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C Milne spacetime metric ?!?!?
C Suggested by Matteo Rossi and E. Onofri (Univ. di Parma, Italy)
C They inted to use thsi metric for simulating an Pre-Big-Bang
C Cosmology, as proposed by Veneziano some year ago
C
C Author : D. Vulcanov (Timsoara, Romania)
C see ../../README for copyright & licensing info
C
C $Header$
#include "cctk.h"
subroutine Exact__Milne(
$ 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
c input arguments
CCTK_REAL x, y, z, 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 coef, x2,y2,z2,t2
C This is a vacuum spacetime with no cosmological constant
Tmunu_flag = .false.
x2= x*x
y2= y*y
z2= z*z
t2= t*t
coef= t2/(1.d0+ x2 +y2+ z2)
gdtt = -1.d0
gdtx = 0.d0
gdty = 0.d0
gdtz = 0.d0
gdxx = coef*(1.d0+y2+z2)
gdyy = coef*(1.d0+x2+z2)
gdzz = coef*(1.d0+x2+y2)
gdxy = -coef*x*y
gdyz = -coef*y*z
gdzx = -coef*x*z
gutt = -1.d0
gutx = 0.d0
guty = 0.d0
gutz = 0.d0
guxx = (1.d0+x2)/(t2)
guyy = (1.d0+y2)/(t2)
guzz = (1.d0+z2)/(t2)
guxy = x*y/(t2)
guyz = y*z/(t2)
guzx = x*z/(t2)
return
end
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