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* Definition of Lorene class Black_hole
*
*/
/*
* Copyright (c) 2005-2007 Keisuke Taniguchi
*
* This file is part of LORENE.
*
* LORENE is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License version 2
* as published by the Free Software Foundation.
*
* LORENE is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with LORENE; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
#ifndef __BLACKHOLE_H_
#define __BLACKHOLE_H_
/*
* $Id: blackhole.h,v 1.4 2014/10/13 08:52:32 j_novak Exp $
* $Log: blackhole.h,v $
* Revision 1.4 2014/10/13 08:52:32 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.3 2008/07/02 20:41:40 k_taniguchi
* Addition of the routines to compute angular momentum
* and modification of the argument of equilibrium_spher.
*
* Revision 1.2 2008/05/15 18:53:37 k_taniguchi
* Change of some parameters and introduction of some
* computational routines.
*
* Revision 1.1 2007/06/22 01:02:57 k_taniguchi
* *** empty log message ***
*
*
* $Header: /cvsroot/Lorene/C++/Include/blackhole.h,v 1.4 2014/10/13 08:52:32 j_novak Exp $
*
*/
// External classes which appear in the declaration of class Black_hole:
//class YYY ;
// Headers Lorene
#include "metric.h"
//-------------------------------//
// Base class Black_hole //
//-------------------------------//
namespace Lorene {
/**
* Base class for black holes.
* \ingroup(star)
*
* According to the 3+1 formalism, the spacetime metric is written
* \f[
* ds^2 = - \alpha^2 dt^2 + \gamma_{ij} ( dx^i + \beta^i dt )
* ( dx^j + \beta^j dt )
* \f]
* where \f$\gamma_{ij}\f$ is the spatial metric.
*
*/
class Black_hole {
// Data :
// -----
protected:
/// Mapping associated with the black hole
Map& mp ;
/** \c true for a Kerr-Schild background, \c false for
* a conformally flat background
*/
bool kerrschild ;
/// Gravitational mass of BH
double mass_bh ;
// Metric quantities
// -----------------
/**
* A function (lapse function * conformal factor) lapconf
* generated by the black hole
*/
Scalar lapconf ; // lapconf = lapconf_rs + lapconf_bh
/// Part of lapconf from the numerical computation
Scalar lapconf_rs ;
/// Part of lapconf from the analytic background
Scalar lapconf_bh ;
/// Lapse function generated by the black hole
Scalar lapse ;
/// Shift vector generated by the black hole
Vector shift ; // shift = shift_rs + shift_bh
/// Part of the shift vector from the numerical computation
Vector shift_rs ;
/// Part of the shift vector from the analytic background
Vector shift_bh ;
/// Conformal factor generated by the black hole
Scalar confo ;
/// Trace of the extrinsic curvature
// Scalar trace_k ;
/** Extrinsic curvature tensor \f$\ A^{ij}\f$
* generated by \c shift , \c lapse , and
* \c confo .
*/
Sym_tensor taij ;
/// Part of the extrinsic curvature tensor
Sym_tensor taij_rs ;
/** Part of the scalar \f$\eta_{ik} \eta_{jl} A^{ij} A^{kl}\f$
* generated by \f$A_{ij}\f$
*/
Scalar taij_quad ;
/// Part of the scalar
Scalar taij_quad_rs ;
/** Flat metric defined on the mapping (Spherical components
* with respect to the mapping of the black hole ).
*/
Metric_flat flat ;
/// Conformal metric \f$\tilde \gamma_{ij}\f$
// Metric tgij ;
// Derived data :
// ------------
protected:
mutable double* p_mass_irr ; /// Irreducible mass of the black hole
mutable double* p_mass_adm ; /// ADM mass
mutable double* p_mass_kom ; /// Komar mass
mutable double* p_rad_ah ; /// Radius of the apparent horizon
mutable double* p_spin_am_bh ; /// Spin angular momentum
/// Total angular momentum of the black hole
mutable Tbl* p_angu_mom_bh ;
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor.
