hole_bhns_global.C

/*
 *  Methods of class Hole_bhns to compute global quantities
 *
 *    (see file hole_bhns.h for documentation).
 *
 */

/*
 *   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
 *
 */

char hole_bhns_global_C[] = "$Header: /cvsroot/Lorene/C++/Source/Hole_bhns/hole_bhns_global.C,v 1.3 2008/07/02 21:10:15 k_taniguchi Exp $" ;

/*
 * $Id: hole_bhns_global.C,v 1.3 2008/07/02 21:10:15 k_taniguchi Exp $
 * $Log: hole_bhns_global.C,v $
 * Revision 1.3  2008/07/02 21:10:15  k_taniguchi
 * A bug removed.
 *
 * Revision 1.2  2008/05/15 19:07:26  k_taniguchi
 * Introduction of the quasilocal spin angular momentum.
 *
 * Revision 1.1  2007/06/22 01:25:15  k_taniguchi
 * *** empty log message ***
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Hole_bhns/hole_bhns_global.C,v 1.3 2008/07/02 21:10:15 k_taniguchi Exp $
 *
 */

// C++ headers
//#include <>

// C headers
#include <math.h>

// Lorene headers
#include "hole_bhns.h"
#include "unites.h"
#include "utilitaires.h"

                    //-----------------------------------------//
                    //          Irreducible mass of BH         //
                    //-----------------------------------------//

double Hole_bhns::mass_irr_bhns() const {

    // Fundamental constants and units
    // -------------------------------
    using namespace Unites ;

    if (p_mass_irr_bhns == 0x0) {   // a new computation is required

        Scalar psi4(mp) ;
    psi4 = pow(confo_tot, 4.) ;
    psi4.std_spectral_base() ;
    psi4.annule_domain(0) ;
    psi4.raccord(1) ;

    double radius_ah = mp.val_r(1,-1.,M_PI/2.,0.) ;

    Map_af& mp_aff= dynamic_cast<Map_af&>(mp) ;

    double a_ah = mp_aff.integrale_surface(psi4, radius_ah) ;
    double mirr = sqrt(a_ah/16./M_PI) / ggrav ;

    p_mass_irr_bhns = new double( mirr ) ;

    }

    return *p_mass_irr_bhns ;

}

          //----------------------------------------------------------//
          //          Quasilocal spin angular momentum of BH          //
          //----------------------------------------------------------//

double Hole_bhns::spin_am_bhns(const Tbl& xi_i, const double& phi_i,
                   const double& theta_i, const int& nrk_phi,
                   const int& nrk_theta) const {

    // Fundamental constants and units
    // -------------------------------
    using namespace Unites ;

    if (p_spin_am_bhns == 0x0) {   // a new computation is required

        double mass = ggrav * mass_bh ;

        Scalar rr(mp) ;
    rr = mp.r ;
    rr.std_spectral_base() ;

    Scalar st(mp) ;
    st = mp.sint ;
    st.std_spectral_base() ;
    Scalar ct(mp) ;
    ct = mp.cost ;
    ct.std_spectral_base() ;
    Scalar sp(mp) ;
    sp = mp.sinp ;
    sp.std_spectral_base() ;
    Scalar cp(mp) ;
    cp = mp.cosp ;
    cp.std_spectral_base() ;

    Vector ll(mp, CON, mp.get_bvect_cart()) ;
    ll.set_etat_qcq() ;
    ll.set(1) = st % cp ;
    ll.set(2) = st % sp ;
    ll.set(3) = ct ;
    ll.std_spectral_base() ;

    double radius_ah = mp.val_r(1,-1.,M_PI/2.,0.) ;

    if (kerrschild) {

      cout << "Not yet prepared!!!" << endl ;
      abort() ;

