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* Definition of Lorene classes Bhole
* Bhole_binaire
*
*/
/*
* Copyright (c) 2000-2001 Philippe Grandclement
*
* 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 as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* 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 __BHOLE_H_
#define __BHOLE_H_
/*
* $Id: bhole.h,v 1.18 2014/10/13 08:52:32 j_novak Exp $
* $Log: bhole.h,v $
* Revision 1.18 2014/10/13 08:52:32 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.17 2007/05/15 12:44:18 p_grandclement
* Scalar version of reevaluate
*
* Revision 1.16 2007/04/24 20:15:30 f_limousin
* Implementation of Dirichlet and Neumann BC for the lapse
*
* Revision 1.15 2006/04/27 09:12:29 p_grandclement
* First try at irrotational black holes
*
* Revision 1.14 2005/08/29 15:10:12 p_grandclement
* Addition of things needed :
* 1) For BBH with different masses
* 2) Provisory files for the mixted binaries (Bh and NS) : THIS IS NOT
* WORKING YET !!!
*
* Revision 1.13 2004/12/02 09:33:04 p_grandclement
* *** empty log message ***
*
* Revision 1.12 2004/03/25 12:35:34 j_novak
* now using namespace Unites
*
* Revision 1.11 2004/03/25 09:14:06 j_novak
* *** empty log message ***
*
* Revision 1.10 2004/03/25 08:53:33 j_novak
* Error in the doc corrected.
*
* Revision 1.9 2004/03/24 17:14:04 j_novak
* Translation of comments to doxygen
*
* Revision 1.8 2003/11/25 07:12:58 k_taniguchi
* Change the argument of update_metric from the class Etoile_bin to Et_bin_nsbh.
*
* Revision 1.7 2003/11/13 13:43:53 p_grandclement
* Addition of things needed for Bhole::update_metric (const Etoile_bin&, double, double)
*
* Revision 1.6 2003/10/24 13:05:48 p_grandclement
* correction of the equations for Bin_ns_bh...
*
* Revision 1.5 2003/02/13 16:40:24 p_grandclement
* Addition of various things for the Bin_ns_bh project, non of them being
* completely tested
*
* Revision 1.4 2003/01/31 16:57:12 p_grandclement
* addition of the member Cmp decouple used to compute the K_ij auto, once
* the K_ij total is known
*
* Revision 1.3 2002/12/18 10:28:49 e_gourgoulhon
*
* Added the set_mp function.
*
* Revision 1.2 2002/09/13 09:17:31 j_novak
* Modif. commentaires
*
* Revision 1.1.1.1 2001/11/20 15:19:27 e_gourgoulhon
* LORENE
*
* Revision 2.45 2001/06/28 15:08:16 eric
* Ajout de la fonction area().
*
* Revision 2.44 2001/05/16 11:32:45 phil
* ajout de init_bhole_seul
*
* Revision 2.43 2001/05/07 12:35:28 phil
* mmodifi commentaires
*
* Revision 2.42 2001/05/07 11:43:43 phil
* *** empty log message ***
*
* Revision 2.41 2001/05/07 11:40:50 phil
* mise a jour des commentaires
*
* Revision 2.40 2001/05/07 09:30:37 phil
* *** empty log message ***
*
* Revision 2.39 2001/05/07 09:28:37 phil
* *** empty log message ***
*
* Revision 2.38 2001/05/07 09:11:31 phil
* *** empty log message ***
*
* Revision 2.37 2001/04/27 09:25:11 phil
* fait_decouple est devenu public
*
* Revision 2.36 2001/04/26 12:04:11 phil
* *** empty log message ***
*
* Revision 2.35 2001/04/05 13:42:40 phil
* *** empty log message ***
*
* Revision 2.34 2001/04/05 13:34:29 phil
* ajout resolution en utilisant phi
*
* Revision 2.33 2001/03/22 10:49:34 phil
* *** empty log message ***
*
* Revision 2.32 2001/03/22 10:41:25 phil
* pleins de modif