*
* @param mp_i Mapping on which the black hole will be defined
*/
Black_hole(Map& mp_i, bool Kerr_schild, double massbh) ;
Black_hole(const Black_hole& ) ; ///< Copy constructor
/** Constructor from a file (see \c sauve(FILE*) )
*
* @param mp_i Mapping on which the black hole will be defined
* @param fich input file (must have been created by the function
* \c sauve )
*/
Black_hole(Map& mp_i, FILE* fich) ;
virtual ~Black_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
void set_der_0x0() const ;
// Mutators / assignment
// ---------------------
public:
/// Assignment to another \c Black_hole
void operator=(const Black_hole&) ;
/// Read/write of the mapping
Map& set_mp() {return mp; } ;
/// Read/write of the gravitational mass of BH [{\tt m\_unit}]
double& set_mass_bh() {return mass_bh; } ;
// Accessors
// ---------
public:
/// Returns the mapping
const Map& get_mp() const {return mp; } ;
/** Returns \c true for a Kerr-Schild background, \c false for
* a Conformally flat one
*/
bool is_kerrschild() const {return kerrschild; } ;
/// Returns the gravitational mass of BH [{\tt m\_unit}]
double get_mass_bh() const {return mass_bh; } ;
/// Returns lapconf generated by the black hole
const Scalar& get_lapconf() const {return lapconf; } ;
/// Returns the part of lapconf from the numerical computation
const Scalar& get_lapconf_rs() const {return lapconf_rs; } ;
/// Returns the lapse function generated by the black hole
const Scalar& get_lapse() const {return lapse; } ;
/// Returns the shift vector generated by the black hole
const Vector& get_shift() const {return shift; } ;
/** Returns the part of the shift vector from
* the numerical computation
*/
const Vector& get_shift_rs() const {return shift_rs; } ;
/// Returns the conformal factor generated by the black hole
const Scalar& get_confo() const {return confo; } ;
// Outputs
// -------
public:
virtual void sauve(FILE *) const ; ///< Save in a file
/// Display
friend ostream& operator<<(ostream& , const Black_hole& ) ;
protected:
/// Operator >> (virtual function called by the operator <<)
virtual ostream& operator>>(ostream& ) const ;
// Global quantities
// -----------------
public:
/// Irreducible mass of the black hole
virtual double mass_irr() const ;
/// ADM mass
virtual double mass_adm() const ;
/// Komar mass
virtual double mass_kom() const ;
/// Radius of the apparent horizon
virtual double rad_ah() const ;
/// Spin angular momentum
double spin_am_bh(bool bclapconf_nd, bool bclapconf_fs,
const Tbl& xi_i, const double& phi_i,
const double& theta_i, const int& nrk_phi,
const int& nrk_theta) const ;
/** Total angular momentum.
*
* @return 1-D {\tt Tbl} of size 3, according to \\
* {\tt angu\_mom()(0)} = $J^x$, \\
* {\tt angu\_mom()(1)} = $J^y$, \\
* {\tt angu\_mom()(2)} = $J^z$.
*/
const Tbl& angu_mom_bh() const ;
// Computational routines
// ----------------------
public:
/** Boundary condition on the apparent horizon of the black hole
* for the lapse function: 2-D \c Valeur
*/
const Valeur bc_lapconf(bool neumann, bool first) const ;
/** Boundary condition on the apparent horizon of the black hole
* for the shift vector of the \fx\f direction: 2-D \c Valeur
*/
const Valeur bc_shift_x(double omega_r) const ;
/** Boundary condition on the apparent horizon of the black hole
* for the shift vector of the \fy\f direction: 2-D \c Valeur
*/
const Valeur bc_shift_y(double omega_r) const ;
/** Boundary condition on the apparent horizon of the black hole
* for the shift vector of the \fz\f direction: 2-D \c Valeur
*/
const Valeur bc_shift_z() const ;
/** Boundary condition on the apparent horizon of the black hole
* for the conformal factor: 2-D \c Valeur
*/
const Valeur bc_confo() const ;
/** Computes \c taij , \c taij_quad from \c shift , \c lapse ,
* \c confo .
