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c The metric given here corresponds to that of flat spacetime
c but with non-trivial spatial coordinates. Basically, I take
c the flat metric in spherical coordinates, define a new
c radial coordinate such that:
c
c r = r ( 1 - a f(r ) )
c new new
c
c where f(r) is a gaussian centered at r=0 with amplitude 1.
c Finally, I transform back to cartesian coordinates.
c For 0 <= a < 1, the transformation above is monotonic.
C
C Author: unknown
C Copyright/License: unknown
C
c $Header$
#include "cctk.h"
#include "cctk_Parameters.h"
subroutine Exact__Minkowski_funny(
$ 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_DECLARE(CCTK_REAL, x,)
CCTK_DECLARE(CCTK_REAL, y,)
CCTK_DECLARE(CCTK_REAL, 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 a,s
CCTK_REAL r,r2,x2,y2,z2
CCTK_REAL f,fp,g11,g22
CCTK_REAL det
c constants
CCTK_REAL zero, one, two
parameter (zero=0.0d0, one=1.0d0, two=2.0d0)
c This is a vacuum spacetime with no cosmological constant
Tmunu_flag = .false.
c Read parameters
a = Minkowski_funny__amplitude
s = Minkowski_funny__sigma
c Find transformation function.
x2 = x**2
y2 = y**2
z2 = z**2
r2 = x2 + y2 + z2
r = sqrt(r2)
f = exp(-r2/s**2)
fp = - two*r/s**2*f
c Give metric components.
g11 = (one - a*(f + r*fp))**2
g22 = (one - a*f)**2
gdtt = - one
gdtx = zero
gdty = zero
gdtz = zero
gdxx = (x2*g11 + (y2 + z2)*g22)/r2
gdyy = (y2*g11 + (x2 + z2)*g22)/r2
gdzz = (z2*g11 + (x2 + y2)*g22)/r2
gdxy = x*y*(g11 - g22)/r2
gdzx = x*z*(g11 - g22)/r2
gdyz = y*z*(g11 - g22)/r2
c Find inverse metric.
gutt = - one
gutx = zero
guty = zero
gutz = zero
det = gdxx*gdyy*gdzz + two*gdxy*gdzx*gdyz
. - gdxx*gdyz**2 - gdyy*gdzx**2 - gdzz*gdxy**2
guxx = (gdyy*gdzz - gdyz**2)/det
guyy = (gdxx*gdzz - gdzx**2)/det
guzz = (gdxx*gdyy - gdxy**2)/det
guxy = (gdzx*gdyz - gdzz*gdxy)/det
guyz = (gdxy*gdzx - gdxx*gdyz)/det
guzx = (gdxy*gdyz - gdyy*gdzx)/det
return
end
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