LORENE
star_bin_extr_curv_xcts.C
1/*
2 * Method of class Star_bin_xcts to compute
3 * the extrinsic curvature tensor
4 * (see file star.h for documentation)
5 */
6
7/*
8 * Copyright (c) 2010 Michal Bejger
9 *
10 * This file is part of LORENE.
11 *
12 * LORENE is free software; you can redistribute it and/or modify
13 * it under the terms of the GNU General Public License version 2
14 * as published by the Free Software Foundation.
15 *
16 * LORENE is distributed in the hope that it will be useful,
17 * but WITHOUT ANY WARRANTY; without even the implied warranty of
18 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19 * GNU General Public License for more details.
20 *
21 * You should have received a copy of the GNU General Public License
22 * along with LORENE; if not, write to the Free Software
23 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
24 *
25 */
26
27char 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 $" ;
28
29/*
30 * $Id: star_bin_extr_curv_xcts.C,v 1.4 2014/10/13 08:53:38 j_novak Exp $
31 * $Log: star_bin_extr_curv_xcts.C,v $
32 * Revision 1.4 2014/10/13 08:53:38 j_novak
33 * Lorene classes and functions now belong to the namespace Lorene.
34 *
35 * Revision 1.3 2014/10/06 15:13:17 j_novak
36 * Modified #include directives to use c++ syntax.
37 *
38 * Revision 1.2 2010/06/15 08:10:29 m_bejger
39 * *** empty log message ***
40 *
41 * Revision 1.1 2010/05/04 07:51:05 m_bejger
42 * Initial version
43 *
44 * $Header: /cvsroot/Lorene/C++/Source/Star/star_bin_extr_curv_xcts.C,v 1.4 2014/10/13 08:53:38 j_novak Exp $
45 *
46 */
47
48// C headers
49#include <cmath>
50
51// Headers Lorene
52#include "star.h"
53
54namespace Lorene {
56
57 // D~_j beta^i
59
60 // Trace of D~_j beta^i :
62
63 // Computation of \hat{A}^{ij}, Eq. 8.130 of arXiv:gr-qc/0703035
64 // -------------------------------------------------------------
65
66 for (int i=1; i<=3; i++)
67 for (int j=1; j<=i; j++) {
68
69 haij_auto.set(i, j) = dbeta(i, j) + dbeta(j, i) -
70 double(2) /double(3) * div_beta * (flat.con())(i,j) ;
71 }
72
73 haij_auto = 0.5 * pow(Psi, 7.) * haij_auto / chi ;
74 //## for comparison: old formulation
75 //haij_auto = 0.5 * haij_auto / nn ;
76
78
79 // Computation of (\hat{A}_{ij}\hat{A}^{ij})_{auto}
80 // ------------------------------------------------
81
83
84 hacar_auto = contract(haij_auto_cov, 0, 1, haij_auto, 0, 1, true) ;
85
86 // The derived quantities are obsolete
87 // -----------------------------------
88
89 del_deriv() ;
90
91}
92}
Time evolution with partial storage (*** under development ***).
Definition evolution.h:371
virtual const Sym_tensor & con() const
Read-only access to the contravariant representation.
Tensor field of valence 0 (or component of a tensorial field).
Definition scalar.h:387
Scalar Psi
Total conformal factor .
Definition star.h:1152
Sym_tensor haij_auto
Part of the extrinsic curvature tensor generated by beta_auto.
Definition star.h:1193
void extrinsic_curvature()
Computes haij_auto and hacar_auto from beta_auto, nn and Psi .
Metric_flat flat
Flat metric defined on the mapping (Spherical components with respect to the mapping of the star) .
Definition star.h:1177
Vector beta_auto
Part of the shift vector generated principally by the star (Spherical components with respect to the ...
Definition star.h:1182
Scalar chi
Total function .
Definition star.h:1155
virtual void del_deriv() const
Deletes all the derived quantities.
Scalar hacar_auto
Part of the scalar generated by beta_auto, i.e.
Definition star.h:1205
Class intended to describe valence-2 symmetric tensors.
Definition sym_tensor.h:223
Tensor handling.
Definition tensor.h:288
const Scalar & divergence(const Metric &) const
The divergence of this with respect to a Metric .
Definition vector.C:381
Cmp pow(const Cmp &, int)
Power .
Definition cmp_math.C:348
Tensor up_down(const Metric &gam) const
Computes a new tensor by raising or lowering all the indices of *this .
const Tensor & derive_con(const Metric &gam) const
Returns the "contravariant" derivative of this with respect to some metric , by raising the last inde...
Definition tensor.C:1014
Scalar & set(const Itbl &ind)
Returns the value of a component (read/write version).
Definition tensor.C:654
virtual void std_spectral_base()
Sets the standard spectal bases of decomposition for each component.
Definition tensor.C:926
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
Lorene prototypes.
Definition app_hor.h:64