*/
void extr_curv_bh() ;
/** Computes a spherical, static black-hole by giving boundary
* conditions on the apparent horizon.
*
* @param neumann [input] \c true for the neumann bc, \c false for
* the dirichlet one for the lapse
* @param first [input] \c true for the first type of bc,
* \c false for the second type
* @param spin_omega [input] spin parameter of the black hole
* @param precis [input] threshold in the relative difference of
* a metric quantity between two succesive steps
* to stop the iterative procedure
* (default value: 1.e-14)
* @param precis_shift [input] threshold in the relative difference
* of the shift vector between two succesive steps
* to stop the iterative procedure
* (default value: 1.e-8)
*/
void equilibrium_spher(bool neumann, bool first, double spin_omega,
double precis = 1.e-14,
double precis_shift = 1.e-8) ;
/** Sets the metric quantities to a spherical, static blach-hole
* analytic solution
*
* @param neumann [input] \c true for the neumann bc, \c false for
* the dirichlet one for the lapse
* @param first [input] \c true for the first type of bc,
* \c false for the second type
*/
void static_bh(bool neumann, bool first) ;
/** Computes a radius of apparent horizon (excised surface)
* in isotropic coordinates
*
* @param neumann [input] \c true for the neumann bc, \c false for
* the dirichlet one for the lapse
* @param first [input] \c true for the first type of bc,
* \c false for the second type
*/
double rah_iso(bool neumann, bool first) const ;
/** Expresses the areal radial coordinate
* by that in spatially isotropic coordinates
*
* @param neumann [input] \c true for the neumann bc, \c false for
* the dirichlet one for the lapse
* @param first [input] \c true for the first type of bc,
* \c false for the second type
*/
const Scalar r_coord(bool neumann, bool first) const ;
/** Compute a forth-order Runge-Kutta integration to the phi
* direction for the solution of the Killing vectors on the
* equator
*
* @param xi_i [input] initial set of the Killing vectors
* at the starting point on the equator
* @param phi_i [input] initial phi coordinate at which the
* integration starts
* @param nrk [input] number of the Runge-Kutta integration
* between two successive collocation points
*/
Tbl runge_kutta_phi_bh(const Tbl& xi_i, const double& phi_i,
const int& nrk) const ;
/** Compute a forth-order Runge-Kutta integration to the theta
* direction for the solution of the Killing vectors
*
* @param xi_i [input] initial set of the Killing vectors
* at the starting point on the equator
* @param theta_i [input] initial theta coordinate at which the
* integration starts
* @param phi [input] fixed phi coordinate during integration to
* the theta direction
* @param nrk [input] number of the Runge-Kutta integration
* between two successive collocation points
*/
Tbl runge_kutta_theta_bh(const Tbl& xi_i, const double& theta_i,
const double& phi, const int& nrk) const ;
/** Compute the Killing vector of a black hole normalized so that
* its affine length is 2 M_PI
*
* @param xi_i [input] initial set of the Killing vectors
* at the starting point on the equator
* @param phi_i [input] initial phi coordinate at which the
* integration starts
* @param theta_i [input] initial theta coordinate at which the
* integration starts
* @param nrk_phi [input] number of the Runge-Kutta integration
* between two successive collocation points
* for the phi direction
* @param nrk_theta [input] number of the Runge-Kutta integration
* between two successive collocation points
* for the theta direction
*/
Vector killing_vect_bh(const Tbl& xi_i, const double& phi_i,
const double& theta_i, const int& nrk_phi,
const int& nrk_theta) const ;
};
ostream& operator<<(ostream& , const Black_hole& ) ;
}
#endif
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