binhor_global.C

/*
 *   Copyright (c) 2005 Francois Limousin
 *                      Jose Luis Jaramillo
 *
 *   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
 *
 */


char binhor_glob_C[] = "$Header: /cvsroot/Lorene/C++/Source/Bin_hor/binhor_global.C,v 1.8 2007/04/13 15:28:55 f_limousin Exp $" ;

/*
 * $Id: binhor_global.C,v 1.8 2007/04/13 15:28:55 f_limousin Exp $
 * $Log: binhor_global.C,v $
 * Revision 1.8  2007/04/13 15:28:55  f_limousin
 * Lots of improvements, generalisation to an arbitrary state of
 * rotation, implementation of the spatial metric given by Samaya.
 *
 * Revision 1.7  2006/05/24 16:56:37  f_limousin
 * Many small modifs.
 *
 * Revision 1.6  2005/09/24 08:31:38  f_limousin
 * Improve the computation of moment_adm() and moment_hor().
 *
 * Revision 1.5  2005/09/13 18:33:15  f_limousin
 * New function vv_bound_cart_bin(double) for computing binaries with
 * berlin condition for the shift vector.
 * Suppress all the symy and asymy in the importations.
 *
 * Revision 1.4  2005/06/09 16:12:04  f_limousin
 * Implementation of amg_mom_adm().
 *
 * Revision 1.3  2005/04/29 14:02:44  f_limousin
 * Important changes : manage the dependances between quantities (for
 * instance psi and psi4). New function write_global(ost).
 *
 * Revision 1.2  2005/03/04 17:09:57  jl_jaramillo
 * Change to avoid warnings
 *
 * Revision 1.1  2005/03/03 13:48:56  f_limousin
 * First version
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Bin_hor/binhor_global.C,v 1.8 2007/04/13 15:28:55 f_limousin Exp $
 *
 */



//standard
#include <stdlib.h>
#include <math.h>

// Lorene
#include "nbr_spx.h"
#include "tensor.h"
#include "isol_hor.h"
#include "proto.h"
#include "utilitaires.h"
//#include "graphique.h"

double Bin_hor::adm_mass() const {
 
   Vector dpsi_un (hole1.psi_auto.derive_con(hole1.ff)) ;
    Vector dpsi_deux (hole2.psi_auto.derive_con(hole2.ff)) ;
    
    Tensor hdirac1 (contract((hole1.hh).derive_cov(hole1.ff),0,2)) ;
    Vector ww (0.125*(hdirac1 - (hole1.hh.trace(hole1.ff)).
              derive_con(hole1.ff))) ;

    double inf = hole1.mp.val_r(hole1.mp.get_mg()->get_nzone()-1, 1., 0., 0.) ;
    
    double masse = dpsi_un.flux(inf, hole1.ff) + 
               dpsi_deux.flux(inf, hole2.ff) +
               ww.flux(inf, hole1.ff) ;
    masse /= -2*M_PI ;
    return masse ;
}

double Bin_hor::komar_mass() const {

    Vector dnn_un (hole1.n_auto.derive_con(hole1.ff)) ;
    Vector dnn_deux (hole2.n_auto.derive_con(hole2.ff)) ;
    
    Vector ww (contract(hole1.hh, 1, hole1.nn.derive_cov(hole1.ff), 0)) ;
           
    double inf = hole1.mp.val_r(hole1.mp.get_mg()->get_nzone()-1, 1., 0., 0.) ;

    double mass = dnn_un.flux(inf, hole1.ff) + 
    dnn_deux.flux(inf, hole2.ff) + 
    ww.flux(inf, hole1.ff) ;
    
    mass /= 4*M_PI ;
    return mass ;
}
    
double Bin_hor::ang_mom_hor() const {
    
    if (omega == 0)
    return 0 ;
    else {
    // Alignement
    double orientation_un = hole1.mp.get_rot_phi() ;
    assert ((orientation_un==0) || (orientation_un==M_PI)) ;
    double orientation_deux = hole2.mp.get_rot_phi() ;
    assert ((orientation_deux==0) || (orientation_deux==M_PI)) ;
    int same_orient = (orientation_un == orientation_deux) ? 1 : -1 ;
    
    // Integral on the first horizon :
    Scalar xa_un (hole1.mp) ;
    xa_un = hole1.mp.xa ;
    xa_un.std_spectral_base() ;
    
    Scalar ya_un (hole1.mp) ;
    ya_un = hole1.mp.ya ;
    ya_un.std_spectral_base() ;
    