    }
    else {  // Isotropic coordinates

      // Sets C/M^2 for each case of the lapse boundary condition
      // --------------------------------------------------------
      double cc ;

      if (bc_lapconf_nd) {  // Neumann boundary condition
        if (bc_lapconf_fs) {  // First condition
          // d(\alpha \psi)/dr = 0
          // ---------------------
          cc = 2. * (sqrt(13.) - 1.) / 3. ;
        }
        else {  // Second condition
          // d(\alpha \psi)/dr = (\alpha \psi)/(2 rah)
          // -----------------------------------------
          cc = 4. / 3. ;
        }
      }
      else {  // Dirichlet boundary condition
        if (bc_lapconf_fs) {  // First condition
          // (\alpha \psi) = 1/2
          // -------------------
          cout << "!!!!! WARNING: Not yet prepared !!!!!" << endl ;
          abort() ;
        }
        else {  // Second condition
          // (\alpha \psi) = 1/sqrt(2.) \psi_KS
          // ----------------------------------
          cout << "!!!!! WARNING: Not yet prepared !!!!!" << endl ;
          abort() ;
          //          cc = 2. * sqrt(2.) ;
        }
      }

      Scalar r_are(mp) ;
      r_are = r_coord(bc_lapconf_nd, bc_lapconf_fs) ;
      r_are.std_spectral_base() ;

      // Killing vector of the spherical components
      Vector killing_spher(mp, COV, mp.get_bvect_spher()) ;
      killing_spher.set_etat_qcq() ;
      killing_spher = killing_vect(xi_i, phi_i, theta_i,
                       nrk_phi, nrk_theta) ;
      killing_spher.std_spectral_base() ;

      killing_spher.set(2) = confo_tot * confo_tot * radius_ah
        * killing_spher(2) ;
      killing_spher.set(3) = confo_tot * confo_tot * radius_ah
        * killing_spher(3) ;
      // killing_spher(3) is already divided by sin(theta)
      killing_spher.std_spectral_base() ;

      // Killing vector of the Cartesian components
      Vector killing(mp, COV, mp.get_bvect_cart()) ;
      killing.set_etat_qcq() ;
      killing.set(1) = (killing_spher(2) * ct * cp - killing_spher(3) * sp)
        / radius_ah ;
      killing.set(2) = (killing_spher(2) * ct * sp + killing_spher(3) * cp)
        / radius_ah ;
      killing.set(3) = - killing_spher(2) * st / radius_ah ;
      killing.std_spectral_base() ;

      // Surface integral <- dzpuis should be 0
      // --------------------------------------
      // Source terms in the surface integral
      Scalar source_1(mp) ;
      source_1 = (ll(1) * (taij_tot_rs(1,1) * killing(1)
                   + taij_tot_rs(1,2) * killing(2)
                   + taij_tot_rs(1,3) * killing(3))
              + ll(2) * (taij_tot_rs(2,1) * killing(1)
                 + taij_tot_rs(2,2) * killing(2)
                 + taij_tot_rs(2,3) * killing(3))
              + ll(3) * (taij_tot_rs(3,1) * killing(1)
                 + taij_tot_rs(3,2) * killing(2)
                 + taij_tot_rs(3,3) * killing(3)))
        / pow(confo_tot, 4.) ;
      source_1.std_spectral_base() ;
      source_1.dec_dzpuis(2) ;  // dzpuis : 2 -> 0

      Scalar source_2(mp) ;
      source_2 = -2. * pow(confo_tot, 3.) * mass * mass * cc
        * sqrt(1. - 2.*mass/r_are/rr + cc*cc*pow(mass/r_are/rr,4.))
        * (ll(1)*killing(1) + ll(2)*killing(2) + ll(3)*killing(3))
        / lapconf_tot / pow(r_are*rr, 3.) ;
      source_2.std_spectral_base() ;

      Scalar source_surf(mp) ;
      source_surf = source_1 + source_2 ;
      source_surf.std_spectral_base() ;
      source_surf.annule_domain(0) ;
      source_surf.raccord(1) ;

      Map_af& mp_aff= dynamic_cast<Map_af&>(mp) ;

      double spin = mp_aff.integrale_surface(source_surf, radius_ah) ;
      double spin_angmom = 0.5 * spin / qpig ;

      p_spin_am_bhns = new double( spin_angmom ) ;

    }

    }

    return *p_spin_am_bhns ;

}

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