*
* Revision 2.31 2001/02/28 13:22:31 phil
* modif vire kk_auto
*
* Revision 2.30 2001/02/12 15:37:42 phil
* ajout calcul de J a linfini
*
* Revision 2.29 2001/01/29 14:29:56 phil
* ajout type rotation
*
* Revision 2.28 2001/01/24 10:57:08 phil
* ajout de set_rayonm
*
* Revision 2.27 2001/01/22 09:29:08 phil
* vire les procedures qui servent pas
*
* Revision 2.26 2001/01/10 09:31:05 phil
* modification de fait_kk_auto (membre de binaire maintenant)
*
* Revision 2.25 2001/01/09 13:38:15 phil
* ajout memebre kk_auto
*
* Revision 2.24 2000/12/21 10:47:07 phil
* retour eventuel a 2.21
*
* Revision 2.21 2000/12/20 09:07:56 phil
* ajout set_statiques
*
* Revision 2.20 2000/12/18 16:40:39 phil
* *** empty log message ***
*
* Revision 2.19 2000/12/18 16:38:04 phil
* ajout convergence vers une masse donnee
*
* Revision 2.18 2000/12/15 16:41:28 phil
* ajout calcul de la separation
*
* Revision 2.17 2000/12/14 10:44:28 phil
* ATTENTION : PASSAGE DE PHI A PSI
*
* Revision 2.16 2000/12/13 15:35:18 phil
* ajout calcul bare_masse
*
* Revision 2.15 2000/12/04 14:29:37 phil
* ajout de grad_n_tot
*
* Revision 2.14 2000/12/01 16:12:52 phil
* *** empty log message ***
*
* Revision 2.13 2000/12/01 14:16:20 phil
* *** empty log message ***
*
* Revision 2.12 2000/11/24 15:14:44 phil
* ajout de find_horizon
*
* Revision 2.11 2000/11/24 09:57:18 phil
* ajout calcul masse et moment pour systeme
*
* Revision 2.10 2000/11/17 10:03:13 phil
* ajout de coal
*
* Revision 2.9 2000/11/15 18:26:29 phil
* simplifaction resolution du shift : on bosse a omega bloque
*
* Revision 2.8 2000/11/15 12:59:50 phil
* changement solve_shift_omega
*
* Revision 2.7 2000/11/15 09:41:03 phil
* *** empty log message ***
*
* Revision 2.6 2000/11/15 09:39:26 phil
* ajout viriel
*
* Revision 2.5 2000/11/03 12:56:41 phil
* ajout de const
*
* Revision 2.4 2000/10/26 08:20:45 phil
* ajout verifie_shift
*
* Revision 2.3 2000/10/23 09:15:12 phil
* modif commentaires
*
* Revision 2.2 2000/10/20 10:51:13 phil
* Modif commentaires (minimale !)
*
* Revision 2.1 2000/10/20 09:27:28 phil
* *** empty log message ***
*
* Revision 2.0 2000/10/20 09:22:04 phil
* *** empty log message ***
*
*
* $Header: /cvsroot/Lorene/C++/Include/bhole.h,v 1.18 2014/10/13 08:52:32 j_novak Exp $
*
*/
#include "tenseur.h"
namespace Lorene {
class Tenseur ;
class Tenseur_sym ;
class Map_af ;
class Bhole_binaire ;
class Et_bin_nsbh ;
#define COROT 0
#define IRROT 1
/**
* Black hole. \ingroup (star)
*
* This class represents a black hole in a comformaly flat approximation. It is
* defined with an affine mapping with a nucleus, not used in calculations, and
* must have, at least two shells. The horizon (i.e. the surface where \e N=0 )
* is located at the inner boudary of the innermost shell (i.e. the domain
* number 1).
*
* It can described either :
*
* \li \b an \b isolated \b black \b hole . The fields of the companion and the total
* fields being zero.
* \li \b a \b black \b hole \b in \b a \b binary \b system . The boost having no direct
* meaning in this case.
*
* The tensor \f$K^{ij}\f$ is the the extrinsic curavature tensor with the conformal
* factor extracted.
*
* The tensor \f$A^{ij}\f$ denotes \f$\nabla^i N^j + \nabla^j N^i-\frac{2}{3}
* \nabla_k N^k \delta^{ij}\f$, that is \f$2NK^{ij}\f$.
