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C Schwarzschild-Lemaitre metric
c (Schwarzschild black hole with cosmological constant)
C Proposed by Lemaitre in 1932
C
C Author : D. Vulcanov (Timisoara, Romania)
C see ../../README for copyright & licensing info
C
C $Header$
#include "cctk.h"
#include "cctk_Parameters.h"
subroutine Exact__Schwarzschild_Lemaitre(
$ 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
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 lam, mas
CCTK_REAL r2, ppp, unu, doi
C This model has a cosmological constant
Tmunu_flag = .true.
lam = Schwarzschild_Lemaitre__Lambda
mas = Schwarzschild_Lemaitre__mass
r2 =x*x+y*y+z*z
ppp=1.0D0 -2.0D0*mas/sqrt(r2) -r2*lam/3.0D0
unu=(1.0D0-ppp)/ppp/r2
doi=(ppp - 1.0D0)/r2
gdtt = -ppp
gdtx = 0.0D0
gdty = 0.0D0
gdtz = 0.0D0
gdxx = 1.0D0 + x*x*unu
gdyy = 1.0D0 + y*y*unu
gdzz = 1.0D0 + z*z*unu
gdxy = x*y*unu
gdyz = y*z*unu
gdzx = z*x*unu
gutt = -1.0D0/ppp
gutx = 0.0D0
guty = 0.0D0
gutz = 0.0D0
guxx = 1.0D0 + x*x*doi
guyy = 1.0D0 + y*y*doi
guzz = 1.0D0 + z*z*doi
guxy = x*y*doi
guyz = y*z*doi
guzx = x*z*doi
return
end
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