LORENE
phys_param.C
1 /*
2  * Method of class Isol_hor to compute physical parameters of the horizon
3  *
4  * (see file isol_hor.h for documentation).
5  *
6  */
7 
8 /*
9  * Copyright (c) 2004 Jose Luis Jaramillo
10  *
11  * This file is part of LORENE.
12  *
13  * LORENE is free software; you can redistribute it and/or modify
14  * it under the terms of the GNU General Public License version 2
15  * as published by the Free Software Foundation.
16  *
17  * LORENE is distributed in the hope that it will be useful,
18  * but WITHOUT ANY WARRANTY; without even the implied warranty of
19  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20  * GNU General Public License for more details.
21  *
22  * You should have received a copy of the GNU General Public License
23  * along with LORENE; if not, write to the Free Software
24  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
25  *
26  */
27 
28 char phys_param_C[] = "$Header: /cvsroot/Lorene/C++/Source/Isol_hor/phys_param.C,v 1.13 2014/10/13 08:53:01 j_novak Exp $" ;
29 
30 /*
31  * $Id: phys_param.C,v 1.13 2014/10/13 08:53:01 j_novak Exp $
32  * $Log: phys_param.C,v $
33  * Revision 1.13 2014/10/13 08:53:01 j_novak
34  * Lorene classes and functions now belong to the namespace Lorene.
35  *
36  * Revision 1.12 2014/10/06 15:13:11 j_novak
37  * Modified #include directives to use c++ syntax.
38  *
39  * Revision 1.11 2005/11/02 16:09:44 jl_jaramillo
40  * changes in boundary_nn_Dir_lapl
41  *
42  * Revision 1.10 2005/04/15 11:54:21 jl_jaramillo
43  * function to compute the expansion of spherical surfaces
44  *
45  * Revision 1.9 2005/03/22 13:25:36 f_limousin
46  * Small changes. The angular velocity and A^{ij} are computed
47  * with a differnet sign.
48  *
49  * Revision 1.8 2005/03/03 10:10:14 f_limousin
50  * Add the function area_hor().
51  *
52  * Revision 1.7 2005/02/07 10:35:42 f_limousin
53  * Minor changes.
54  *
55  * Revision 1.6 2004/12/22 18:16:16 f_limousin
56  * Mny different changes.
57  *
58  * Revision 1.5 2004/11/18 12:30:01 jl_jaramillo
59  * Definition of b_tilde
60  *
61  * Revision 1.4 2004/10/29 15:44:13 jl_jaramillo
62  * ADM angular momentum added.
63  *
64  * Revision 1.3 2004/09/17 13:37:21 f_limousin
65  * Correction of an error in calculation of the radius
66  *
67  * Revision 1.2 2004/09/09 16:54:53 f_limousin
68  * Add the 2 lines $Id: phys_param.C,v 1.13 2014/10/13 08:53:01 j_novak Exp $Log: for CVS
69  *
70  *
71  *
72  * $Header: /cvsroot/Lorene/C++/Source/Isol_hor/phys_param.C,v 1.13 2014/10/13 08:53:01 j_novak Exp $
73  *
74  */
75 
76 // C++ headers
77 #include "headcpp.h"
78 
79 // C headers
80 #include <cstdlib>
81 #include <cassert>
82 
83 // Lorene headers
84 #include "isol_hor.h"
85 #include "metric.h"
86 #include "evolution.h"
87 #include "unites.h"
88 #include "scalar.h"
89 #include "vector.h"
90 #include "graphique.h"
91 #include "utilitaires.h"
92 
93 
94 namespace Lorene {
96 
97  Vector get_radial_vect (ff.get_mp(), CON, *(ff.get_triad()) ) ;
98 
99  get_radial_vect.set(1) = gam_uu()(1,1) ;
100 
101  get_radial_vect.set(2) = gam_uu()(1,2) ;
102 
103  get_radial_vect.set(3) = gam_uu()(1,3) ;
104 
105  get_radial_vect = get_radial_vect / sqrt(gam_uu()(1,1)) ;
106 
107  get_radial_vect.std_spectral_base() ;
108 
109 
110  return get_radial_vect ;
111 
112 }
113 
114 
115 // Think of defining this as a pointer
117 