*
*/
class Bhole {
// Data :
protected:
Map_af& mp ; ///< Affine mapping.
double rayon ; ///< Radius of the horizon in LORENE's units.
double omega ; ///< Angular velocity in LORENE's units.
double omega_local ; ///< local angular velocity
int rot_state ; ///< State of rotation
double lapse_hori ; /// Lapse on the horizon
/**
* Cartesian components of the boost in the reference frame.
*/
double* boost ;
double regul ; ///< Intensity of the correction on the shift vector.
Tenseur n_auto ; ///< Part of \e N generated by the hole.
Tenseur n_comp ; ///<Part of \e N generated by the companion hole.
Tenseur n_tot ; ///< Total \e N .
Tenseur psi_auto ; ///< Part of \f$\Psi\f$ generated by the hole.
Tenseur psi_comp ; ///< Part of \f$\Psi\f$ generated by the companion hole.
Tenseur psi_tot ; ///< Total \f$\Psi\f$.
Tenseur grad_n_tot ; ///< Total gradient of \e N .
Tenseur grad_psi_tot ; ///< Total gradient of \f$\Psi\f$.
Tenseur shift_auto ; ///< Part of \f$\beta^i\f$ generated by the hole.
Tenseur_sym taij_auto ; ///< Part of \f$A^{ij}\f$ generated by the hole.
Tenseur_sym taij_comp ;///< Part of \f$A^{ij}\f$ generated by the companion hole.
/**
* Total \f$A^{ij}\f$, which must be zero on the horizon of the
* regularisation on the shift has been done.
*/
Tenseur_sym taij_tot ;
Tenseur_sym tkij_auto ; ///< Auto \f$K^{ij}\f$.
Tenseur_sym tkij_tot ; ///< Total \f$K^{ij}\f$.
/**
* Function used to construct the part of \f$K^{ij}\f$ generated by the hole
* from the total \f$K^{ij}\f$. Only used for a binary system.
*
* Mainly this \c Cmp is 1 around the hole and 0 around the companion
* and the sum of \c decouple for the hole and his companion is 1
* everywhere.
*/
Cmp decouple ;
//Constructors :
public:
/**
* Standard constructor. All the fields are set to zero, except
* \c rayon , which value is deducted from the \c mapping
*/
Bhole (Map_af& mapping) ;
Bhole (const Bhole&) ; ///< Constructor by copy
Bhole (Map_af&, FILE*, bool old=false) ; ///< Constructor from a \c Map_af and a file
~Bhole() ; ///< Destructor
public:
//sauvegarde
void sauve (FILE* fich) const ; ///< Write on a file
public:
void operator= (const Bhole&) ; ///< Affectation
/// Returns the mapping (readonly).
const Map_af& get_mp() const {return mp;} ;
/// Read/write of the mapping
Map_af& set_mp() {return mp; } ;
/**
* Returns the radius of the horizon.
*/
double get_rayon() const {return rayon;} ;
/**
* Sets the radius of the horizon to \c ray .
*/
void set_rayon(double ray) {rayon = ray ;} ;
/**
* Returns the angular velocity.
*/
double get_omega() const {return omega;} ;
/**
* Sets the angular velocity to \c ome .
*/
void set_omega(double ome) {omega = ome ;} ;
/**
* Returns the local angular velocity.
*/
double get_omega_local() const {return omega_local;} ;
/**
* Sets the local angular velocity to \c ome .
*/
void set_omega_local(double ome) {omega_local = ome ;} ;
/**
* Returns the state of rotation.
*/
double get_rot_state() const {return rot_state;} ;
/**
* Returns the state of rotation.
*/
void set_rot_state(int rotation) {rot_state = rotation;} ;
/**
* Returns the cartesian components of the boost with respect to the
* reference frame.
*/
double* get_boost () const {return boost;} ;
void set_boost (double vx, double vy, double vz) {
boost[0] = vx ; boost[1] = vy ; boost[2] = vz ;
}
/**
* Returns the intensity of the regularisation on \f$\vec{N}\f$.
*/
double get_regul() const {return regul;} ;
/**
* Returns the part of \e N generated by the hole.