    Sym_tensor tkij_un (hole1.aa) ;
    tkij_un.change_triad(hole1.mp.get_bvect_cart()) ;

    Vector vecteur_un (hole1.mp, CON, hole1.mp.get_bvect_cart()) ;
    for (int i=1 ; i<=3 ; i++)
        vecteur_un.set(i) = -ya_un*tkij_un(1, i)+
        xa_un * tkij_un(2, i) ;
    vecteur_un.annule_domain(hole1.mp.get_mg()->get_nzone()-1) ;
    vecteur_un.change_triad (hole1.mp.get_bvect_spher()) ;
    
    Scalar integrant_un (hole1.get_psi4()*hole1.psi*hole1.psi
                 *vecteur_un(1)) ;
    double moment_un = hole1.mp.integrale_surface
        (integrant_un, hole1.radius+1e-12)/8/M_PI ;
    
    //Integral on the second horizon :
    Scalar xa_deux (hole2.mp) ;
    xa_deux = hole2.mp.xa ;
    xa_deux.std_spectral_base() ;
    
    Scalar ya_deux (hole2.mp) ;
    ya_deux = hole2.mp.ya ;
    ya_deux.std_spectral_base() ;
    
    Sym_tensor tkij_deux (hole2.aa) ;
    tkij_deux.change_triad(hole2.mp.get_bvect_cart()) ;

    Vector vecteur_deux (hole2.mp, CON, hole2.mp.get_bvect_cart()) ;
    for (int i=1 ; i<=3 ; i++)
        vecteur_deux.set(i) = -ya_deux*tkij_deux(1, i)+
        xa_deux * tkij_deux(2, i) ;
    vecteur_deux.annule_domain(hole2.mp.get_mg()->get_nzone()-1) ;
    vecteur_deux.change_triad (hole2.mp.get_bvect_spher()) ;
    
    Scalar integrant_deux (hole2.get_psi4()*hole2.psi*hole2.psi
                   *vecteur_deux(1)) ;
    double moment_deux = hole2.mp.integrale_surface
        (integrant_deux, hole2.radius+1e-12)/8/M_PI ;
    
    return moment_un+same_orient*moment_deux ;
    }
}



double Bin_hor::ang_mom_adm() const {
/*    
    Scalar integrand_un (hole1.k_dd()(1,3) - hole1.gam_dd()(1,3) * hole1.trK) ;
    
    integrand_un.mult_rsint() ;  // in order to pass from the triad components
    
    double mom = hole1.mp.integrale_surface_infini(integrand_un) ;    
    mom /= 8*M_PI ;
    return mom ;
*/

    if (omega == 0)
    return 0 ;
    else {
    // Alignement 
    double orientation_un = hole1.mp.get_rot_phi() ;
    assert ((orientation_un==0) || (orientation_un==M_PI)) ;
    double orientation_deux = hole2.mp.get_rot_phi() ;
    assert ((orientation_deux==0) || (orientation_deux==M_PI)) ;
    int same_orient = (orientation_un == orientation_deux) ? 1 : -1 ;
    
    // Construction of an auxiliar grid and mapping
    int nzones = hole1.mp.get_mg()->get_nzone() ;
    double* bornes = new double [nzones+1] ;
    double courant = (hole1.mp.get_ori_x()-hole2.mp.get_ori_x())+1 ;
    for (int i=nzones-1 ; i>0 ; i--) {
    bornes[i] = courant ;
    courant /= 2. ;
    }
    bornes[0] = 0 ;
    bornes[nzones] = __infinity ;
    
    Map_af mapping (*hole1.mp.get_mg(), bornes) ;
    
    delete [] bornes ; 
    
    // Construction of k_total
    Sym_tensor k_total (mapping, CON, mapping.get_bvect_cart()) ;
    
    Vector shift_un (mapping, CON, mapping.get_bvect_cart()) ;
    Vector shift_deux (mapping, CON, mapping.get_bvect_cart()) ;
    
    Vector beta_un (hole1.beta_auto) ;
    Vector beta_deux (hole2.beta_auto) ;
    beta_un.change_triad(hole1.mp.get_bvect_cart()) ;
    beta_deux.change_triad(hole2.mp.get_bvect_cart()) ;
    
    shift_un.set(1).import(beta_un(1)) ;
    shift_un.set(2).import(beta_un(2)) ;
    shift_un.set(3).import(beta_un(3)) ;
    
    shift_deux.set(1).import(same_orient*beta_deux(1)) ;
    shift_deux.set(2).import(same_orient*beta_deux(2)) ;
    shift_deux.set(3).import(beta_deux(3)) ;
    
