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/*
* 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 1.4 2014/10/13 08:52:55 j_novak Exp $" ;
/*
* $Id: et_bin_bhns_extr_upmetr.C,v 1.4 2014/10/13 08:52:55 j_novak Exp $
* $Log: et_bin_bhns_extr_upmetr.C,v $
* Revision 1.4 2014/10/13 08:52:55 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.3 2014/10/06 15:13:08 j_novak
* Modified #include directives to use c++ syntax.
*
* 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 1.4 2014/10/13 08:52:55 j_novak Exp $
*
*/
// C headers
#include <cmath>
// Lorene headers
#include "et_bin_bhns_extr.h"
#include "etoile.h"
#include "coord.h"
#include "unites.h"
//-----------------------------------------------------------//
// No relaxation for a fixed BH background //
//-----------------------------------------------------------//
namespace Lorene {
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() ;
}
}
}
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