*/
const Tenseur& get_n_auto() const {return n_auto ;} ;
/**
* Returns the part of \e N generated by the hole as a cmp
*/
Cmp return_n_auto() const {return n_auto() ;} ;
/**
* Returns the part of \e N generated by the companion hole.
*/
const Tenseur& get_n_comp() const {return n_comp ;} ;
/**
* Returns the total \e N .
*/
const Tenseur& get_n_tot() const {return n_tot ;} ;
/**
* Returns the part of \f$\Psi\f$ generated by the hole.
*/
const Tenseur& get_psi_auto() const {return psi_auto ;} ;
/**
* Returns the part of \f$\Psi\f$ generated by the hole as a cmp
*/
Cmp return_psi_auto() const {return psi_auto() ;} ;
/**
* Returns the part of \f$\Psi\f$ generated by the companion hole.
*/
const Tenseur& get_psi_comp() const {return psi_comp ;} ;
/**
* Returns the total \f$\Psi\f$.
*/
const Tenseur& get_psi_tot() const {return psi_tot ;} ;
/**
* Returns the gradient of \f$\Psi\f$.
*/
const Tenseur& get_grad_psi_tot() const {return grad_psi_tot ;} ;
/**
* Returns the gradient of \e N .
*/
const Tenseur& get_grad_n_tot() const {return grad_n_tot ;} ;
/**
* Returns the part of \f$\beta^i\f$ generated by the hole.
*/
const Tenseur& get_shift_auto() const {return shift_auto ;} ;
Cmp return_shift_auto(int i) const {return shift_auto(i) ;} ;
/**
* Returns the part of \f$A^{ij}\f$ generated by the hole.
*/
const Tenseur& get_taij_auto() const {return taij_auto ;} ;
/**
* Returns the part of \f$A^{ij}\f$ generated by the companion hole.
*/
const Tenseur& get_taij_comp() const {return taij_comp ;} ;
/**
* Returns the total \f$A^{ij}\f$.
*/
const Tenseur& get_taij_tot() const {return taij_tot ;}
/**
* Returns the total \f$K^{ij}\f$.
*/
const Tenseur& get_tkij_tot() const {return tkij_tot ;}
/**
* Returns the part of \f$K^{ij}\f$ generated by the hole.
*/
const Tenseur& get_tkij_auto() const {return tkij_auto ;}
/**
* Returns the function used to construct \c tkij_auto from \c tkij_tot .
*/
const Cmp get_decouple() const {return decouple ;}
Cmp& set_n_auto() {return n_auto.set() ;}
Cmp& set_psi_auto() {return psi_auto.set() ;}
void set_lapse_hori(double xx) {lapse_hori = xx;}
public:
/**
* Imports the part of \e N due to the companion hole \c comp . The
* total \e N is then calculated.
*
* It also imports the gradient of \e N and construct the total \f$\nabla N\f$.
*/
void fait_n_comp (const Bhole& comp) ;
/**
* Imports the part of \f$\Psi\f$ due to the companion hole \c comp . The
* total \f$\Psi\f$ is then calculated.
*
* It also imports the gradient of \f$\Psi\f$ and construct the total \f$\nabla \Psi\f$.
*/
void fait_psi_comp (const Bhole& comp) ;
/**
* Imports the part of \e N due to the companion ns \c comp . The
* total \e N is then calculated.
*
* It also imports the gradient of \e N and construct the total \f$\nabla N\f$.
*/
void fait_n_comp (const Et_bin_nsbh& comp) ;
/**
* Imports the part of \f$\Psi\f$ due to the companion ns \c comp . The
* total \f$\Psi\f$ is then calculated.
*
* It also imports the gradient of \f$\Psi\f$ and construct the total \f$\nabla \Psi\f$.
*/
void fait_psi_comp (const Et_bin_nsbh& comp) ;
/**
* Calculates the part of \f$A^{ij}\f$ generated by \c shift_auto .
*/
void fait_taij_auto () ;
/**
* Corrects \c shift_auto in such a way that the total \f$A^{ij}\f$ is
* equal to zero in the horizon, which should ensure the regularity
* of \f$K^{ij}\f$, using the stored values of the boost and the angular
* velocity.
*
* \b WARNING : this should only be used for a black hole in
* a binary system \c Bhole_binaire or \c Bin_ns_bh .
