1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
|
C Here we added the matter variables for several of the metrics
C you can find in "src" directory through the components of the
C stress-eergy tensor. Being different in specific cases it is
C necessary to check first which metric is running.
C Author : Dumitru Vulcanov (Timisoara, Romania)
C $Header$
C Varianta cu un singur param. (raza initiala) pt Rob-Walker
#include "param_defs.inc"
c
c FIXME:
c If we could be certain that this code were always compiled as Fortran 90,
c the decode here could be done with a case statement, which ought to give
c better performance than the if-else chain we use now. But in practice
c Cactus has enough other overheads that this is not bothering with...
c
c
c ***** KLUDGE *****
c
c This code is #include-d into various evolution thorns, and alas does not
c have direct access to thorn Exact parameters. Instead, this code must
c use the restricted-grid-scalar copies of the parameters. In practice,
c this means changing "__" to "___" in all parameter names (but not in the
c #define constants in "param_defs.inc"). See the comments in param.ccl
c for further information on this.
c
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
ccccc Minkowski spacetime cccccccccccccccccccccccccccccccccccccccccccccccccccccc
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
if (decoded_exact_model .eq. EXACT__Minkowski) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Minkowski_shift) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Minkowski_funny) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Minkowski_gauge_wave) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Minkowski_conf_wave) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
ccccc black hole spacetimes cccccccccccccccccccccccccccccccccccccccccccccccccccc
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
elseif (decoded_exact_model .eq. EXACT__Schwarzschild_EF) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Schwarzschild_PG) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Schwarzschild_Novikov) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Kerr_BoyerLindquist) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Kerr_KerrSchild) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c Schwarzschild-Lemaitre spacetime
c (Schwarzschild black hole with cosmological constant)
c
elseif (decoded_exact_model .eq. EXACT__Schwarzschild_Lemaitre) then
razsch2=x(i,j,k)*x(i,j,k)+y(i,j,k)*y(i,j,k)+z(i,j,k)*z(i,j,k)
coefsch=-Schwarzschild_Lemaitre___Lambda/(8.0D0*pi)
pppsch=1.0D0-2.0D0*Schwarzschild_Lemaitre___mass/sqrt(razsch2)
& -Schwarzschild_Lemaitre___Lambda*razsch2/3.0D0
unusch=(1.0D0-pppsch)/pppsch/razsch2
Ttt = Ttt-coefsch*pppsch
Ttx = Ttx
Tty = Tty
Ttz = Ttz
Txx = Txx+coefsch*(1.0D0+x(i,j,k)*x(i,j,k)*unusch)
Tyy = Tyy+coefsch*(1.0D0+y(i,j,k)*y(i,j,k)*unusch)
Tzz = Tzz+coefsch*(1.0D0+z(i,j,k)*z(i,j,k)*unusch)
Txy = Txy+coefsch*x(i,j,k)*y(i,j,k)*unusch
Txz = Txz+coefsch*x(i,j,k)*z(i,j,k)*unusch
Tyz = Tyz+coefsch*y(i,j,k)*z(i,j,k)*unusch
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
elseif (decoded_exact_model .eq. EXACT__multi_BH) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Alvi) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Thorne_fakebinary) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
