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/*
* Method of class Etoile_bin to compute the extrinsic curvature tensor
*
*/
/*
* Copyright (c) 2000-2001 Eric Gourgoulhon
*
* 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 as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* 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_extr_curv_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_extr_curv.C,v 1.6 2014/10/13 08:52:55 j_novak Exp $" ;
/*
* $Id: et_bin_extr_curv.C,v 1.6 2014/10/13 08:52:55 j_novak Exp $
* $Log: et_bin_extr_curv.C,v $
* Revision 1.6 2014/10/13 08:52:55 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.5 2005/08/29 15:21:37 p_grandclement
* Suppression of Etoile_bion::fait_taij_auto, that was not used (I think)
*
* Revision 1.4 2003/02/13 16:40:25 p_grandclement
* Addition of various things for the Bin_ns_bh project, non of them being
* completely tested
*
* Revision 1.3 2003/01/17 13:33:35 f_limousin
* Add comments
*
* Revision 1.2 2002/12/10 14:20:43 k_taniguchi
* Change the multiplication "*" to "%".
*
* Revision 1.1.1.1 2001/11/20 15:19:28 e_gourgoulhon
* LORENE
*
* Revision 2.0 2000/03/07 14:51:49 eric
* *** empty log message ***
*
*
* $Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_extr_curv.C,v 1.6 2014/10/13 08:52:55 j_novak Exp $
*
*/
// Headers Lorene
#include "etoile.h"
namespace Lorene {
void Etoile_bin::extrinsic_curvature(){
// Components of shift_auto with respect to the Cartesian triad
// (d/dx, d/dy, d/dz) of the mapping :
Tenseur shift_auto_local = shift_auto ;
shift_auto_local.change_triad( mp.get_bvect_cart() ) ;
// Gradient (partial derivatives with respect to the Cartesian coordinates
// of the mapping)
// D_j N^i
Tenseur dn = shift_auto_local.gradient() ;
// Return to the absolute reference frame
dn.change_triad(ref_triad) ;
// Trace of D_j N^i = divergence of N^i :
Tenseur divn = contract(dn, 0, 1) ;
// Computation of A^2 K^{ij}
// See Eq (49) from Gourgoulhon et al. (2001)
// -----------------------------------------
tkij_auto.set_etat_qcq() ;
for (int i=0; i<3; i++) {
for (int j=i; j<3; j++) {
tkij_auto.set(i, j) = dn(i, j) + dn(j, i) ;
}
tkij_auto.set(i, i) -= double(2) /double(3) * divn() ;
}
tkij_auto = - 0.5 * tkij_auto / nnn ;
tkij_auto.set_std_base() ;
// Computation of A^2 K_{ij} K^{ij}
// --------------------------------
akcar_auto.set_etat_qcq() ;
akcar_auto.set() = 0 ;
akcar_auto.set_std_base() ;
for (int i=0; i<3; i++) {
for (int j=0; j<3; j++) {
akcar_auto.set() += tkij_auto(i, j) % tkij_auto(i, j) ;
}
}
akcar_auto.set_std_base() ;
akcar_auto = a_car % akcar_auto ;
}
}
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