*
* @param comp [input] : the part of \f$\beta^i\f$ generated by the companion
* hole.
*/
void regularise_shift (const Tenseur& comp) ;
/**
* Computes the viriel error, that is the difference between the ADM and the Komar
* masses, calculated by the asymptotic behaviours of respectively \f$\Psi\f$ and \e N .
*
* \b WARNING this should only be used for an isolated black hole.
*/
double viriel_seul () const ;
/**
* Sets the values of the fields to :
* \li \c n_auto \f$= \frac{1}{2}-2\frac{a}{r}\f$
* \li \c n_comp \f$= \frac{1}{2}\f$
* \li \c psi_auto \f$= \frac{1}{2}+\frac{a}{r}\f$
* \li \c psi_comp \f$= \frac{1}{2}\f$
*
* \e a being the radius of the hole, the other fields being set to zero.
*/
void init_bhole () ;
/**
* Set the inital values to those of Kerr
* @param masse [input] : ADM mass in LORENE's units.
* @param moment [input] : \f$\frac{J}{M}=a\f$, in LORENE's units.
*
* The radius \f$r_0\f$ of \c *this is supposed to be equal to
* \f$\frac{1}{2}\sqrt{M^2-a^2}\f$.
*
* The fields have then the following values~:
*
* \li \f$\Omega = \frac{a}{2M\sqrt{M^2-a^2}}\f$
*
* \li \f$\Psi^4 =
* 1+\frac{2M}{r}+\frac{3M^2+a^2\cos^2\theta}{2r^2}+\frac{2Mr_0^2}{r^3}+
* \frac{r_0^4}{r^4}\f$.
* \li \f$N = \left(1-\frac{2MR}{\Sigma}+\frac{4a^2M^2R^2\sin^2\theta}
* {\Sigma^2\left(R^2+a^2\right)+2a^2\Sigma R\sin^2\theta}\right)^{\frac{1}{2}}\f$
* \li \f$N^\phi = \frac{2aMR}{\Sigma\left(R^2+a^2\right)+2a^2MR\sin^2\theta}\f$
* \end {itemize}
* where~:
*
* \li \f$R = r+\frac{M^2-a^2}{4r}+M\f$.
* \li \f$\Sigma = R^2+a^2-2MR\f$
* \li \f$r_0\f$ is equal to \c rayon .
*
*/
void init_kerr (double masse, double moment) ;
/**
* Solves the equation for \e N ~:
* \f[
*\Delta N = -\frac{2}{\Psi}\nabla_i \Psi \nabla^i N
* + N \Psi^4 K_{ij} K^{ij}
* \f]
* with the condition that \c N =0 on the horizon.
* @param relax [input] : the relaxation parameter.
*
* \b WARNING this should only be used for an isolated black hole.
*/
void solve_lapse_seul (double relax) ;
/**
* Solves the equation for \f$\Psi\f$~:
* \f[
* \Delta \Psi = - \frac{\Psi^5} {8} K_{ij}K^{ij}
* \f]
* with the condition that \f$\partial_r \Psi =-\frac{1}{2 {\tt rayon}}
* f\left(\theta, \phi\right)\f$ on the horizon, where \c f is
* the value of \f$\Psi\f$ on the horizon at the preceeding step.
* @param relax [input] : the relaxation parameter.
*
* \b WARNING this should only be used for an isolated black hole.
*/
void solve_psi_seul (double relax) ;
/**
* Solves the equation for \f$\vec{\beta}\f$~:
* \f[
*\Delta \beta^i +\frac{1}{3} \nabla^i \left(\nabla_j \beta^j\right)
* = -6A^{ij}\frac{\nabla_j \Psi}{\Psi} + 2 K^{ij}\nabla_j N
* \f]
* with \f$\vec{\beta} = -\Omega \vec{m} - \vec{V}\f$ on the horizon,
* \f$\vec{V}\f$ being the boost and \f$\vec{m} = \frac{\partial}{\partial \phi}\f$.
* The solution is solved using Oohara-scheme and an iteration.
* @param precis [input] : parameter for the Oohara-solver which is an iterative
scheme.
* @param relax [input] : the relaxation parameter.
*
* \b WARNING this should only be used for an isolated black hole.
