate of the horizon
* @param NorKappa_i FALSE: use of boundary value for the lapse
* TRUE use of boundary value for the surface gravity
* (Warning! not implemented yet!)
* @param NoK_i value either for the lapse or surface gravity.
* @param isCF_i FALSE: Full GR 3+1 equations to be verified
* TRUE: IWM approximation used in determination of the
* spacetime geometry;
* @param fich input file (must have been created by the function
* \c sauve)
*/
Isol_hole(const Map& mp_i, double Omega_i, bool NorKappa_i, Scalar NoK_i, bool isCF_i, FILE* fich) ;
virtual ~Isol_hole() ; ///< Destructor
// Memory management
// -----------------
protected:
/// Deletes all the derived quantities
virtual void del_deriv() const ;
/// Sets to \c 0x0 all the pointers on derived quantities
virtual void set_der_0x0() const ;
// Mutators / assignment
// ---------------------
public:
/// Assignment to another \c Isol_hole
void operator=(const Isol_hole&) ;
/** Computes a quasi-stationary 3-slice from the chosen parameters.
*
* @param precis [input] threshold in the relative difference between
* the radial shift for two consecutive steps
* to stop the iterative procedure (default value: 1.e-11)
*/
void compute_stat_metric(double precis, double relax, int mer_max, int mer_max2, bool isvoid = true) ;
/** Computes the rhs of hyperbolic equation for conformal metric
*assuming statioarity;
*WARNING; up to now, we are only able to handle void spacetimes.
*/
void secmembre_kerr(Sym_tensor& source_hh);
// Accessors
// ---------
public:
/// Returns the mapping
const Map& get_mp() const {return mp; } ;
/// Returns the rotation rate
double get_Omega() const {return Omega ;} ;
/// Returns the boundary value used for the lapse (if it is the one used)
const Scalar& get_boundN() const{
if (NorKappa == false){
return boundNoK;
}
else cout << "The boundary condition is imposed on the surface gravity!" << endl;
}
/// Returns the surface gravity value at the boundary (if it is the one used)
const Scalar& get_Kappa() const{
if(NorKappa == true){
return boundNoK;
}
else cout << "The boundary condition is imposed on the lapse!" <<endl;
}
/// Returns the lapse function \e N
const Scalar& get_lapse() const {return lapse;} ;
/// Returns the conformal factor
const Scalar& get_conf_fact() const {return conf_fact;};
/// Returns the shift vector \f$\beta^i\f$.
const Vector& get_shift() const {return shift;} ;
/// Returns the deviation tensor \f$ h^{ij} \f$.
const Sym_tensor& get_hij() const {return hij;} ;
/// Returns the rescaled tracefree extrinsic curvature \f$\hat{A}^{ij}\f$.
const Sym_tensor& get_hatA() const {return hatA;} ;
// Outputs
// -------
public:
virtual void sauve(FILE* ) const ; ///< Save in a file
void Einstein_errors(); ///< Prints out errors in Einstein equations for the data obtained.
// Global quantities
// -----------------
public:
/** Spheroid at the excised boundary associated with the black hole
* MOTS on the slice. Set by default at the position \f$ r=1 \f$.
*/
Spheroid hor() ;
/// Computation of the ADM mass of the BH spacetime.
double adm_mass() ;
/** Computation of the Komar angular momentum w.r.t. assumed
*rotational symmetry
*/
double komar_angmom() ;
/**Computation of the Virial residual, as difference at infinity
*between the ADM mass and the Komar integral associated to the mass.
*/
double virial_residue() ;
};
}
#endif
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