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#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Functions.h"
#include "cctk_Parameters.h"
subroutine qlm_killing_test (CCTK_ARGUMENTS, hn)
use cctk
use qlm_boundary
use qlm_derivs
use qlm_variables
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_FUNCTIONS
DECLARE_CCTK_PARAMETERS
integer :: hn
CCTK_REAL :: qq(2,2), dqq(2,2,2)
CCTK_REAL :: xi(2), dxi(2,2)
CCTK_REAL :: lqq(2,2)
CCTK_REAL :: delta_space(2)
integer :: i,j
integer :: a, b, c
CCTK_REAL :: theta, phi
if (veryverbose/=0) then
call CCTK_INFO ("Testing Killing vector field")
end if
delta_space(:) = (/ qlm_delta_theta(hn), qlm_delta_phi(hn) /)
! Calculate the coordinates
do j = 1+qlm_nghostsphi(hn), qlm_nphi(hn)-qlm_nghostsphi(hn)
do i = 1+qlm_nghoststheta(hn), qlm_ntheta(hn)-qlm_nghoststheta(hn)
theta = qlm_origin_theta(hn) + (i-1)*qlm_delta_theta(hn)
phi = qlm_origin_phi(hn) + (j-1)*qlm_delta_phi(hn)
! 2-metric on the horizon
qq(1,1) = qlm_qtt(i,j,hn)
qq(1,2) = qlm_qtp(i,j,hn)
qq(2,2) = qlm_qpp(i,j,hn)
qq(2,1) = qq(1,2)
dqq(1,1,1) = qlm_dqttt(i,j)
dqq(1,2,1) = qlm_dqtpt(i,j)
dqq(2,2,1) = qlm_dqppt(i,j)
dqq(1,1,2) = qlm_dqttp(i,j)
dqq(1,2,2) = qlm_dqtpp(i,j)
dqq(2,2,2) = qlm_dqppp(i,j)
dqq(2,1,:) = dqq(1,2,:)
xi(1) = qlm_xi_t(i,j,hn)
xi(2) = qlm_xi_p(i,j,hn)
dxi(1,1:2) = deriv (qlm_xi_t(:,:,hn), i, j, delta_space)
dxi(2,1:2) = deriv (qlm_xi_p(:,:,hn), i, j, delta_space)
! L_xi q_ab = q_cb d_a xi^c + q_ac d_b xi^c + xi^c d_c q_ab
do a=1,2
do b=1,2
lqq(a,b) = 0
do c=1,2
lqq(a,b) = lqq(a,b) + qq(c,b) * dxi(c,a) &
& + qq(a,c) * dxi(c,b) &
& + xi(c) * dqq(a,b,c)
end do
end do
end do
qlm_lqtt(i,j,hn) = lqq(1,1)
qlm_lqtp(i,j,hn) = lqq(1,2)
qlm_lqpp(i,j,hn) = lqq(2,2)
end do
end do
call set_boundary (CCTK_PASS_FTOF, hn, qlm_lqtt(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_lqtp(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_lqpp(:,:,hn), +1)
end subroutine qlm_killing_test
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