LORENE
et_bin_bhns_extr_upmetr.C
1 /*
2  * Methods Et_bin_bhns_extr::update_metric_extr_ks
3  * and Et_bin_bhns_extr::update_metric_extr_cf
4  *
5  * (see file et_bin_bhns_extr.h for documentation).
6  *
7  */
8 
9 /*
10  * Copyright (c) 2004-2005 Keisuke Taniguchi
11  *
12  * This file is part of LORENE.
13  *
14  * LORENE is free software; you can redistribute it and/or modify
15  * it under the terms of the GNU General Public License version 2
16  * as published by the Free Software Foundation.
17  *
18  * LORENE is distributed in the hope that it will be useful,
19  * but WITHOUT ANY WARRANTY; without even the implied warranty of
20  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
21  * GNU General Public License for more details.
22  *
23  * You should have received a copy of the GNU General Public License
24  * along with LORENE; if not, write to the Free Software
25  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
26  *
27  */
28 
29 
30 
31 /*
32  * $Id: et_bin_bhns_extr_upmetr.C,v 1.5 2016/12/05 16:17:52 j_novak Exp $
33  * $Log: et_bin_bhns_extr_upmetr.C,v $
34  * Revision 1.5 2016/12/05 16:17:52 j_novak
35  * Suppression of some global variables (file names, loch, ...) to prevent redefinitions
36  *
37  * Revision 1.4 2014/10/13 08:52:55 j_novak
38  * Lorene classes and functions now belong to the namespace Lorene.
39  *
40  * Revision 1.3 2014/10/06 15:13:08 j_novak
41  * Modified #include directives to use c++ syntax.
42  *
43  * Revision 1.2 2005/02/28 23:16:37 k_taniguchi
44  * Modification to include the case of the conformally flat background metric
45  *
46  * Revision 1.1 2004/11/30 20:51:32 k_taniguchi
47  * *** empty log message ***
48  *
49  *
50  * $Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_bhns_extr_upmetr.C,v 1.5 2016/12/05 16:17:52 j_novak Exp $
51  *
52  */
53 
54 // C headers
55 #include <cmath>
56 
57 // Lorene headers
58 #include "et_bin_bhns_extr.h"
59 #include "etoile.h"
60 #include "coord.h"
61 #include "unites.h"
62 
63  //-----------------------------------------------------------//
64  // No relaxation for a fixed BH background //
65  //-----------------------------------------------------------//
66 
67 namespace Lorene {
68 void Et_bin_bhns_extr::update_metric_extr(const double& mass,
69  const double& sepa)
70 {
71 
72  using namespace Unites ;
73 
74  if (kerrschild) {
75 
76  // Computation of quantities coming from the companion (K-S BH)
77  // ------------------------------------------------------------
78 
79  const Coord& xx = mp.x ;
80  const Coord& yy = mp.y ;
81  const Coord& zz = mp.z ;
82 
83  Tenseur r_bh(mp) ;
84  r_bh.set_etat_qcq() ;
85  r_bh.set() = pow( (xx+sepa)*(xx+sepa) + yy*yy + zz*zz, 0.5) ;
86  r_bh.set_std_base() ;
87 
88  Tenseur xx_con(mp, 1, CON, ref_triad) ;
89  xx_con.set_etat_qcq() ;
90  xx_con.set(0) = xx + sepa ;
91  xx_con.set(1) = yy ;
92  xx_con.set(2) = zz ;
93  xx_con.set_std_base() ;
94 
95  Tenseur xsr_con(mp, 1, CON, ref_triad) ;
96  xsr_con = xx_con / r_bh ;
97  xsr_con.set_std_base() ;
98 
99  Tenseur msr(mp) ;
100  msr = ggrav * mass / r_bh ;
101  msr.set_std_base() ;
102 
103  Tenseur lapse_bh(mp) ;
104  lapse_bh = 1. / sqrt( 1.+2.*msr ) ;
105  lapse_bh.set_std_base() ;
106 
108  logn_comp.set() = log( lapse_bh() ) ;
110 
112  beta_comp.set() = log( lapse_bh() ) ;
113  // conformal factor of KS-BH is unity
115 
117 
118  shift_comp.set(0) = -2.*lapse_bh()*lapse_bh()*msr()*xsr_con(0) ;
119  shift_comp.set(1) = -2.*lapse_bh()*lapse_bh()*msr()*xsr_con(1) ;
120  shift_comp.set(2) = -2.*lapse_bh()*lapse_bh()*msr()*xsr_con(2) ;