ccccc cosmological spacetimes cccccccccccccccccccccccccccccccccccccccccccccccccc
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c Lemaitre spacetime
c
elseif (decoded_exact_model .eq. EXACT__Lemaitre) then
unu1 = sqrt(3.0D0*Lemaitre___Lambda)
& * CCTK_time * (Lemaitre___kappa+1.0D0) / (2.0D0)
raz = Lemaitre___R0*(cosh(unu1)
& + sqrt(1.0D0+8.0D0*pi*Lemaitre___epsilon0
& /Lemaitre___Lambda)
& *sinh(unu1))
& **(2.0D0/(3.0D0*Lemaitre___kappa+3.0D0))
raz2 = raz*raz
treiori = -Lemaitre___Lambda*raz2/8.0D0/pi
& +Lemaitre___epsilon0*Lemaitre___kappa
& *raz**(-3.0D0*Lemaitre___kappa-1.0D0)
Ttt = Ttt + Lemaitre___Lambda/8.0D0/pi
& + Lemaitre___epsilon0*raz**(-3.0D0*(Lemaitre___kappa+1.0D0))
Txx = Txx + treiori
Tyy = Tyy + treiori
Tzz = Tzz + treiori
Txy = Txy
Tyz = Tyz
Txz = Txz
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
ccc
ccc this metric doesnt work and has been moved to ../../archive/
ccc
ccc Robertson-Walker spacetime
ccc
cc elseif (decoded_exact_model .eq. EXACT__Robertson_Walker) then
cc rr2 = x(i,j,k)*x(i,j,k)+y(i,j,k)*y(i,j,k)+z(i,j,k)*z(i,j,k)
cc
cc if (Robertson_Walker___pressure .gt. 0) then
cc aha1 = Robertson_Walker___k * (Robertson_Walker___R0**2)
cc & / (8.0D0*pi*(raza(i,j,k)**2))
cc aha2 = Robertson_Walker___k/(1.0D0 - Robertson_Walker___k*rr2)
cc
cc Ttt = Ttt + 3.0D0*aha1/(raza(i,j,k)*raza(i,j,k))
cc Txx = Txx + aha1*(1.0D0 + aha2*x(i,j,k)*x(i,j,k))
cc Tyy = Tyy + aha1*(1.0D0 + aha2*y(i,j,k)*y(i,j,k))
cc Tzz = Tzz + aha1*(1.0D0 + aha2*z(i,j,k)*z(i,j,k))
cc Txy = Txy + aha1*aha2*x(i,j,k)*y(i,j,k)
cc Txz = Txz + aha1*aha2*x(i,j,k)*z(i,j,k)
cc Tyz = Tyz + aha1*aha2*y(i,j,k)*y(i,j,k)
cc else
cc Ttt = Ttt+Robertson_Walker___rho * (Robertson_Walker___R0**3)
cc & / (raza(i,j,k)**3)
cc Txx = Txx
cc Tyy = Tyy
cc Tzz = Tzz
cc Txy = Txy
cc Txz = Txz
cc Tyz = Tyz
cc endif
cc
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c de Sitter spacetime
c
elseif (decoded_exact_model .eq. EXACT__de_Sitter) then
Ttt = Ttt + 1.0D0/6.0D0/pi/(CCTK_time**2)
Ttx = Ttx
Tty = Tty
Ttz = Ttz
Txx = Txx
Tyy = Tyy
Tzz = Tzz
Txy = Txy
Txz = Txz
Tyz = Tyz
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c de Sitter spacetime with cosmological constant
c
elseif (decoded_exact_model .eq. EXACT__de_Sitter_Lambda) then
aaaa = de_Sitter_Lambda___scale/(8.0D0*pi)
bbbb = aaaa*exp(2.0D0*sqrt(de_Sitter_Lambda___scale/3.0D0)*CCTK_time)
Ttt = Ttt + aaaa
Ttx = Ttx
Tty = Tty
Ttz = Ttz
Txx = Txx - bbbb
Tyy = Tyy - bbbb
Tzz = Tzz - bbbb
Txy = Txy
Txz = Txz
Tyz = Tyz
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c anti-de Sitter spacetime with cosmological constant
c
elseif (decoded_exact_model .eq. EXACT__anti_de_Sitter_Lambda) then
aaaa1 = anti_de_Sitter_Lambda___scale/(8.0D0*pi)
bbbb1 = aaaa1*exp(2.0D0*sqrt(-anti_de_Sitter_Lambda___scale/3.0D0)
& *x(i,j,k))
Ttt = Ttt + bbbb1
Ttx = Ttx
Tty = Tty
Ttz = Ttz
Txx = Txx - aaaa1
Tyy = Tyy - bbbb1
Tzz = Tzz - bbbb1
Txy = Txy
Txz = Txz
Tyz = Tyz
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
elseif (decoded_exact_model .eq. EXACT__Bianchi_I) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Goedel) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c Bertotti spacetime
