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
 *
 */

 

/*
 * $Id: strot_dirac_upmetr.C,v 1.6 2023/12/20 10:16:19 j_novak Exp $
 * $Log: strot_dirac_upmetr.C,v $
 * Revision 1.6  2023/12/20 10:16:19  j_novak
 * New options in Star_rot_Dirac/rotstar_dirac: a flag to choose between GR, CFC and CFC+ A^{ij}_{TT}=0 (as described n Cordero_Carrion et al. 2009).
 *
 * Revision 1.5  2016/12/05 16:18:16  j_novak
 * Suppression of some global variables (file names, loch, ...) to prevent redefinitions
 *
 * 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 1.6 2023/12/20 10:16:19 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 ) ;

    if (relat_type == 3) {
      // Computation of \hat{A}^{ij}
      Sym_tensor aa_tmp = psi4*psi2*aa ; // \hat{A}^{ij} = \psi^6 A^{ij}
      aa_tmp.inc_dzpuis() ;
      
      // We take only the longitudinal part to set \hat{A}^{ij}_{TT} = 0
      Vector xi = aa_tmp.longit_pot(flat) ;
      aa = xi.ope_killing_conf(flat)/(psi4*psi2) ;
    }
    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() ;

}



}