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
29char et_bin_bhns_extr_upmetr_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_bhns_extr_upmetr.C,v 1.4 2014/10/13 08:52:55 j_novak Exp $" ;
30
31/*
32 * $Id: et_bin_bhns_extr_upmetr.C,v 1.4 2014/10/13 08:52:55 j_novak Exp $
33 * $Log: et_bin_bhns_extr_upmetr.C,v $
34 * Revision 1.4 2014/10/13 08:52:55 j_novak
35 * Lorene classes and functions now belong to the namespace Lorene.
36 *
37 * Revision 1.3 2014/10/06 15:13:08 j_novak
38 * Modified #include directives to use c++ syntax.
39 *
40 * Revision 1.2 2005/02/28 23:16:37 k_taniguchi
41 * Modification to include the case of the conformally flat background metric
42 *
43 * Revision 1.1 2004/11/30 20:51:32 k_taniguchi
44 * *** empty log message ***
45 *
46 *
47 * $Header: /cvsroot/Lorene/C++/Source/Etoile/et_bin_bhns_extr_upmetr.C,v 1.4 2014/10/13 08:52:55 j_novak Exp $
48 *
49 */
50
51// C headers
52#include <cmath>
53
54// Lorene headers
55#include "et_bin_bhns_extr.h"
56#include "etoile.h"
57#include "coord.h"
58#include "unites.h"
59
60 //-----------------------------------------------------------//
61 // No relaxation for a fixed BH background //
62 //-----------------------------------------------------------//
63
64namespace Lorene {
66 const double& sepa)
67{
68
69 using namespace Unites ;
70
71 if (kerrschild) {
72
73 // Computation of quantities coming from the companion (K-S BH)
74 // ------------------------------------------------------------
75
76 const Coord& xx = mp.x ;
77 const Coord& yy = mp.y ;
78 const Coord& zz = mp.z ;
79
80 Tenseur r_bh(mp) ;
81 r_bh.set_etat_qcq() ;
82 r_bh.set() = pow( (xx+sepa)*(xx+sepa) + yy*yy + zz*zz, 0.5) ;
83 r_bh.set_std_base() ;
84
85 Tenseur xx_con(mp, 1, CON, ref_triad) ;
86 xx_con.set_etat_qcq() ;
87 xx_con.set(0) = xx + sepa ;
88 xx_con.set(1) = yy ;
89 xx_con.set(2) = zz ;
90 xx_con.set_std_base() ;
91
92 Tenseur xsr_con(mp, 1, CON, ref_triad) ;
93 xsr_con = xx_con / r_bh ;
94 xsr_con.set_std_base() ;
95
96 Tenseur msr(mp) ;
97 msr = ggrav * mass / r_bh ;
98 msr.set_std_base() ;
99
100 Tenseur lapse_bh(mp) ;
101 lapse_bh = 1. / sqrt( 1.+2.*msr ) ;
102 lapse_bh.set_std_base() ;
103
105 logn_comp.set() = log( lapse_bh() ) ;
107
109 beta_comp.set() = log( lapse_bh() ) ;
110 // conformal factor of KS-BH is unity
112
114
115 shift_comp.set(0) = -2.*lapse_bh()*lapse_bh()*msr()*xsr_con(0) ;
116 shift_comp.set(1) = -2.*lapse_bh()*lapse_bh()*msr()*xsr_con(1) ;
117 shift_comp.set(2) = -2.*lapse_bh()*lapse_bh()*msr()*xsr_con(2) ;
118
121
122 // Lapse function N
123 // ----------------
124
125 nnn = exp( unsurc2 * logn_auto ) * lapse_bh ;
126
127 nnn.set_std_base() ;
128
129 // Conformal factor A^2
130 // --------------------
131
132 a_car = exp ( 2.*unsurc2*(beta_auto - logn_auto) ) ;
133
135
136 // Shift vector N^i
137 // ----------------
138
140
141 // Derivative of metric coefficients
142 // ----------------------------------
143
