et_bin_bhns_extr_upmetr.C

/*
 *  Methods Et_bin_bhns_extr::update_metric_extr_ks
 *  and Et_bin_bhns_extr::update_metric_extr_cf
 *
 *    (see file et_bin_bhns_extr.h for documentation).
 *
 */

/*
 *   Copyright (c) 2004-2005 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 et_bin_bhns_extr_upmetr_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_bhns_extr_upmetr.C,v 1.2 2005/02/28 23:16:37 k_taniguchi Exp $" ;

/*
 * $Id: et_bin_bhns_extr_upmetr.C,v 1.2 2005/02/28 23:16:37 k_taniguchi Exp $
 * $Log: et_bin_bhns_extr_upmetr.C,v $
 * Revision 1.2  2005/02/28 23:16:37  k_taniguchi
 * Modification to include the case of the conformally flat background metric
 *
 * Revision 1.1  2004/11/30 20:51:32  k_taniguchi
 * *** empty log message ***
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_bhns_extr_upmetr.C,v 1.2 2005/02/28 23:16:37 k_taniguchi Exp $
 *
 */

// C headers
#include<math.h>

// Lorene headers
#include "et_bin_bhns_extr.h"
#include "etoile.h"
#include "coord.h"
#include "unites.h"

          //-----------------------------------------------------------//
          //          No relaxation for a fixed BH background          //
          //-----------------------------------------------------------//

void Et_bin_bhns_extr::update_metric_extr(const double& mass,
                      const double& sepa)
{

  using namespace Unites ;

    if (kerrschild) {

        // Computation of quantities coming from the companion (K-S BH)
        // ------------------------------------------------------------

        const Coord& xx = mp.x ;
    const Coord& yy = mp.y ;
    const Coord& zz = mp.z ;

    Tenseur r_bh(mp) ;
    r_bh.set_etat_qcq() ;
    r_bh.set() = pow( (xx+sepa)*(xx+sepa) + yy*yy + zz*zz, 0.5) ;
    r_bh.set_std_base() ;

    Tenseur xx_con(mp, 1, CON, ref_triad) ;
    xx_con.set_etat_qcq() ;
    xx_con.set(0) = xx + sepa ;
    xx_con.set(1) = yy ;
    xx_con.set(2) = zz ;
    xx_con.set_std_base() ;

    Tenseur xsr_con(mp, 1, CON, ref_triad) ;
    xsr_con = xx_con / r_bh ;
    xsr_con.set_std_base() ;

    Tenseur msr(mp) ;
    msr = ggrav * mass / r_bh ;
    msr.set_std_base() ;

    Tenseur lapse_bh(mp) ;
    lapse_bh = 1. / sqrt( 1.+2.*msr ) ;
    lapse_bh.set_std_base() ;

    logn_comp.set_etat_qcq() ;
    logn_comp.set() = log( lapse_bh() ) ;
    logn_comp.set_std_base() ;

    beta_comp.set_etat_qcq() ;
    beta_comp.set() = log( lapse_bh() ) ; 
                                 // conformal factor of KS-BH is unity
    beta_comp.set_std_base() ;

    shift_comp.set_etat_qcq() ;

    shift_comp.set(0) = -2.*lapse_bh()*lapse_bh()*msr()*xsr_con(0) ;
    shift_comp.set(1) = -2.*lapse_bh()*lapse_bh()*msr()*xsr_con(1) ;
    shift_comp.set(2) = -2.*lapse_bh()*lapse_bh()*msr()*xsr_con(2) ;

    shift_comp.set_std_base() ;
    shift_comp.set_triad( ref_triad ) ;

    // Lapse function N
    // ----------------

    nnn = exp( unsurc2 * logn_auto ) * lapse_bh ;

    nnn.set_std_base() ;

    // Conformal factor A^2
    // --------------------

    a_car = exp ( 2.*unsurc2*(beta_auto - logn_auto) ) ;

    a_car.set_std_base() ;

    // Shift vector N^i
    // ----------------

    shift = shift_auto + shift_comp ;

    // Derivative of metric coefficients
    // ----------------------------------

    // ... (d/dX,d/dY,d/dZ)(logn_auto) :
    d_logn_auto_regu = logn_auto_regu.gradient() ;    // (d/dx, d/dy, d/dz)
    d_logn_auto_regu.change_triad(ref_triad) ;   // -->  (d/dX, d/dY, d/dZ)

    if ( *(d_logn_auto_div.get_triad()) != ref_triad ) {

        // Change the basis from spherical coordinate to Cartesian one
        d_logn_auto_div.change_triad( mp.get_bvect_cart() ) ;