121 
124 
125  // Lapse function N
126  // ----------------
127 
128  nnn = exp( unsurc2 * logn_auto ) * lapse_bh ;
129 
130  nnn.set_std_base() ;
131 
132  // Conformal factor A^2
133  // --------------------
134 
135  a_car = exp ( 2.*unsurc2*(beta_auto - logn_auto) ) ;
136 
137  a_car.set_std_base() ;
138 
139  // Shift vector N^i
140  // ----------------
141 
143 
144  // Derivative of metric coefficients
145  // ----------------------------------
146 
147  // ... (d/dX,d/dY,d/dZ)(logn_auto) :
148  d_logn_auto_regu = logn_auto_regu.gradient() ; // (d/dx, d/dy, d/dz)
149  d_logn_auto_regu.change_triad(ref_triad) ; // --> (d/dX, d/dY, d/dZ)
150 
151  if ( *(d_logn_auto_div.get_triad()) != ref_triad ) {
152 
153  // Change the basis from spherical coordinate to Cartesian one
155 
156  // Change the basis from mapping coordinate to absolute one
158 
159  }
160 
162 
163  // ... (d/dX,d/dY,d/dZ)(beta_auto) :
164  d_beta_auto = beta_auto.gradient() ; // (d/dx, d/dy, d/dz)
165  d_beta_auto.change_triad(ref_triad) ; // --> (d/dX, d/dY, d/dZ)
166 
167  if (relativistic) {
168  // ... extrinsic curvature (tkij_auto and akcar_auto)
169  extrinsic_curv_extr(mass, sepa) ;
170  }
171 
172  // The derived quantities are obsolete
173  // -----------------------------------
174 
176 
177  }
178  else {
179 
180  // Computation of quantities coming from the companion (CF Sch. BH)
181  // ----------------------------------------------------------------
182 
183  const Coord& xx = mp.x ;
184  const Coord& yy = mp.y ;
185  const Coord& zz = mp.z ;
186 
187  Tenseur r_bh(mp) ;
188  r_bh.set_etat_qcq() ;
189  r_bh.set() = pow( (xx+sepa)*(xx+sepa) + yy*yy + zz*zz, 0.5) ;
190  r_bh.set_std_base() ;
191 
192  Tenseur msr(mp) ;
193  msr = ggrav * mass / r_bh ;
194  msr.set_std_base() ;
195 
196  Tenseur lapse_bh(mp) ;
197  lapse_bh = (1.-0.5*msr) / (1.+0.5*msr) ;
198  lapse_bh.set_std_base() ;
199 
201  logn_comp.set() = log( lapse_bh() ) ;
203 
204  Tenseur lappsi(mp) ;
205  lappsi = 1. - 0.25*msr*msr ;
206  lappsi.set_std_base() ;
207 
209  beta_comp.set() = log( lappsi() ) ;
211 
213 
214  shift_comp.set(0) = 0. ;
215  shift_comp.set(1) = 0. ;
216  shift_comp.set(2) = 0. ;
217 
220 
221  // Lapse function N
222  // ----------------
223 
224  nnn = exp( unsurc2 * logn_auto ) * lapse_bh ;
225 
226  nnn.set_std_base() ;
227 
228  // Conformal factor A^2
229  // --------------------
230 
232  - logn_auto - logn_comp) ) ;
233 
234  a_car.set_std_base() ;
235 
236  // Shift vector N^i
237  // ----------------
238 
240 
241  // Derivative of metric coefficients
242  // ----------------------------------
243 
244  // ... (d/dX,d/dY,d/dZ)(logn_auto) :
245  d_logn_auto_regu = logn_auto_regu.gradient() ; // (d/dx, d/dy, d/dz)
246  d_logn_auto_regu.change_triad(ref_triad) ; // --> (d/dX, d/dY, d/dZ)
247 
248  if ( *(d_logn_auto_div.get_triad()) != ref_triad ) {
249 
250  // Change the basis from spherical coordinate to Cartesian one
252 
253  // Change the basis from mapping coordinate to absolute one
255 
256  }
257 
259 
260  // ... (d/dX,d/dY,d/dZ)(beta_auto) :
261  d_beta_auto = beta_auto.gradient() ; // (d/dx, d/dy, d/dz)
262  d_beta_auto.change_triad(ref_triad) ; // --> (d/dX, d/dY, d/dZ)
263 
264  if (relativistic) {
265  // ... extrinsic curvature (tkij_auto and akcar_auto)
266  extrinsic_curv_extr(mass, sepa) ;
267  }
268 
269  // The derived quantities are obsolete
270  // -----------------------------------
271 
273 
274  }
275 
276 }
277 }
Cmp log(const Cmp &)
Neperian logarithm.