144 // ... (d/dX,d/dY,d/dZ)(logn_auto) :
145 d_logn_auto_regu = logn_auto_regu.gradient() ; // (d/dx, d/dy, d/dz)
146 d_logn_auto_regu.change_triad(ref_triad) ; // --> (d/dX, d/dY, d/dZ)
147
148 if ( *(d_logn_auto_div.get_triad()) != ref_triad ) {
149
150 // Change the basis from spherical coordinate to Cartesian one
152
153 // Change the basis from mapping coordinate to absolute one
155
156 }
157
159
160 // ... (d/dX,d/dY,d/dZ)(beta_auto) :
161 d_beta_auto = beta_auto.gradient() ; // (d/dx, d/dy, d/dz)
162 d_beta_auto.change_triad(ref_triad) ; // --> (d/dX, d/dY, d/dZ)
163
164 if (relativistic) {
165 // ... extrinsic curvature (tkij_auto and akcar_auto)
166 extrinsic_curv_extr(mass, sepa) ;
167 }
168
169 // The derived quantities are obsolete
170 // -----------------------------------
171
173
174 }
175 else {
176
177 // Computation of quantities coming from the companion (CF Sch. BH)
178 // ----------------------------------------------------------------
179
180 const Coord& xx = mp.x ;
181 const Coord& yy = mp.y ;
182 const Coord& zz = mp.z ;
183
184 Tenseur r_bh(mp) ;
185 r_bh.set_etat_qcq() ;
186 r_bh.set() = pow( (xx+sepa)*(xx+sepa) + yy*yy + zz*zz, 0.5) ;
187 r_bh.set_std_base() ;
188
189 Tenseur msr(mp) ;
190 msr = ggrav * mass / r_bh ;
191 msr.set_std_base() ;
192
193 Tenseur lapse_bh(mp) ;
194 lapse_bh = (1.-0.5*msr) / (1.+0.5*msr) ;
195 lapse_bh.set_std_base() ;
196
198 logn_comp.set() = log( lapse_bh() ) ;
200
201 Tenseur lappsi(mp) ;
202 lappsi = 1. - 0.25*msr*msr ;
203 lappsi.set_std_base() ;
204
206 beta_comp.set() = log( lappsi() ) ;
208
210
211 shift_comp.set(0) = 0. ;
212 shift_comp.set(1) = 0. ;
213 shift_comp.set(2) = 0. ;
214
217
218 // Lapse function N
219 // ----------------
220
221 nnn = exp( unsurc2 * logn_auto ) * lapse_bh ;
222
223 nnn.set_std_base() ;
224
225 // Conformal factor A^2
226 // --------------------
227
229 - logn_auto - logn_comp) ) ;
230
232
233 // Shift vector N^i
234 // ----------------
235
237
238 // Derivative of metric coefficients
239 // ----------------------------------
240
241 // ... (d/dX,d/dY,d/dZ)(logn_auto) :
242 d_logn_auto_regu = logn_auto_regu.gradient() ; // (d/dx, d/dy, d/dz)
243 d_logn_auto_regu.change_triad(ref_triad) ; // --> (d/dX, d/dY, d/dZ)
244
245 if ( *(d_logn_auto_div.get_triad()) != ref_triad ) {
246
247 // Change the basis from spherical coordinate to Cartesian one
249
250 // Change the basis from mapping coordinate to absolute one
252
253 }
254
256
257 // ... (d/dX,d/dY,d/dZ)(beta_auto) :
258 d_beta_auto = beta_auto.gradient() ; // (d/dx, d/dy, d/dz)
259 d_beta_auto.change_triad(ref_triad) ; // --> (d/dX, d/dY, d/dZ)
260
261 if (relativistic) {
262 // ... extrinsic curvature (tkij_auto and akcar_auto)
263 extrinsic_curv_extr(mass, sepa) ;
264 }
265
266 // The derived quantities are obsolete
267 // -----------------------------------
268
270
271 }
272
273}
274}
Active physical coordinates and mapping derivatives.
