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c Schwarzschild spacetime in Painleve [e-acute on last e]-Gullstrand
c coordinates. These have a *flat* 3-metric, and are described in
c detail in Martel and Poisson, gr-qc/0001069
C
C Author: unknown
C Copyright/License: unknown
C
c $Header$
#include "cctk.h"
#include "cctk_Parameters.h"
subroutine Exact__Schwarzschild_PG(
$ 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 variables
CCTK_REAL eps, m
CCTK_REAL r, bx, by, bz, b2
C This is a vacuum spacetime with no cosmological constant
Tmunu_flag = .false.
C Get parameters of the exact solution.
eps = Schwarzschild_PG__epsilon
m = Schwarzschild_PG__mass
r = max(sqrt(x**2 + y**2 + z**2), eps)
bx = sqrt(2.d0 * m / r) * x / r
by = sqrt(2.d0 * m / r) * y / r
bz = sqrt(2.d0 * m / r) * z / r
b2 = 2.d0 * m / r
gdtt = - 1.d0 + b2
gdtx = bx
gdty = by
gdtz = bz
gdxx = 1.d0
gdyy = 1.d0
gdzz = 1.d0
gdxy = 0.d0
gdyz = 0.d0
gdzx = 0.d0
gutt = - 1.d0
gutx = bx
guty = by
gutz = bz
guxx = 1.d0 - bx**2
guyy = 1.d0 - by**2
guzz = 1.d0 - bz**2
guxy = - bx * by
guyz = - by * bz
guzx = - bz * bx
return
end
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