strot_dirac_upmetr.C
/*
* Function Star_rot_Dirac::update_metric
*
* (see file star_rot_dirac.h for documentation).
*
*/
/*
* Copyright (c) 2005 Lap-Ming Lin & Jerome Novak
*
* 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 strot_dirac_upmetr_C[] = "$Header: /cvsroot/Lorene/C++/Source/Star/strot_dirac_upmetr.C,v 1.4 2014/10/13 08:53:40 j_novak Exp $" ;
/*
* $Id: strot_dirac_upmetr.C,v 1.4 2014/10/13 08:53:40 j_novak Exp $
* $Log: strot_dirac_upmetr.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 2005/03/25 13:47:26 j_novak
* Added the update of log(Q).
*
* Revision 1.2 2005/02/17 17:30:55 f_limousin
* Change the name of some quantities to be consistent with other classes
* (for instance nnn is changed to nn, shift to beta, beta to lnq...)
*
* Revision 1.1 2005/01/31 08:51:48 j_novak
* New files for rotating stars in Dirac gauge (still under developement).
*
*
* $Header: /cvsroot/Lorene/C++/Source/Star/strot_dirac_upmetr.C,v 1.4 2014/10/13 08:53:40 j_novak Exp $
*
*/
// Lorene headers
#include "star_rot_dirac.h"
#include "utilitaires.h"
#include "unites.h"
namespace Lorene {
void Star_rot_Dirac::update_metric(){
// Lapse function
// ---------------
nn = exp( logn ) ;
nn.std_spectral_base() ; // set the bases for spectral expansions
// Quantity log(Q)
//----------------
lnq = log(qqq) ;
lnq.std_spectral_base() ;
// Comformal factor $\Psi^4$
// -------------------------
psi4 = (qqq * qqq) / (nn * nn) ;
psi4.std_spectral_base() ;
// Factor $\Psi^2$
// ----------------
psi2 = sqrt( psi4 ) ;
psi2.std_spectral_base() ;
// Quantity $ln( \Psi )$
// ---------------------
ln_psi = 0.5*log( psi2 ) ;
ln_psi.std_spectral_base() ;
// Conformal metric $\tilde{\gamma}$
// --------------------------------------
tgamma = flat.con() + hh ; // contravariant representation
// $\tilde{\gamma}^{ij}$
// Physical metric $\gamma$
// -----------------------------
gamma = tgamma.con() / psi4 ; // contravariant representation
// $\gamma^{ij}$
// Quantities $A^{ij}$, $\tilde{A}_{ij}, and $\tilde{A}_{ij} A^{ij}$
// -----------------------------------------------------------------
aa = ( beta.ope_killing_conf(flat) - hh.derive_lie(beta))
/ ( 2*nn ) ;
taa = aa.up_down(tgamma) ;
aa_quad = contract(taa, 0, 1, aa, 0, 1) ;
aa_quad.std_spectral_base() ;
// The derived quantities are no longer up to date :
// ------------------------------------------------
del_deriv() ;
}
}
Lorene::Star_rot_Dirac::aa
Sym_tensor aa
Definition star_rot_dirac.h:87
Lorene::Star_rot_Dirac::hh
Sym_tensor_trans hh
is defined by .
Definition star_rot_dirac.h:96
Lorene::Star_rot_Dirac::ln_psi
Scalar ln_psi
Definition star_rot_dirac.h:67
Lorene::Star_rot_Dirac::qqq
Scalar qqq
Definition star_rot_dirac.h:66
Lorene::Star_rot_Dirac::del_deriv
virtual void del_deriv() const
Deletes all the derived quantities.
Definition star_rot_dirac.C:218
Lorene::Star_rot_Dirac::psi2
Scalar psi2
Definition star_rot_dirac.h:65
Lorene::Star_rot_Dirac::flat
const Metric_flat & flat
flat metric (spherical components)
Definition star_rot_dirac.h:84
Lorene::Star_rot_Dirac::taa
Sym_tensor taa
Definition star_rot_dirac.h:88
Lorene::Star_rot_Dirac::update_metric
void update_metric()
Computes metric quantities from known potentials.
Definition strot_dirac_upmetr.C:59
Lorene::Star_rot_Dirac::psi4
Scalar psi4
Conformal factor .
Definition star_rot_dirac.h:64
Lorene::Star_rot_Dirac::aa_quad
Scalar aa_quad
Definition star_rot_dirac.h:89
Lorene::Star_rot_Dirac::tgamma
Metric tgamma
Definition star_rot_dirac.h:86
Lorene::Star::logn
Scalar logn
Logarithm of the lapse N .
Definition star.h:222
Lorene::Star::nn
Scalar nn
Lapse function N .
Definition star.h:225
Lorene::Star::gamma
Metric gamma
3-metric
Definition star.h:235
Lorene::Star::beta
Vector beta
Shift vector.
Definition star.h:228
Lorene::sqrt
Cmp sqrt(const Cmp &)
Square root.
Definition cmp_math.C:220
Lorene::exp
Cmp exp(const Cmp &)
Exponential.
Definition cmp_math.C:270
Lorene::log
Cmp log(const Cmp &)
Neperian logarithm.
Definition cmp_math.C:296
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