Definition coord.h:90
bool kerrschild
Indicator of the background metric: true for the Kerr-Shild metric, false for the conformally flat on...
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-...
void extrinsic_curv_extr(const double &mass, const double &sepa)
Computes tkij_auto and akcar_auto from shift_auto , nnn and a_car .
Tenseur shift_comp
Part of the shift vector generated principaly by the companion star.
Definition etoile.h:895
Tenseur d_beta_auto
Gradient of beta_auto (Cartesian components with respect to ref_triad )
Definition etoile.h:879
Tenseur d_logn_auto
Gradient of logn_auto (Cartesian components with respect to ref_triad )
Definition etoile.h:859
const Base_vect & ref_triad
Reference triad ("absolute frame"), with respect to which the components of all the member Tenseur 's...
Definition etoile.h:828
Tenseur logn_comp
Part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principaly by ...
Definition etoile.h:854
Tenseur beta_comp
Part of the logarithm of AN generated principaly by the companion star.
Definition etoile.h:874
virtual void del_deriv() const
Deletes all the derived quantities.
Definition etoile_bin.C:447
Tenseur shift_auto
Part of the shift vector generated principaly by the star.
Definition etoile.h:889
Tenseur d_logn_auto_regu
Gradient of logn_auto_regu (Cartesian components with respect to ref_triad )
Definition etoile.h:864
Tenseur logn_auto_regu
Regular part of the logarithm of the part of the lapse N generated principaly by the star.
Definition etoile.h:491
Tenseur nnn
Total lapse function.
Definition etoile.h:509
Tenseur logn_auto
Total of the logarithm of the part of the lapse N generated principaly by the star.
Definition etoile.h:484
Map & mp
Mapping associated with the star.
Definition etoile.h:429
Tenseur d_logn_auto_div
Gradient of logn_auto_div (if k_div!=0 )
Definition etoile.h:501
bool relativistic
Indicator of relativity: true for a relativistic star, false for a Newtonian one.
Definition etoile.h:437
Tenseur shift
Total shift vector.
Definition etoile.h:512
Tenseur beta_auto
Logarithm of the part of the product AN generated principaly by by the star.
Definition etoile.h:506
Tenseur a_car
Total conformal factor .
Definition etoile.h:515
double unsurc2
: unsurc2=1 for a relativistic star, 0 for a Newtonian one.
Definition etoile.h:442
const Base_vect_cart & get_bvect_cart() const
Returns the Cartesian basis associated with the coordinates (x,y,z) of the mapping,...
Definition map.h:791
Coord y
y coordinate centered on the grid
Definition map.h:727
Coord z
z coordinate centered on the grid
Definition map.h:728
Coord x
x coordinate centered on the grid
Definition map.h:726
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition tenseur.h:301
const Base_vect * get_triad() const
Returns the vectorial basis (triad) on which the components are defined.
Definition tenseur.h:704
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition tenseur.C:824
void set_etat_qcq()
Sets the logical state to ETATQCQ (ordinary state).
Definition tenseur.C:636
const Tenseur & gradient() const
Returns the gradient of *this (Cartesian coordinates)
Definition tenseur.C:1542
void set_std_base()
Set the standard spectal basis of decomposition for each component.
Definition tenseur.C:1170
void change_triad(const Base_vect &new_triad)
Sets a new vectorial basis (triad) of decomposition and modifies the components accordingly.
Definition tenseur.C:668
void set_triad(const Base_vect &new_triad)
Assigns a new vectorial basis (triad) of decomposition.
Definition tenseur.C:674
Cmp sqrt(const Cmp &)
Square root.
Definition cmp_math.C:220
Cmp exp(const Cmp &)
Exponential.
Definition cmp_math.C:270
Cmp pow(const Cmp &, int)
Power .
Definition cmp_math.C:348
Cmp log(const Cmp &)
Neperian logarithm.
Definition cmp_math.C:296
Lorene prototypes.
Definition app_hor.h:64
Standard units of space, time and mass.