star_bin_extr_curv_xcts.C
/*
* Method of class Star_bin_xcts to compute
* the extrinsic curvature tensor
* (see file star.h for documentation)
*/
/*
* Copyright (c) 2010 Michal Bejger
*
* 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 star_bin_extr_curv_xcts_C[] = "$Header: /cvsroot/Lorene/C++/Source/Star/star_bin_extr_curv_xcts.C,v 1.4 2014/10/13 08:53:38 j_novak Exp $" ;
/*
* $Id: star_bin_extr_curv_xcts.C,v 1.4 2014/10/13 08:53:38 j_novak Exp $
* $Log: star_bin_extr_curv_xcts.C,v $
* Revision 1.4 2014/10/13 08:53:38 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.3 2014/10/06 15:13:17 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.2 2010/06/15 08:10:29 m_bejger
* *** empty log message ***
*
* Revision 1.1 2010/05/04 07:51:05 m_bejger
* Initial version
*
* $Header: /cvsroot/Lorene/C++/Source/Star/star_bin_extr_curv_xcts.C,v 1.4 2014/10/13 08:53:38 j_novak Exp $
*
*/
// C headers
#include <cmath>
// Headers Lorene
#include "star.h"
namespace Lorene {
void Star_bin_xcts::extrinsic_curvature() {
// D~_j beta^i
const Tensor& dbeta = beta_auto.derive_con(flat) ;
// Trace of D~_j beta^i :
Scalar div_beta = beta_auto.divergence(flat) ;
// Computation of \hat{A}^{ij}, Eq. 8.130 of arXiv:gr-qc/0703035
// -------------------------------------------------------------
for (int i=1; i<=3; i++)
for (int j=1; j<=i; j++) {
haij_auto.set(i, j) = dbeta(i, j) + dbeta(j, i) -
double(2) /double(3) * div_beta * (flat.con())(i,j) ;
}
haij_auto = 0.5 * pow(Psi, 7.) * haij_auto / chi ;
//## for comparison: old formulation
//haij_auto = 0.5 * haij_auto / nn ;
haij_auto.std_spectral_base() ;
// Computation of (\hat{A}_{ij}\hat{A}^{ij})_{auto}
// ------------------------------------------------
Sym_tensor haij_auto_cov = haij_auto.up_down(flat) ;
hacar_auto = contract(haij_auto_cov, 0, 1, haij_auto, 0, 1, true) ;
// The derived quantities are obsolete
// -----------------------------------
del_deriv() ;
}
}
Lorene::Scalar
Tensor field of valence 0 (or component of a tensorial field).
Definition scalar.h:387
Lorene::Star_bin_xcts::Psi
Scalar Psi
Total conformal factor .
Definition star.h:1152
Lorene::Star_bin_xcts::haij_auto
Sym_tensor haij_auto
Part of the extrinsic curvature tensor generated by beta_auto.
Definition star.h:1193
Lorene::Star_bin_xcts::extrinsic_curvature
void extrinsic_curvature()
Computes haij_auto and hacar_auto from beta_auto, nn and Psi .
Definition star_bin_extr_curv_xcts.C:55
Lorene::Star_bin_xcts::flat
Metric_flat flat
Flat metric defined on the mapping (Spherical components with respect to the mapping of the star) .
Definition star.h:1177
Lorene::Star_bin_xcts::beta_auto
Vector beta_auto
Part of the shift vector generated principally by the star (Spherical components with respect to the ...
Definition star.h:1182
Lorene::Star_bin_xcts::chi
Scalar chi
Total function .
Definition star.h:1155
Lorene::Star_bin_xcts::del_deriv
virtual void del_deriv() const
Deletes all the derived quantities.
Definition star_bin_xcts.C:304
Lorene::Star_bin_xcts::hacar_auto
Scalar hacar_auto
Part of the scalar generated by beta_auto, i.e.
Definition star.h:1205
Lorene::Sym_tensor
Class intended to describe valence-2 symmetric tensors.
Definition sym_tensor.h:223
Lorene::Tensor
Tensor handling.
Definition tensor.h:288
Lorene::pow
Cmp pow(const Cmp &, int)
Power .
Definition cmp_math.C:348
Lorene::contract
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
Definition tenseur_operateur.C:279
Lorene
Lorene prototypes.
Definition app_hor.h:64