    Vector shift_tot (shift_un+shift_deux) ;
    shift_tot.std_spectral_base() ;
    shift_tot.annule(0, nzones-2) ;

    // Substract the residuals
    shift_tot.inc_dzpuis(2) ;
    shift_tot.dec_dzpuis(2) ;
    
    const Metric_flat& flat0 (mapping.flat_met_cart()) ;

    k_total = shift_tot.ope_killing_conf(flat0) / 2. ;
    //- flat0.con() * hole1.trK;

    for (int lig=1 ; lig<=3 ; lig++)
        for (int col=lig ; col<=3 ; col++)
        k_total.set(lig, col).mult_r_ced() ;
    
    Vector vecteur_un (mapping, CON, mapping.get_bvect_cart()) ;
    for (int i=1 ; i<=3 ; i++)
        vecteur_un.set(i) = k_total(1, i) ;
    vecteur_un.change_triad (mapping.get_bvect_spher()) ;
    Scalar integrant_un (vecteur_un(1)) ;
    
    Vector vecteur_deux (mapping, CON, mapping.get_bvect_cart()) ;
    for (int i=1 ; i<=3 ; i++)
        vecteur_deux.set(i) = k_total(2, i) ;
    vecteur_deux.change_triad (mapping.get_bvect_spher()) ;
    Scalar integrant_deux (vecteur_deux(1)) ;
    
    // Multiplication by y and x :
    integrant_un.set_spectral_va() = integrant_un.get_spectral_va()
        .mult_st() ;
    integrant_un.set_spectral_va() = integrant_un.get_spectral_va()
        .mult_sp() ;
    
    integrant_deux.set_spectral_va() = integrant_deux.get_spectral_va()
        .mult_st() ;
    integrant_deux.set_spectral_va() = integrant_deux.get_spectral_va()
        .mult_cp() ;
    
    double moment = mapping.integrale_surface_infini (-integrant_un
                              +integrant_deux) ;
    
    moment /= 8*M_PI ;
    
    return moment ;
    }
}


/*
double Bin_hor::proper_distance(const int nr) const {
    

    // On determine les rayons coordonnes des points limites de l'integrale :
    double x_un = hole1.mp.get_ori_x() - hole1.rayon ;
    double x_deux = hole2.mp.get_ori_x() + hole2.rayon ;
    
    // Les coefficients du changement de variable :
    double pente = 2./(x_un-x_deux) ;
    double constante = - (x_un+x_deux)/(x_un-x_deux) ;
    
    
    double ksi ; // variable d'integration.
    double xabs ; // x reel.
    double air_un, theta_un, phi_un ; // coordonnee spheriques 1
    double air_deux, theta_deux, phi_deux ; // coordonnee spheriques 2
    
    double* coloc = new double[nr] ;
    double* coef = new double[nr] ;
    int* deg = new int[3] ;
    deg[0] = 1 ; deg[1] = 1 ; deg[2] = nr ;
    
    for (int i=0 ; i<nr ; i++) {
    ksi = -cos (M_PI*i/(nr-1)) ;
    xabs = (ksi-constante)/pente ;
    
    hole1.mp.convert_absolute (xabs, 0, 0, air_un, theta_un, phi_un) ;
    hole2.mp.convert_absolute (xabs, 0, 0, air_deux, theta_deux, phi_deux) ;
    
    coloc[i] = pow (hole1.psi_auto().val_point (air_un, theta_un, phi_un) +
           hole2.psi_auto().val_point (air_deux, theta_deux, phi_deux), 2.) ;
    }
    
    // On prend les coefficients de la fonction
    cfrcheb(deg, deg, coloc, deg, coef) ;
    
    // On integre
    double* som = new double[nr] ;
    som[0] = 2 ;
    for (int i=2 ; i<nr ; i+=2)
    som[i] = 1./(i+1)-1./(i-1) ;
    for (int i=1 ; i<nr ; i+=2)
    som[i] = 0 ;
    
    double res = 0 ;
    for (int i=0 ; i<nr ; i++)
    res += som[i]*coef[i] ;
    
    res /= pente ;
    
    delete [] deg ;
    delete [] coef ;
    delete [] coloc ;
    delete [] som ;
   
    return res ;

}
*/

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