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C Goedel spacetime !!!!
C See: S. Hawking, G.F.R. Ellis, The Large
C Scale Structure of space-time, Cambridge, 1973
C
C Author : D. Vulcanov (Timsioara, Romania)
C see ../../README for copyright & licensing info
C
C $Header$
#include "cctk.h"
#include "cctk_Parameters.h"
subroutine Exact__Goedel(
$ x, y, z, t,
$ gdtt, gdtx, gdty, gdtz,
$ gdxx, gdyy, gdzz, gdxy, gdyz, gdzx,
$ gutt, gutx, guty, gutz,
$ guxx, guyy, guzz, guxy, guyz, guzx,
$ psi, Tmunu_flag)
implicit none
DECLARE_CCTK_PARAMETERS
c input arguments
CCTK_REAL x
CCTK_DECLARE(CCTK_REAL, y,)
CCTK_DECLARE(CCTK_REAL, z,)
CCTK_DECLARE(CCTK_REAL, t,)
c output arguments
CCTK_REAL gdtt, gdtx, gdty, gdtz,
$ gdxx, gdyy, gdzz, gdxy, gdyz, gdzx,
$ gutt, gutx, guty, gutz,
$ guxx, guyy, guzz, guxy, guyz, guzx
CCTK_DECLARE(CCTK_REAL, psi,)
LOGICAL Tmunu_flag
c local variables
CCTK_REAL arad
C This is a vacuum spacetime with no cosmological constant
Tmunu_flag = .false.
arad = Goedel__scale
gdtt = -arad*arad
gdtx = 0.d0
gdty = 0.d0
gdtz = 0.d0
gdxx = (1/2)*arad*arad*exp(x)*exp(x)
gdyy = -arad*arad
gdzz = arad*arad*exp(x)
gdxy = 0.d0
gdyz = 0.d0
gdzx = arad*arad*exp(x)
gutt = -1/(arad*arad)
gutx = 0.d0
guty = 0.d0
gutz = 0.d0
guxx = -2/(arad*arad*exp(x)*exp(x))
guyy = -1/(arad*arad)
guzz = -1/(arad*arad*exp(x))
guxy = 0.d0
guyz = 0.d0
guzx = 2/(arad*arad*exp(x))
return
end
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