*/
void solve_shift_seul (double precis, double relax) ;
/**
* Corrects the shift in the innermost shell, so that it remains \f$
* {\mathcal{C}}^2\f$ and that \f$A^{ij}\f$ equals zero on the horizon.
*
* \c regul is then, the relative difference between the shift before
* and after the regularisation.
*
* \b WARNING this should only be used for an isolated black hole.
*/
void regularise_seul () ;
/**
* Solves the equation for \e N ~:
* \f[
*\Delta N = -\frac{2}{\Psi}\nabla_i \Psi \nabla^i N
* + N \Psi^4 K_{ij} K^{ij}
* \f]
* with the condition that \c N =0 on the horizon.
* @param relax [input] : the relaxation parameter.
*
* \b WARNING this should only be used for BH in a \c Bin_ns_bh .
*/
void solve_lapse_with_ns (double relax, int bound_nn,
double lim_nn) ;
/**
* Solves the equation for \f$\Psi\f$~:
* \f[
(\Delta \Psi = - \frac{\Psi^5} {8} K_{ij}K^{ij}
* \f]
* with the condition that \f$\partial_r \Psi=-\frac{1}{2 {\tt rayon}}
* f\left(\theta, \phi\right)\f$ on the horizon, where \c f is the value of \f$\Psi\f$ on
* the horizon at the preceeding step.
* @param relax [input] : the relaxation parameter.
*
* \b WARNING this should only be used for BH in a \c Bin_ns_bh .
*/
void solve_psi_with_ns (double relax) ;
/**
* Solves the equation for \f$\vec{\beta}\f$~:
* \f[
*\Delta \beta^i +\frac{1}{3} \nabla^i \left(\nabla_j \beta^j\right)
* = -6A^{ij}\frac{\nabla_j \Psi}{\Psi} + 2 K^{ij}\nabla_j N
* \f]
* with \f$\vec{\beta} = -\Omega \vec{m} - \vec{V}\f$ on the horizon,
* \f$\vec{V}\f$ being the boost and \f$\vec{m} = \frac{\partial}{\partial \phi}\f$.
* The solution is solved using Oohara-scheme and an iteration.
* @param ns [input] : the companion.
* @param precis [input] : parameter for the Oohara-solver which is an iterative
scheme.
* @param relax [input] : the relaxation parameter.
*
* \b WARNING this should only be used for BH in a \c Bin_ns_bh .
*/
void solve_shift_with_ns (const Et_bin_nsbh& ns,
double precis, double relax,
int bound_nn, double lim_nn) ;
void equilibrium (const Et_bin_nsbh& ns, double precis, double relax,
int bound_nn, double lim_nn) ;
void update_metric (const Et_bin_nsbh& ns) ;
/**
* Calculates the total \f$K^{ij}\f$. The regularisation of the shift must be done
* before to ensure regularity.
*/
void fait_tkij() ;
/// Computes the area of the throat.
double area() const ;
/**
* Calculates the ADM mass of the black hole using :
* \f$M = -\frac{1}{2 \pi} \oint_{\infty} \nabla^i \Psi {\mathrm d} S_i\f$.
*
* \b WARNING this should only be used for an isolated black hole.
*/
double masse_adm_seul () const ;
/**
* Calculates the Komar mass of the black hole using :
* \f$M = \frac{1}{4 \pi} \oint_{\infty} \nabla^i N {\mathrm d} S_i\f$.
*
* \b WARNING this should only be used for an isolated black hole.
*/
double masse_komar_seul() const ;
/**
* Calculates the angular momentum of the black hole using the formula at infinity :
* \f$ J = -\frac{1}{8 \pi} \oint_{\infty} K_j^i m^j {\mathrm d}S_i\f$
* where \f$\vec{m} = \frac{\partial}{\partial \phi}\f$.
*
*\b WARNING It supposes that the boost is zero and should only be
* used for an isolated black hole..
*/
double moment_seul_inf() const ;
/**
* Calculates the angular momentum of the black hole using the formula on the horizon :
* \f$ J = -\frac{1}{8 \pi} \oint_{H} \Psi^6 K_j^i m^j {\mathrm d}S_i\f$
* where \f$\vec{m} = \frac{\partial}{\partial \phi}\f$ and \e H denotes the horizon.
