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/*
* Methods of the class Kerr_QI
*
* (see file compobj.h for documentation).
*
*/
/*
* Copyright (c) 2013 Claire Some, Eric Gourgoulhon
*
* 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 kerr_QI_C[] = "$Header: /cvsroot/Lorene/C++/Source/Compobj/kerr_QI.C,v 1.4 2014/10/13 08:52:49 j_novak Exp $" ;
/*
* $Id: kerr_QI.C,v 1.4 2014/10/13 08:52:49 j_novak Exp $
* $Log: kerr_QI.C,v $
* Revision 1.4 2014/10/13 08:52:49 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.3 2013/04/04 08:53:47 e_gourgoulhon
* Minor improvements
*
* Revision 1.2 2013/04/03 12:09:50 e_gourgoulhon
* New computation of b_car
*
* Revision 1.1 2013/04/02 23:17:18 e_gourgoulhon
* New class Kerr_QI
*
*
* $Header: /cvsroot/Lorene/C++/Source/Compobj/kerr_QI.C,v 1.4 2014/10/13 08:52:49 j_novak Exp $
*
*/
// C headers
#include <cassert>
// Lorene headers
#include "compobj.h"
#include "unites.h"
//--------------//
// Constructors //
//--------------//
// Standard constructor
// --------------------
namespace Lorene {
Kerr_QI::Kerr_QI(Map& mpi, double mass, double a_over_m) :
Compobj_QI(mpi)
{
mm = mass ;
aa = a_over_m * mm ;
double mm2 = mm*mm ;
double aa2 = aa*aa ;
double hh = sqrt(mm2-aa2) ; // Eq. (98)
double hh2 = hh*hh ;
double r_hor = hh / double(2) ; // Eq. (10)
const Coord& r = mp.r ; // r field
const Coord& cost = mp.cost ; // cos(theta) field
const Coord& sint = mp.sint ; // sin(theta) field
Mtbl r2 = r*r ;
Mtbl cost2 = cost*cost ;
Mtbl sint2 = sint*sint ;
// A^2
a_car = 1 + 2*mm/r + (3*mm2 + aa2*(2*cost2-1))/(2*r2) + hh2*mm/(2*r*r2) +
hh2*hh2/(16*r2*r2) ; // Eq. (121)
a_car.set_domain(0) = 1 ;
a_car.std_spectral_base() ;
// Boyer-Lindquist radial coordinate and associated quantities:
Mtbl rBL = r + hh2/(4*r) + mm ; // Eq. (110)
Mtbl rBL2 = rBL*rBL ;
Mtbl sigma = rBL2 + aa2*cost2 ; // Eq. (93)
Mtbl rBLovr = 1 + mm/r + r_hor*r_hor/r2 ; // R/r
// B^2
b_car = rBLovr * ( rBLovr + 2*aa2*mm*sint2 / (r*sigma) ) + aa2 / r2 ; // Eq. (125)
b_car.set_domain(0) = 1 ;
b_car.std_spectral_base() ;
bbb = sqrt(b_car) ;
bbb.std_spectral_base() ;
// N
nn = (1 - r_hor*r_hor / r2) / bbb ; // Eq. (81) + (10)
nn.set_domain(0) = 1 ;
nn.std_spectral_base() ;
// N^phi
nphi = 2*aa*mm / (sigma*(rBL+aa2/rBL) + 2*aa2*mm*sint2) ; // Eq. (126)
if (nphi.get_etat() == ETATQCQ) {
nphi.set_domain(0) = 0 ;
}
nphi.std_spectral_base() ;
// Pointers of derived quantities initialized to zero :
set_der_0x0() ;
}
// Copy constructor
// --------------------
Kerr_QI::Kerr_QI(const Kerr_QI& other) :
Compobj_QI(other),
mm(other.mm),
aa(other.aa)
{
// Pointers of derived quantities initialized to zero :
set_der_0x0() ;
}
// Constructor from a file
// -----------------------
Kerr_QI::Kerr_QI(Map& mpi, FILE* fich) :
Compobj_QI(mpi)
{
// Pointers of derived quantities initialized to zero :
set_der_0x0() ;
// Read of the saved fields:
// ------------------------
}
//------------//
// Destructor //
//------------//
Kerr_QI::~Kerr_QI(){
del_deriv() ;
}
//----------------------------------//
// Management of derived quantities //
//----------------------------------//
void Kerr_QI::del_deriv() const {
Compobj_QI::del_deriv() ;
Kerr_QI::set_der_0x0() ;
}
void Kerr_QI::set_der_0x0() const {
}
//--------------//
// Assignment //
//--------------//
// Assignment to another Kerr_QI
// --------------------------------
void Kerr_QI::operator=(const Kerr_QI& other) {
// Assignment of quantities common to all the derived classes of Compobj_QI
Compobj_QI::operator=(other) ;
mm = other.mm ;
aa = other.aa ;
del_deriv() ; // Deletes all derived quantities
}
//--------------//
// Outputs //
//--------------//
// Save in a file
// --------------
void Kerr_QI::sauve(FILE* fich) const {
}
// Printing
// --------
ostream& Kerr_QI::operator>>(ostream& ost) const {
using namespace Unites ;
Compobj_QI::operator>>(ost) ;
ost << endl << "Kerr spacetime in quasi-isotropic coordinates (class Kerr_QI) " << endl ;
ost << "M = " << mm << " a = " << aa << endl ;
return ost ;
}
//-------------------------//
// Computational methods //
//-------------------------//
}
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