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c Schwarzschild metric in Eddington-Finkelstein coordinates,
c as per MTW box 31.2
C
C Author: unknown
C Copyright/License: unknown
C
c $Header$
#include "cctk.h"
#include "cctk_Parameters.h"
subroutine Exact__Schwarzschild_EF(
$ 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, 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_REAL psi
LOGICAL Tmunu_flag
c local static variables
CCTK_REAL eps, m
c local variables
CCTK_REAL r
C This is a vacuum spacetime with no cosmological constant
Tmunu_flag = .false.
C Get parameters of the exact solution.
eps = Schwarzschild_EF__epsilon
m = Schwarzschild_EF__mass
r = max(sqrt(x**2 + y**2 + z**2), eps)
gdtt = - (1.d0 - 2.d0 * m / r)
gdtx = 2.d0 * m * x / r**2
gdty = 2.d0 * m * y / r**2
gdtz = 2.d0 * m * z / r**2
gdxx = 1.d0 + 2.d0 * m * x**2 / r**3
gdyy = 1.d0 + 2.d0 * m * y**2 / r**3
gdzz = 1.d0 + 2.d0 * m * z**2 / r**3
gdxy = 2.d0 * m * x * y / r**3
gdyz = 2.d0 * m * y * z / r**3
gdzx = 2.d0 * m * z * x / r**3
gutt = - (1.d0 + 2.d0 * m / r)
gutx = 2.d0 * m * x / r**2
guty = 2.d0 * m * y / r**2
gutz = 2.d0 * m * z / r**2
guxx = 1.d0 - 2.d0 * m * x**2 / r**3
guyy = 1.d0 - 2.d0 * m * y**2 / r**3
guzz = 1.d0 - 2.d0 * m * z**2 / r**3
guxy = - 2.d0 * m * x * y / r**3
guyz = - 2.d0 * m * y * z / r**3
guzx = - 2.d0 * m * z * x / r**3
return
end
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