c
elseif (decoded_exact_model .eq. EXACT__Bertotti) then
bass = Bertotti___Lambda/(8.0D0*pi)
term1 = bass*exp(2.0D0*sqrt(-Bertotti___Lambda)*x(i,j,k))
term2 = bass*exp(2.0D0*sqrt(-Bertotti___Lambda)*z(i,j,k))
Ttt = Ttt + term1
Ttx = Ttx
Tty = Tty
Ttz = Ttz
Txx = Txx - bass
Tyy = Tyy - term2
Tzz = Tzz - bass
Txy = Txy
Txz = Txz
Tyz = Tyz
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c Kasner-like spacetime
c
elseif (decoded_exact_model .eq. EXACT__Kasner_like) then
kkkk=Kasner_like___q*(2.0D0-3.0D0*Kasner_like___q)
& /(8.0D0*pi*(CCTK_time**2))
Ttt = Ttt + kkkk
Ttx = Ttx
Tty = Tty
Ttz = Ttz
Txx = Txx + kkkk*CCTK_time**(2.0D0*Kasner_like___q)
Tyy = Tyy + kkkk*CCTK_time**(2.0D0*Kasner_like___q)
Tzz = Tzz + kkkk*CCTK_time**(2.0D0-4.0D0*Kasner_like___q)
Txy = Txy
Txz = Txz
Tyz = Tyz
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
elseif (decoded_exact_model .eq. EXACT__Kasner_axisymmetric) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c generalized Kasner spacetime
c
elseif (decoded_exact_model .eq. EXACT__Kasner_generalized) then
kkkk1 = ( Kasner_generalized___p1 - Kasner_generalized___p1**2
& + Kasner_generalized___p2 - Kasner_generalized___p2**2
& - Kasner_generalized___p1*Kasner_generalized___p2 )
& / (8.0D0*pi*(CCTK_time**2))
Ttt = Ttt + kkkk1
Ttx = Ttx
Tty = Tty
Ttz = Ttz
Txx = Txx+kkkk1*CCTK_time**(2.0D0*Kasner_generalized___p1)
Tyy = Tyy+kkkk1*CCTK_time**(2.0D0*Kasner_generalized___p2)
Tzz = Tzz+kkkk1*CCTK_time**(2.0D0-2.0D0*Kasner_generalized___p1
& -2.0D0*Kasner_generalized___p2)
Txy = Txy
Txz = Txz
Tyz = Tyz
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
elseif (decoded_exact_model .eq. EXACT__Gowdy_wave) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
elseif (decoded_exact_model .eq. EXACT__Milne) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
ccccc miscellaneous spacetimes ccccccccccccccccccccccccccccccccccccccccccccccccc
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
elseif (decoded_exact_model .eq. EXACT__boost_rotation_symmetric) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__bowl) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c constant density star
c
elseif (decoded_exact_model .eq. EXACT__constant_density_star) then
rr = sqrt(x(i,j,k)*x(i,j,k)+y(i,j,k)*y(i,j,k)+
& z(i,j,k)*z(i,j,k))
star_m = constant_density_star___mass
star_r = constant_density_star___radius
r3 = star_r**3
if (rr.le.star_r) then
unu = 3.0D0*sqrt(1.0D0-2.0D0*star_m/star_r)
doi = sqrt(1.0D0-2.0D0*star_m*rr*rr/r3)
trei= star_m*(unu-3.0D0*doi)/(2*pi*(unu-doi)*r3)
Ttt = Ttt + 3.0D0*star_m*
& (5.0D0-9.0D0*star_m/star_r - unu*doi
& -star_m*rr*rr/r3)/(8.0D0*pi*r3)
Txx = Txx -trei*(1.0D0+2.0D0*star_m*x(i,j,k)*x(i,j,k)/
& (doi*doi*r3))/2.0D0
Tyy = Tyy -trei*(1.0D0+2.0D0*star_m*y(i,j,k)*y(i,j,k)/
& (doi*doi*r3))/2.0D0
Tzz = Tzz -trei*(1.0D0+2.0D0*star_m*z(i,j,k)*z(i,j,k)/
& (doi*doi*r3))/2.0D0
Txy = Txy -trei*star_m*x(i,j,k)*y(i,j,k)/(doi*doi*r3)
Tyz = Tyz -trei*star_m*y(i,j,k)*z(i,j,k)/(doi*doi*r3)
Txz = Txz -trei*star_m*x(i,j,k)*z(i,j,k)/(doi*doi*r3)
endif
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
else
call CCTK_WARN(0,"Unknown value of Exact::decoded_exact_model")
endif
|