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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 Author : D. Vulcanov (Timsoara, Romania)
-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)
-
- implicit none
-
-c Input.
-
- CCTK_REAL x, y, z, t
-
-c Output.
-
- CCTK_REAL gdtt, gdtx, gdty, gdtz,
- $ gdxx, gdyy, gdzz, gdxy, gdyz, gdzx,
- $ gutt, gutx, guty, gutz,
- $ guxx, guyy, guzz, guxy, guyz, guzx,
- $ coef, x2,y2,z2,t2
-
- 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