118  Vector get_radial_vect (ff.get_mp(), CON, *(ff.get_triad()) ) ;
119 
120  get_radial_vect.set(1) = (met_gamt.con())(1,1) ;
121 
122  get_radial_vect.set(2) = (met_gamt.con())(1,2) ;
123 
124  get_radial_vect.set(3) = (met_gamt.con())(1,3) ;
125 
126  get_radial_vect = get_radial_vect / sqrt((met_gamt.con())(1,1)) ;
127 
128  get_radial_vect.std_spectral_base() ;
129 
130 
131  return get_radial_vect ;
132 
133 }
134 
135 
136 const Scalar Isol_hor::b_tilde()const {
137 
138  Scalar tmp = contract( beta(), 0, met_gamt.radial_vect()
139  .down(0, met_gamt), 0) ;
140 
141  return tmp ;
142 
143 }
144 
145 
147 
148  Scalar tmp = sqrt( gam_dd()(2,2) * gam_dd()(3,3) - gam_dd()(2,3)
149  * gam_dd()(2,3)) ;
150 
151  tmp.std_spectral_base() ;
152 
153  return tmp ;
154 
155 }
156 
157 double Isol_hor::area_hor() const {
158 
159  Scalar integrand (darea_hor()) ;
160  integrand.raccord(1) ;
161 
162  return mp.integrale_surface(integrand, radius + 1e-15) ;
163 
164 }
165 
166 
167 double Isol_hor::radius_hor() const {
168 
169  double resu = area_hor() / (4. * M_PI);
170 
171  resu = pow(resu, 1./2.) ;
172 
173  return resu ;
174 
175 }
176 
177 
178 double Isol_hor::ang_mom_hor()const {
179 
180  // Vector \partial_phi
181  Vector phi (ff.get_mp(), CON, *(ff.get_triad()) ) ;
182 
183  Scalar tmp (ff.get_mp() ) ;
184  tmp = 1 ;
185  tmp.std_spectral_base() ;
186  tmp.mult_rsint() ;
187 
188  phi.set(1) = 0. ;
189  phi.set(2) = 0. ;
190  phi.set(3) = tmp ;
191 
192  Scalar k_rphi = contract(contract( radial_vect_hor(), 0, k_dd(), 0), 0,
193  phi, 0) / (8. * M_PI) ;
194 
195  Scalar integrand = k_rphi * darea_hor() ; // we correct with the curved
196  // element of area
197 
198  double ang_mom = mp.integrale_surface(integrand, radius + 1e-15) ;
199 
200  return ang_mom ;
201 
202 }
203 
204 
205 // Mass (fundamental constants made 1)
206 double Isol_hor::mass_hor()const {
207 
208  double rr = radius_hor() ;
209 
210  double tmp = sqrt( pow( rr, 4) + 4 * pow( ang_mom_hor(), 2) ) / ( 2 * rr ) ;
211 
212  return tmp ;
213 
214 }
215 
216 
217 // Surface gravity
218 double Isol_hor::kappa_hor() const{
219 
220  double rr = radius_hor() ;
221 
222  double jj = ang_mom_hor() ;
223 
224  double tmp = (pow( rr, 4) - 4 * pow( jj, 2)) / ( 2 * pow( rr, 3)
225  * sqrt( pow( rr, 4) + 4 * pow( jj, 2) ) ) ;
226 
227  return tmp ;
228 
229 }
230 
231 
232 // Orbital velocity
233 double Isol_hor::omega_hor()const {
234 
235  double rr = radius_hor() ;
236 
237  double jj = ang_mom_hor() ;
238 
239  double tmp = 2 * jj / ( rr * sqrt( pow( rr, 4) + 4 * pow( jj, 2) ) ) ;
240 
241  return tmp ;
242 
243 }
244 
245 
246 // ADM angular momentum
247 
248 double Isol_hor::ang_mom_adm()const {
249 
250  Scalar integrand = (k_dd()(1,3) - gam_dd()(1,3) * trk()) / (8. * M_PI) ;
251 
252  integrand.mult_rsint() ; // in order to pass from the triad
253  // component to the coordinate basis
254 
255  double tmp = mp.integrale_surface_infini(integrand) ;
256 
257  return tmp ;
258 
259 }
260 
261 // Expansion
262 
264 
265  Scalar expa = contract(gam().radial_vect().derive_cov(gam()), 0,1)
266  + contract(contract(k_dd(), 0, gam().radial_vect(), 0),
267  0, gam().radial_vect(), 0) - trk() ;
268 
269  return expa ;
270 }
271 }
Scalar expansion() const
Expansion of the outgoing null normal ( )
Definition: phys_param.C:263
const Scalar darea_hor() const
Element of area of the horizon.
