et_bin_bhns_extr_kinema.C

/*
 *  Method Et_bin_bhns_extr::kinematics_extr_ks
 *  and Et_bin_bhns_extr::kinematics_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_kinema_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_bhns_extr_kinema.C,v 1.2 2005/02/28 23:15:09 k_taniguchi Exp $" ;

/*
 * $Id: et_bin_bhns_extr_kinema.C,v 1.2 2005/02/28 23:15:09 k_taniguchi Exp $
 * $Log: et_bin_bhns_extr_kinema.C,v $
 * Revision 1.2  2005/02/28 23:15:09  k_taniguchi
 * Modification to include the case of the conformally flat background metric
 *
 * Revision 1.1  2004/11/30 20:49:58  k_taniguchi
 * *** empty log message ***
 *
 *
 * $Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_bhns_extr_kinema.C,v 1.2 2005/02/28 23:15:09 k_taniguchi Exp $
 *
 */

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

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

  using namespace Unites ;

    if (kerrschild) {

        int nz = mp.get_mg()->get_nzone() ;
    int nzm1 = nz - 1 ;

    // --------------------
    // Computation of B^i/N
    // --------------------

    //  1/ Computation of  - omega m^i

    const Coord& xa = mp.xa ;
    const Coord& ya = mp.ya ;

    bsn.set_etat_qcq() ;

    bsn.set(0) = omega * ya ;
    bsn.set(1) = - omega * xa ;
    bsn.set(2) = 0 ;

    bsn.annule(nzm1, nzm1) ;    // set to zero in the ZEC

    //  2/ Addition of shift and division by lapse

    bsn = ( bsn + shift ) / nnn ;

    bsn.annule(nzm1, nzm1) ;    // set to zero in the ZEC
    bsn.set_std_base() ;   // set the bases for spectral expansions

    //-------------------------
    // Centrifugal potentatial
    //-------------------------

    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_cov(mp, 1, COV, ref_triad) ;
    xx_cov.set_etat_qcq() ;
    xx_cov.set(0) = xx + sepa ;
    xx_cov.set(1) = yy ;
    xx_cov.set(2) = zz ;
    xx_cov.set_std_base() ;

    Tenseur xsr_cov(mp, 1, COV, ref_triad) ;
    xsr_cov = xx_cov / r_bh ;
    xsr_cov.set_std_base() ;

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

    if (relativistic) {

        // Lorentz factor between the co-orbiting observer and
        // the Eulerian one

        Tenseur tmp1(mp) ;
        tmp1.set_etat_qcq() ;
        tmp1.set() = 0 ;
        tmp1.set_std_base() ;

        for (int i=0; i<3; i++)
            tmp1.set() += xsr_cov(i) % bsn(i) ;

        tmp1.set_std_base() ;

        Tenseur tmp2 = 2.*msr % tmp1 % tmp1 ;
        tmp2.set_std_base() ;

        for (int i=0; i<3; i++)
            tmp2.set() += bsn(i) % bsn(i) ;

        tmp2 = a_car % tmp2 ;

        Tenseur gam0 = 1 / sqrt( 1 - tmp2 ) ;

        pot_centri = - log( gam0 ) ;

    }
    else {
        cout << "BH-NS binary system should be relativistic !!!" << endl ;
        abort() ;
    }

    pot_centri.annule(nzm1, nzm1) ; // set to zero in the external domain
    pot_centri.set_std_base() ;   // set the bases for spectral expansions

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

    Etoile_bin::del_deriv() ;

    }
    else {

        int nz = mp.get_mg()->get_nzone() ;
    int nzm1 = nz - 1 ;

    // --------------------
    // Computation of B^i/N
    // --------------------

    //  1/ Computation of  - omega m^i

    const Coord& xa = mp.xa ;
    const Coord& ya = mp.ya ;

    bsn.set_etat_qcq() ;

    bsn.set(0) = omega * ya ;
    bsn.set(1) = - omega * xa ;
    bsn.set(2) = 0 ;

    bsn.annule(nzm1, nzm1) ;    // set to zero in the ZEC

    //  2/ Addition of shift and division by lapse

    bsn = ( bsn + shift ) / nnn ;

    bsn.annule(nzm1, nzm1) ;    // set to zero in the ZEC
    bsn.set_std_base() ;   // set the bases for spectral expansions

    //-------------------------
    // Centrifugal potentatial
    //-------------------------

    if (relativistic) {

        // Lorentz factor between the co-orbiting observer and
        // the Eulerian one

        Tenseur tmp(mp) ;
        tmp.set_etat_qcq() ;
        tmp.set() = 0. ;
        tmp.set_std_base() ;

        for (int i=0; i<3; i++)
            tmp.set() += bsn(i) % bsn(i) ;

        tmp = a_car % tmp ;

        Tenseur gam0 = 1 / sqrt( 1 - tmp ) ;

        pot_centri = - log( gam0 ) ;

    }
    else {
        cout << "BH-NS binary system should be relativistic !!!" << endl ;
        abort() ;
    }

    pot_centri.annule(nzm1, nzm1) ; // set to zero in the external domain
    pot_centri.set_std_base() ;   // set the bases for spectral expansions

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

    Etoile_bin::del_deriv() ;

    }

}

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