        // Change the basis from mapping coordinate to absolute one
        d_logn_auto_div.change_triad( ref_triad ) ;

    }

    d_logn_auto = d_logn_auto_regu + d_logn_auto_div ;

    // ... (d/dX,d/dY,d/dZ)(beta_auto) :
    d_beta_auto = beta_auto.gradient() ;    // (d/dx, d/dy, d/dz)
    d_beta_auto.change_triad(ref_triad) ;   // -->  (d/dX, d/dY, d/dZ)

    if (relativistic) {
        // ... extrinsic curvature (tkij_auto and akcar_auto)
        extrinsic_curv_extr(mass, sepa) ;
    }

    // The derived quantities are obsolete
    // -----------------------------------

    Etoile_bin::del_deriv() ;

    }
    else {

        // Computation of quantities coming from the companion (CF Sch. BH)
        // ----------------------------------------------------------------

        const Coord& xx = mp.x ;
    const Coord& yy = mp.y ;
    const Coord& zz = mp.z ;

    Tenseur r_bh(mp) ;
    r_bh.set_etat_qcq() ;
    r_bh.set() = pow( (xx+sepa)*(xx+sepa) + yy*yy + zz*zz, 0.5) ;
    r_bh.set_std_base() ;

    Tenseur msr(mp) ;
    msr = ggrav * mass / r_bh ;
    msr.set_std_base() ;

    Tenseur lapse_bh(mp) ;
    lapse_bh = (1.-0.5*msr) / (1.+0.5*msr) ;
    lapse_bh.set_std_base() ;

    logn_comp.set_etat_qcq() ;
    logn_comp.set() = log( lapse_bh() ) ;
    logn_comp.set_std_base() ;

    Tenseur lappsi(mp) ;
    lappsi = 1. - 0.25*msr*msr ;
    lappsi.set_std_base() ;

    beta_comp.set_etat_qcq() ;
    beta_comp.set() = log( lappsi() ) ;
    beta_comp.set_std_base() ;

    shift_comp.set_etat_qcq() ;

    shift_comp.set(0) = 0. ;
    shift_comp.set(1) = 0. ;
    shift_comp.set(2) = 0. ;

    shift_comp.set_std_base() ;
    shift_comp.set_triad( ref_triad ) ;

    // Lapse function N
    // ----------------

    nnn = exp( unsurc2 * logn_auto ) * lapse_bh ;

    nnn.set_std_base() ;

    // Conformal factor A^2
    // --------------------

    a_car = exp ( 2.*unsurc2*(beta_auto + beta_comp
                  - logn_auto - logn_comp) ) ;

    a_car.set_std_base() ;

    // Shift vector N^i
    // ----------------

    shift = shift_auto + shift_comp ;

    // Derivative of metric coefficients
    // ----------------------------------

    // ... (d/dX,d/dY,d/dZ)(logn_auto) :
    d_logn_auto_regu = logn_auto_regu.gradient() ;  // (d/dx, d/dy, d/dz)
    d_logn_auto_regu.change_triad(ref_triad) ; // -->  (d/dX, d/dY, d/dZ)

    if ( *(d_logn_auto_div.get_triad()) != ref_triad ) {

        // Change the basis from spherical coordinate to Cartesian one
        d_logn_auto_div.change_triad( mp.get_bvect_cart() ) ;

        // Change the basis from mapping coordinate to absolute one
        d_logn_auto_div.change_triad( ref_triad ) ;

    }

    d_logn_auto = d_logn_auto_regu + d_logn_auto_div ;

    // ... (d/dX,d/dY,d/dZ)(beta_auto) :
    d_beta_auto = beta_auto.gradient() ;    // (d/dx, d/dy, d/dz)
    d_beta_auto.change_triad(ref_triad) ;   // -->  (d/dX, d/dY, d/dZ)

    if (relativistic) {
        // ... extrinsic curvature (tkij_auto and akcar_auto)
        extrinsic_curv_extr(mass, sepa) ;
    }

    // The derived quantities are obsolete
    // -----------------------------------

    Etoile_bin::del_deriv() ;

    }

}

---