Definition: phys_param.C:146
Metric met_gamt
3 metric tilde
Definition: isol_hor.h:326
const Scalar b_tilde() const
Radial component of the shift with respect to the conformal metric.
Definition: phys_param.C:136
double ang_mom_hor() const
Angular momentum (modulo)
Definition: phys_param.C:178
double ang_mom_adm() const
ADM angular Momentum
Definition: phys_param.C:248
double kappa_hor() const
Surface gravity
Definition: phys_param.C:218
double radius
Radius of the horizon in LORENE's units.
Definition: isol_hor.h:266
double mass_hor() const
Mass computed at the horizon
Definition: phys_param.C:206
double radius_hor() const
Radius of the horizon.
Definition: phys_param.C:167
const Vector tradial_vect_hor() const
Vector radial normal tilde.
Definition: phys_param.C:116
Map_af & mp
Affine mapping.
Definition: isol_hor.h:260
const Vector radial_vect_hor() const
Vector radial normal.
Definition: phys_param.C:95
double area_hor() const
Area of the horizon.
Definition: phys_param.C:157
double omega_hor() const
Orbital velocity
Definition: phys_param.C:233
double integrale_surface_infini(const Cmp &ci) const
Performs the surface integration of ci at infinity.
double integrale_surface(const Cmp &ci, double rayon) const
Performs the surface integration of ci on the sphere of radius rayon .
const Base_vect * get_triad() const
Returns the vectorial basis (triad) on which the metric is defined.
Definition: metric.h:309
virtual const Sym_tensor & con() const
Read-only access to the contravariant representation.
Definition: metric.C:290
virtual const Vector & radial_vect() const
Returns the radial vector normal to a spherical slicing and pointing toward spatial infinity.
Definition: metric.C:362
const Map & get_mp() const
Returns the mapping.
Definition: metric.h:202
Tensor field of valence 0 (or component of a tensorial field).
Definition: scalar.h:387
void raccord(int n)
Performs the matching of the nucleus with respect to the first shell.
virtual void std_spectral_base()
Sets the spectral bases of the Valeur va to the standard ones for a scalar field.
Definition: scalar.C:784
void mult_rsint()
Multiplication by everywhere; dzpuis is not changed.
virtual const Sym_tensor & gam_dd() const
Induced metric (covariant components ) at the current time step (jtime )
virtual const Sym_tensor & k_dd() const
Extrinsic curvature tensor (covariant components ) at the current time step (jtime )
virtual const Sym_tensor & gam_uu() const
Induced metric (contravariant components ) at the current time step (jtime )
const Metric_flat & ff
Pointer on the flat metric with respect to which the conformal decomposition is performed.
Definition: time_slice.h:507
virtual const Scalar & trk() const
Trace K of the extrinsic curvature at the current time step (jtime )
virtual const Vector & beta() const
shift vector at the current time step (jtime )
const Metric & gam() const
Induced metric at the current time step (jtime )
Tensor field of valence 1.
Definition: vector.h:188
virtual void std_spectral_base()
Sets the standard spectal bases of decomposition for each component.
Definition: vector.C:316
Scalar & set(int)
Read/write access to a component.
Definition: vector.C:296
Cmp sqrt(const Cmp &)
Square root.
Definition: cmp_math.C:220
Cmp pow(const Cmp &, int)
Power .
Definition: cmp_math.C:348
Tensor down(int ind, const Metric &gam) const
Computes a new tensor by lowering an index of *this.
Tenseur contract(const Tenseur &, int id1, int id2)
Self contraction of two indices of a Tenseur .
Lorene prototypes.
Definition: app_hor.h:64