*
*\b WARNING It supposes that the boost is zero and should only be
* used for an isolated black hole..
*/
double moment_seul_hor() const ;
/*
* local angular momentum
*/
double local_momentum() const ;
/**
* Initiates the black hole for a resolution with \f$\Phi = \log \Psi\f$.
*/
void init_bhole_phi () ;
/**
* Initiates for a single the black hole.
*
* \b WARNING It supposes that the boost is zero and should only be
* used for an isolated black hole..
*/
void init_bhole_seul () ;
friend class Bhole_binaire ; ///< Binary black hole system.
friend class Bin_ns_bh ; ///< Binary NS-BH
} ;
/**
* Binary black holes system. \ingroup (star)
*
* This class is intended for dealing with binary black holes configurations
* in the conformaly flat approximation.
*/
class Bhole_binaire {
// data :
private:
// les deux trous noirs.
Bhole hole1 ; ///< Black hole one
Bhole hole2 ; ///< Black hole two
// Tableau sur les deux trous.
Bhole* holes[2] ; ///< Array on the black holes
double pos_axe ; /// Position of the axis of rotation
double omega ; ///< Angular velocity
public:
// constructeurs & destructeur
Bhole_binaire(Map_af& mp1, Map_af& mp2) ; ///< Standard constructor
Bhole_binaire(const Bhole_binaire& ) ; ///< Copy
~Bhole_binaire() ; ///< Destructor
public:
// trucs pour modifier
void operator=(const Bhole_binaire&) ; ///< Affectation operator
/**
* Read/write of a component of the system. \c i must be equal to
* 1 or 2.
*/
Bhole& set(int i)
{ assert( (i==1) || (i==2) );
return *holes[i-1] ;} ;
/**
* Sets the orbital velocity to \c ome
*/
void set_omega(double ome) {omega = ome ;
hole1.set_omega (ome) ;
hole2.set_omega (ome) ;} ;
void set_pos_axe (double) ;
public:
// trucs pour lire :
/**
* Read only of a component of the system. \c i must be equal to
* 1 or 2.
*/
const Bhole& operator()(int i) const
{ assert( (i==1) || (i==2) );
return *holes[i-1] ;} ;
/// Returns the angular velocity
double get_omega() const {return omega; } ;
/**
* Initialisation of the system. Each hole is set close to a Schwarzschild one
* and the parts of the fields generated by
* the companion are calculated.
*
* The angular velocity is set to zero.
*/
void init_bhole_binaire() ;
/**
* Computes the viriel error, that is the difference between the ADM and the Komar
* masses, calculated by the asymptotic behaviours of respectively \f$\Psi\f$ and \e N .
*/
double viriel() const ;
/**
* Solves the equation for the lapse~:
* \f[
* \Delta N_a = -\frac{2}{\Psi}\nabla_i \Psi_a \nabla^i N + N \Psi^4 K_{ij}K_a^{ij}
* \f]
* The fields are the total values excpet those with subscript \f$_a\f$, which are
* the fields generated by each holes (\e a = 1, 2). The boundary conditions are
* such that \e N =0 on both horizons.
* The companion contributions are then obtained.
* @param precis [input] : precision, for the boudary conditions are
* obtained by iteration.
* @param relax [input] : relaxation parameter.
*/
void solve_lapse (double precis, double relax) ;
/**
* Solves the equation for the conformal factor~:
* \f[
*\Delta \Psi_a = -\frac {\Psi^5}{8} K_{ij}K_a^{ij}
* \f]
* The fields are the total values excpet those with subscript \f$_a\f$, which are
* the fields generated by each holes (\e a = 1, 2). The boundary conditions are such that
* \f$\partial_r \Psi = -\frac{1}{2 r_0} f\left(\theta, \phi\right)\f$ on both horizons, \f$r_0\f$ being
* the radii of those horizons and \e f the value of \f$\Psi\f$ on the
* horizons at the preceeding step. The companion contributions are then
* obtained.
* @param precis [input] : precision, for the boudary conditions are being
* obtained by iteration.
* @param relax [input] : relaxation parameter.
