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/*
* Methods Et_bin_bhns_extr::update_metric_der_comp_extr_ks
* and Et_bin_bhns_extr::update_metric_der_comp_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_um_der_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_bhns_extr_um_der.C,v 1.4 2014/10/13 08:52:55 j_novak Exp $" ;
/*
* $Id: et_bin_bhns_extr_um_der.C,v 1.4 2014/10/13 08:52:55 j_novak Exp $
* $Log: et_bin_bhns_extr_um_der.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 23:15:52 k_taniguchi
* Modification to include the case of the conformally flat background metric
*
* Revision 1.1 2004/11/30 20:51:09 k_taniguchi
* *** empty log message ***
*
*
* $Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_bhns_extr_um_der.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"
namespace Lorene {
void Et_bin_bhns_extr::update_metric_der_comp_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_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 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() ;
// Computation of d_logn_comp
// --------------------------
Tenseur lapse_bh2(mp) ; // lapse_bh * lapse_bh
lapse_bh2 = 1. / (1.+2.*msr) ;
lapse_bh2.set_std_base() ;
d_logn_comp.set_etat_qcq() ;
d_logn_comp.set(0) = lapse_bh2()%msr()%xsr_cov(0)/r_bh() ;
d_logn_comp.set(1) = lapse_bh2()%msr()%xsr_cov(1)/r_bh() ;
d_logn_comp.set(2) = lapse_bh2()%msr()%xsr_cov(2)/r_bh() ;
d_logn_comp.set_std_base() ;
d_logn_comp.change_triad(ref_triad) ;
// Computation of d_beta_comp (Just the same that d_logn_comp)
// --------------------------
d_beta_comp = d_logn_comp ;
d_beta_comp.change_triad(ref_triad) ;
// Computation of tkij_comp
// ------------------------
/** The definition of tkij_comp:
* A_{tot}^2 A_{BH}^{ij} =-0.5/nnn*(DN_{BH}+DN_{BH}-2/3gammaDN_{BH})
*/
// Components of shift_comp with respect to the Cartesian triad
// (d/dx, d/dy, d/dz) of the mapping :
// Computation of A^2 A^{ij}
// -------------------------
tkij_comp.set_etat_qcq() ;
for (int i=0; i<3; i++) {
for (int j=i; j<3; j++) {
tkij_comp.set(i, j) = - 3.*xsr_con(i) % xsr_con(j)
- 2*msr() % xsr_con(i) % xsr_con(j) ;
}
tkij_comp.set(i, i) += 1. + 2.*msr() ;
}
tkij_comp = (double(2)/double(3)) * pow(lapse_bh2, 3.) % msr
% (2.*tkij_comp +3.*msr % tkij_comp) / nnn / r_bh ;
tkij_comp.set_triad(ref_triad) ;
tkij_comp.set_std_base() ;
if (relativistic) {
// Computation of akcar_comp
// -------------------------
Tenseur lapse_bh8(mp) ;
lapse_bh8 = 1. / pow(1.+2.*msr, 4.) ;
lapse_bh8.set_std_base() ;
akcar_comp.set_etat_qcq() ;
akcar_comp.set() = 0 ;
akcar_comp.set() = 8.*lapse_bh8()
* pow(2.*msr()+3.*msr()*msr(), 2.) / 3.
/ nnn() / nnn() / r_bh() / r_bh() ;
akcar_comp.set_std_base() ;
akcar_comp = a_car % akcar_comp ;
}
// 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 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 msr(mp) ;
msr = ggrav * mass / r_bh ;
msr.set_std_base() ;
// Computation of d_logn_comp
// --------------------------
Tenseur tmp(mp) ;
tmp = 1. / (1. - 0.25*msr*msr) ;
tmp.set_std_base() ;
d_logn_comp.set_etat_qcq() ;
d_logn_comp.set(0) = tmp()%msr()%xx_cov(0)/r_bh()/r_bh() ;
d_logn_comp.set(1) = tmp()%msr()%xx_cov(1)/r_bh()/r_bh() ;
d_logn_comp.set(2) = tmp()%msr()%xx_cov(2)/r_bh()/r_bh() ;
d_logn_comp.set_std_base() ;
d_logn_comp.change_triad(ref_triad) ;
// Computation of d_beta_comp
// --------------------------
d_beta_comp.set_etat_qcq() ;
d_beta_comp.set(0) = 0.5*tmp()%msr()%msr()%xx_cov(0)/r_bh()/r_bh() ;
d_beta_comp.set(1) = 0.5*tmp()%msr()%msr()%xx_cov(1)/r_bh()/r_bh() ;
d_beta_comp.set(2) = 0.5*tmp()%msr()%msr()%xx_cov(2)/r_bh()/r_bh() ;
d_beta_comp.set_std_base() ;
d_beta_comp.change_triad(ref_triad) ;
// Computation of tkij_comp
// ------------------------
// Computation of A^2 A^{ij}
// -------------------------
tkij_comp.set_etat_qcq() ;
for (int i=0; i<3; i++) {
for (int j=i; j<3; j++) {
tkij_comp.set(i, j) = 0. ;
}
}
tkij_comp.set_triad(ref_triad) ;
tkij_comp.set_std_base() ;
if (relativistic) {
// Computation of akcar_comp
// -------------------------
akcar_comp.set_etat_qcq() ;
akcar_comp.set() = 0 ;
akcar_comp.set_std_base() ;
}
// The derived quantities are obsolete
// -----------------------------------
Etoile_bin::del_deriv() ;
}
}
}
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