C Lemaitre type universe - FRW with k =0, p=k rho and 
C cosmological constant
C
C Author : D. Vulcanov (Timisoara, Romania)
C see ../../README for copyright & licensing info
C
C $Header$


#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Functions.h"


      subroutine Exact__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
      DECLARE_CCTK_FUNCTIONS      

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 ka, la, e0, r0
      CCTK_REAL unu, ra, ra2, Pii

c this model sets the stress-energy tensor in the "CalcTmunu" code
      Tmunu_flag = .true.

      ka = Lemaitre__kappa
      e0 = Lemaitre__epsilon0
      la = Lemaitre__Lambda 
      r0 = Lemaitre__R0

       Pii = acos(-1.0D0)

       unu = sqrt(3.0D0*la)*t*(ka+1.0D0)/(2.0D0)

       ra  = r0*(cosh(unu)+sqrt(1.0D0+8.0D0*Pii*e0/la)*sinh(unu))**
     &       (2.0D0/(3.0D0*ka+3.0D0)) 

       ra2 = ra*ra  
 
      gdtt = -1.0D0 
      gdtx = 0.0D0 
      gdty = 0.0D0
      gdtz = 0.0D0
      gdxx = ra2
      gdyy = ra2
      gdzz = ra2
      gdxy = 0.0D0
      gdyz = 0.0D0
      gdzx = 0.0D0

      gutt = -1.0D0
      gutx = 0.0D0
      guty = 0.0D0
      gutz = 0.0D0
      guxx = 1.0D0/ra2
      guyy = 1.0D0/ra2
      guzz = 1.0D0/ra2
      guxy = 0.0D0
      guyz = 0.0D0
      guzx = 0.0D0
 


      return
      end