*/
void solve_psi (double precis, double relax) ;
/**
* Solves the equation for the shift, using the Oohara-Nakarmure scheme~:
* \f[
*\Delta \beta_a^i +\frac{1}{3} \nabla^i \left(\nabla_j \beta_a^j\right) =
* -6A^{ij}\frac{\nabla_i \Psi_a}{\Psi} + 2K^{ij}\nabla_j N_a
* \f]
* using the current \f$\Omega\f$ for the boudary conditions~:
* \f$\vec{N} = -\Omega \vec{m}\f$ on both horizons.
* The fields are the total values excpet those with subscript \f$_a\f$, which are
* the fields generated by each holes (\c a = 1, 2). The companion contributions are then
* obtained.
* @param precis [input] : precision for the solver, the boundary
* conditions and the inversion of the operator being
* obtained by iteration.
* @param relax [input] : relaxation parameter.
*/
void solve_shift (double precis, double relax) ;
/**
* Calculation af the extrinsic curvature tensor.
*
* The regularisation of the shifts must have been done. All the
* contributions of \f$A^{ij}\f$ are then calculated and the total tensor
* must be zero on both horizons. The computation is done to avoid every singularity
* close to the horizons (division by \e N =0) for it is done in the coefficient space
* in the two regions surrounding the holes.
*/
void fait_tkij () ;
/**
* Calculates {tt decouple} which is used to obtain \c tkij_auto by the formula :
* \c tkij_auto = \c decouple * \c tkij_tot .
* (see the membre {tt Cmp decouple for more precisions about its value).
*
*/
void fait_decouple () ;
public:
/**
* Initialize the systeme to Misner Lindquist solution, that is solving for \e N and
* \f$Psi\f$ in the case \f$\Omega = 0\f$.
* @param precis [input] : precision for the convergence (on \e N ).
* @param relax [input] : relaxation parameter.
*/
void set_statiques (double precis, double relax) ;
/**
* Solves the equation for a particular angular velocity, the systeme being
* initialized to Misner-Lindquist solution.
* @param precis [input] : precision for the convergence (on \f$\beta\f$).
* @param relax [input] : relaxation parameter.
* @param nbre_ome [input] : number of intermediates velocities to go from 0 to
* \c omega , typically 10.
* @param sortie [input] : flag for the output on files (0 no output files).
* @returns : the virial error.
*/
void coal (double precis, double relax, int nbre_ome, double search_ome,
double m1, double m2, const int sortie = 0) ;
/**
* Calculates the ADM mass of the system using :
* \f$M = -\frac{1}{2 \pi} \oint_{\infty} \nabla^i \Psi {\mathrm d} S_i\f$.
*/
double adm_systeme() const ;
/**
* Calculates the Komar mass of the system using :
* \f$M = \frac{1}{4 \pi} \oint_{\infty} \nabla^i N {\mathrm d} S_i\f$.
*/
double komar_systeme() const ;
/**
* Calculates the angular momentum of the black hole using the formula at infinity :
* \f$ J = -\frac{1}{8 \pi} \oint_{\infty} K_j^i m^j {\mathrm d}S_i\f$
* where \f$\vec{m} = \frac{\partial}{\partial \phi}\f$.
*/
double moment_systeme_inf() ;
/**
* Calculates the angular momentum of the black hole using the formula on the horizon :
* \f$ J = -\sum_{a= 1, 2} \frac{1}{8 \pi} \oint_{H_a} \Psi^6 K_j^i m^j {\mathrm d}S_i\f$
* where \f$\vec{m} = \frac{\partial}{\partial \phi}\f$ and \f$H_a\f$ denotes the horizon
* of the hole \e a .
*
*/
double moment_systeme_hor() const ;
/**
* Calculation of the proper distance between the two spheres of inversion,
* along the x axis.
* @param nr [input] : number of points used for the calculation.
*/
double distance_propre(const int nr = 65) const ;
Tbl linear_momentum_systeme_inf() const ;
/**
* Solve the equation for the logarithm of \f$\Psi\f$.
*/
void solve_phi (double precision, double relax) ;
/**
* Initiates the system for a resolution using the logarithm of \f$\Psi\f$.
*/
void init_phi() ;
} ;
}
#endif
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