Definition: cmp_math.C:299
Tenseur shift_comp
Part of the shift vector generated principaly by the companion star.
Definition: etoile.h:898
const Base_vect & ref_triad
Reference triad ("absolute frame"), with respect to which the components of all the member Tenseur &#39;s...
Definition: etoile.h:831
Cmp exp(const Cmp &)
Exponential.
Definition: cmp_math.C:273
void set_triad(const Base_vect &new_triad)
Assigns a new vectorial basis (triad) of decomposition.
Definition: tenseur.C:690
Cmp sqrt(const Cmp &)
Square root.
Definition: cmp_math.C:223
void set_std_base()
Set the standard spectal basis of decomposition for each component.
Definition: tenseur.C:1186
Tenseur logn_auto_regu
Regular part of the logarithm of the part of the lapse N generated principaly by the star...
Definition: etoile.h:494
Lorene prototypes.
Definition: app_hor.h:67
Standard units of space, time and mass.
Tenseur nnn
Total lapse function.
Definition: etoile.h:512
void update_metric_extr(const double &mass, const double &sepa)
Computes metric coefficients from known potentials, when the companion is a black hole with the Kerr-...
double unsurc2
: unsurc2=1 for a relativistic star, 0 for a Newtonian one.
Definition: etoile.h:445
bool kerrschild
Indicator of the background metric: true for the Kerr-Shild metric, false for the conformally flat on...
Tenseur d_beta_auto
Gradient of beta_auto (Cartesian components with respect to ref_triad )
Definition: etoile.h:882
Tenseur shift
Total shift vector.
Definition: etoile.h:515
Tenseur shift_auto
Part of the shift vector generated principaly by the star.
Definition: etoile.h:892
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition: tenseur.C:840
void change_triad(const Base_vect &new_triad)
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
Definition: tenseur.C:684
virtual void del_deriv() const
Deletes all the derived quantities.
Definition: etoile_bin.C:450
Tenseur logn_comp
Part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principaly by ...
Definition: etoile.h:857
Tenseur d_logn_auto
Gradient of logn_auto (Cartesian components with respect to ref_triad )
Definition: etoile.h:862
const Base_vect * get_triad() const
Returns the vectorial basis (triad) on which the components are defined.
Definition: tenseur.h:707
Tenseur beta_comp
Part of the logarithm of AN generated principaly by the companion star.
Definition: etoile.h:877
Map & mp
Mapping associated with the star.
Definition: etoile.h:432
Cmp pow(const Cmp &, int)
Power .
Definition: cmp_math.C:351
Active physical coordinates and mapping derivatives.
Definition: coord.h:90
void extrinsic_curv_extr(const double &mass, const double &sepa)
Computes tkij_auto and akcar_auto from shift_auto , nnn and a_car .
Tenseur a_car
Total conformal factor .
Definition: etoile.h:518
bool relativistic
Indicator of relativity: true for a relativistic star, false for a Newtonian one. ...
Definition: etoile.h:440
const Base_vect_cart & get_bvect_cart() const
Returns the Cartesian basis associated with the coordinates (x,y,z) of the mapping, i.e.
Definition: map.h:809
Tenseur logn_auto
Total of the logarithm of the part of the lapse N generated principaly by the star.
Definition: etoile.h:487
Tenseur d_logn_auto_regu
Gradient of logn_auto_regu (Cartesian components with respect to ref_triad )
Definition: etoile.h:867
Coord y
y coordinate centered on the grid
Definition: map.h:745
Coord x
x coordinate centered on the grid
Definition: map.h:744
Tenseur beta_auto
Logarithm of the part of the product AN generated principaly by by the star.
Definition: etoile.h:509
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition: tenseur.C:652
Tenseur d_logn_auto_div
Gradient of logn_auto_div (if k_div!=0 )
Definition: etoile.h:504
Coord z
z coordinate centered on the grid
Definition: map.h:746
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition: tenseur.h:304
const Tenseur & gradient() const
Returns the gradient of *this (Cartesian coordinates)
Definition: tenseur.C:1558