star_bhns_extr_curv.C
/*
* Method of class Star_bhns to compute the extrinsic curvature tensor
*
* (see file star_bhns.h for documentation).
*
*/
/*
* Copyright (c) 2005-2007 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 star_bhns_extr_curv_C[] = "$Header: /cvsroot/Lorene/C++/Source/Star_bhns/star_bhns_extr_curv.C,v 1.4 2014/10/13 08:53:40 j_novak Exp $" ;
/*
* $Id: star_bhns_extr_curv.C,v 1.4 2014/10/13 08:53:40 j_novak Exp $
* $Log: star_bhns_extr_curv.C,v $
* Revision 1.4 2014/10/13 08:53:40 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.3 2014/10/06 15:13:16 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.2 2008/05/15 19:14:24 k_taniguchi
* Change of some parameters.
*
* Revision 1.1 2007/06/22 01:31:05 k_taniguchi
* *** empty log message ***
*
*
* $Header: /cvsroot/Lorene/C++/Source/Star_bhns/star_bhns_extr_curv.C,v 1.4 2014/10/13 08:53:40 j_novak Exp $
*
*/
// C++ headers
//#include <>
// C headers
#include <cmath>
// Lorene headers
#include "star_bhns.h"
namespace Lorene {
void Star_bhns::extr_curv_bhns() {
// Computation of \tilde{A}_{NS}^{ij}
// ----------------------------------
Scalar divshift(mp) ;
divshift = d_shift_auto(1,1) + d_shift_auto(2,2)
+ d_shift_auto(3,3) ;
divshift.std_spectral_base() ;
Sym_tensor flat_taij(mp, CON, mp.get_bvect_cart()) ;
flat_taij.set_etat_qcq() ;
for (int i=1; i<=3; i++) {
for (int j=1; j<=3; j++) {
flat_taij.set(i,j) = d_shift_auto(i,j)
+ d_shift_auto(j,i)
- 2. * divshift * flat.con()(i,j) / 3. ;
}
}
flat_taij.std_spectral_base() ;
taij_auto = 0.5 * pow(confo_auto+0.5, 7.) * flat_taij
/ (lapconf_auto+0.5) ;
taij_auto.std_spectral_base() ;
// Computation of \tilde{A}_{NS}^{ij} \tilde{A}^{NS}_{ij}
// ------------------------------------------------------
Sym_tensor flat_dshift(mp, COV, mp.get_bvect_cart()) ;
flat_dshift.set_etat_qcq() ;
for (int i=1; i<=3; i++) {
for (int j=1; j<=3; j++) {
flat_dshift.set(i,j) =
flat.cov()(j,1) % d_shift_auto(i,1)
+ flat.cov()(j,2) % d_shift_auto(i,2)
+ flat.cov()(j,3) % d_shift_auto(i,3)
+ flat.cov()(i,1) % d_shift_auto(j,1)
+ flat.cov()(i,2) % d_shift_auto(j,2)
+ flat.cov()(i,3) % d_shift_auto(j,3)
- 2. * divshift % flat.cov()(i,j) / 3. ;
}
}
flat_dshift.std_spectral_base() ;
Sym_tensor taij_down(mp, COV, mp.get_bvect_cart()) ;
taij_down.set_etat_qcq() ;
taij_down = 0.5 * pow(confo_auto+0.5, 7.) * flat_dshift
/ (lapconf_auto+0.5) ;
taij_down.std_spectral_base() ;
taij_quad_auto = 0. ;
for (int i=1; i<=3; i++) {
for (int j=1; j<=3; j++) {
taij_quad_auto += taij_down(i,j) % taij_auto(i,j) ;
}
}
taij_quad_auto.std_spectral_base() ;
}
}
Lorene::Scalar
Tensor field of valence 0 (or component of a tensorial field).
Definition scalar.h:387
Lorene::Scalar::std_spectral_base
virtual void std_spectral_base()
Sets the spectral bases of the Valeur va to the standard ones for a scalar field.
Definition scalar.C:784
Lorene::Star_bhns::flat
Metric_flat flat
Flat metric defined on the mapping (Spherical components with respect to the mapping of the star ).
Definition star_bhns.h:192
Lorene::Star_bhns::taij_auto
Sym_tensor taij_auto
Part of the extrinsic curvature tensor generated by shift_auto , lapse_auto , and confo_auto .
Definition star_bhns.h:182
Lorene::Star_bhns::lapconf_auto
Scalar lapconf_auto
Lapconf function generated by the star.
Definition star_bhns.h:113
Lorene::Star_bhns::d_shift_auto
Tensor d_shift_auto
Derivative of the shift vector generated by the star .
Definition star_bhns.h:149
Lorene::Star_bhns::extr_curv_bhns
void extr_curv_bhns()
Computes taij_auto , taij_quad_auto from shift_auto , lapse_auto , confo_auto .
Definition star_bhns_extr_curv.C:60
Lorene::Star_bhns::taij_quad_auto
Scalar taij_quad_auto
Part of the scalar generated by .
Definition star_bhns.h:187
Lorene::Star_bhns::confo_auto
Scalar confo_auto
Conformal factor generated by the star.
Definition star_bhns.h:157
Lorene::Star::mp
Map & mp
Mapping associated with the star.
Definition star.h:180
Lorene::Sym_tensor
Class intended to describe valence-2 symmetric tensors.
Definition sym_tensor.h:223
Lorene::pow
Cmp pow(const Cmp &, int)
Power .
Definition cmp_math.C:348
Lorene::Tensor::set_etat_qcq
virtual void set_etat_qcq()
Sets the logical state of all components to ETATQCQ (ordinary state).
Definition tensor.C:481
Lorene::Tensor::set
Scalar & set(const Itbl &ind)
Returns the value of a component (read/write version).
Definition tensor.C:654
Lorene::Tensor::std_spectral_base
virtual void std_spectral_base()
Sets the standard spectal bases of decomposition for each component.
Definition tensor.C:926
Lorene
Lorene prototypes.
Definition app_hor.h:64