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#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Functions.h"
#include "cctk_Parameters.h"
subroutine qlm_calc_newman_penrose (CCTK_ARGUMENTS, hn)
use adm_metric
use cctk
use classify
use constants
use qlm_boundary
use qlm_derivs
use qlm_variables
use ricci4
use tensor
use tensor4
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_FUNCTIONS
DECLARE_CCTK_PARAMETERS
integer :: hn
CCTK_REAL, parameter :: zero=0, one=1, two=2, half=1/two
CCTK_REAL :: ll(0:3), nn(0:3)
CCTK_COMPLEX :: mm(0:3)
CCTK_REAL :: nabla_ll(0:3,0:3), nabla_nn(0:3,0:3)
CCTK_COMPLEX :: nabla_mm(0:3,0:3)
CCTK_REAL :: t0, t1, t2
logical :: ce0, ce1, ce2
CCTK_REAL :: delta_space(2)
integer :: i, j
integer :: a, b
CCTK_REAL :: theta, phi
if (veryverbose/=0) then
call CCTK_INFO ("Calculating Newman-Penrose quantities")
end if
t0 = qlm_time(hn)
t1 = qlm_time_p(hn)
t2 = qlm_time_p_p(hn)
ce0 = qlm_have_valid_data(hn) == 0
ce1 = qlm_have_valid_data_p(hn) == 0
ce2 = qlm_have_valid_data_p_p(hn) == 0
delta_space(:) = (/ qlm_delta_theta(hn), qlm_delta_phi(hn) /)
if (qlm_nghoststheta(hn)<2 .or. qlm_nghostsphi(hn)<2) call CCTK_WARN (0, "internal error")
! 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)
! Get the stuff from the arrays
ll(0) = qlm_l0(i,j,hn)
ll(1) = qlm_l1(i,j,hn)
ll(2) = qlm_l2(i,j,hn)
ll(3) = qlm_l3(i,j,hn)
nn(0) = qlm_n0(i,j,hn)
nn(1) = qlm_n1(i,j,hn)
nn(2) = qlm_n2(i,j,hn)
nn(3) = qlm_n3(i,j,hn)
mm(0) = qlm_m0(i,j,hn)
mm(1) = qlm_m1(i,j,hn)
mm(2) = qlm_m2(i,j,hn)
mm(3) = qlm_m3(i,j,hn)
nabla_ll(:,:) = qlm_tetrad_derivs(i,j)%nabla_ll(:,:)
nabla_nn(:,:) = qlm_tetrad_derivs(i,j)%nabla_nn(:,:)
nabla_mm(:,:) = qlm_tetrad_derivs(i,j)%nabla_mm(:,:)
! kappa = - m^a l^b D_b l_a
! tau = - m^a n^b D_b l_a
! sigma = - m^a m^b D_b l_a
! rho = - m^a ~m^b D_b l_a [ ~m = congj(m) ]
qlm_npkappa (i,j,hn) = 0
qlm_nptau (i,j,hn) = 0
qlm_npsigma (i,j,hn) = 0
qlm_nprho (i,j,hn) = 0
! epsilon = - 1/2 ( n^a l^b D_b l_a - ~m^a l^b D_b m_a )
! gamma = - 1/2 ( n^a n^b D_b l_a - ~m^a n^b D_b m_a )
! beta = - 1/2 ( n^a m^b D_b l_a - ~m^a m^b D_b m_a )
! alpha = - 1/2 ( n^a ~m^b D_b l_a - ~m^a ~m^b D_b m_a )
qlm_npepsilon(i,j,hn) = 0
qlm_npgamma (i,j,hn) = 0
qlm_npbeta (i,j,hn) = 0
qlm_npalpha (i,j,hn) = 0
! pi = ~m^a l^b D_b n_a
! nu = ~m^a n^b D_b n_a
! mu = ~m^a m^b D_b n_a
! lambda = ~m^a ~m^b D_b n_a
qlm_nppi (i,j,hn) = 0
qlm_npnu (i,j,hn) = 0
qlm_npmu (i,j,hn) = 0
qlm_nplambda (i,j,hn) = 0
!!$ qlm_lie_l_npsigma(i,j,hn) = 0
!!$ qlm_lie_n_npsigma(i,j,hn) = 0
!!$ ! Theta is the expansion
!!$ ! Theta_(l) is (- 2 Re rho)
!!$ ! Theta_(n) is (+ 2 Re mu)
!!$ ! Theta_(T) is [Theta_(l) + Theta_(n)] / sqrt(2)
!!$ ! Theta_(S) is [Theta_(l) - Theta_(n)] / sqrt(2)
!!$ qlm_lie_l_theta_l(i,j,hn) = 0
!!$ qlm_lie_l_theta_n(i,j,hn) = 0
!!$ qlm_lie_n_theta_l(i,j,hn) = 0
!!$ qlm_lie_n_theta_n(i,j,hn) = 0
do a=0,3
do b=0,3
qlm_npkappa (i,j,hn) = qlm_npkappa (i,j,hn) - mm(a) * ll(b) * nabla_ll(a,b)
qlm_nptau (i,j,hn) = qlm_nptau (i,j,hn) - mm(a) * nn(b) * nabla_ll(a,b)
qlm_npsigma (i,j,hn) = qlm_npsigma (i,j,hn) - mm(a) * mm(b) * nabla_ll(a,b)
qlm_nprho (i,j,hn) = qlm_nprho (i,j,hn) - mm(a) * conjg(mm(b)) * nabla_ll(a,b)
qlm_npepsilon(i,j,hn) = qlm_npepsilon(i,j,hn) - half * (nn(a) * ll(b) * nabla_ll(a,b) - conjg(mm(a)) * ll(b) * nabla_mm(a,b))
qlm_npgamma (i,j,hn) = qlm_npgamma (i,j,hn) - half * (nn(a) * nn(b) * nabla_ll(a,b) - conjg(mm(a)) * nn(b) * nabla_mm(a,b))
qlm_npbeta (i,j,hn) = qlm_npbeta (i,j,hn) - half * (nn(a) * mm(b) * nabla_ll(a,b) - conjg(mm(a)) * mm(b) * nabla_mm(a,b))
qlm_npalpha (i,j,hn) = qlm_npalpha (i,j,hn) - half * (nn(a) * conjg(mm(b)) * nabla_ll(a,b) - conjg(mm(a)) * conjg(mm(b)) * nabla_mm(a,b))
qlm_nppi (i,j,hn) = qlm_nppi (i,j,hn) + conjg(mm(a)) * ll(b) * nabla_nn(a,b)
qlm_npnu (i,j,hn) = qlm_npnu (i,j,hn) + conjg(mm(a)) * nn(b) * nabla_nn(a,b)
qlm_npmu (i,j,hn) = qlm_npmu (i,j,hn) + conjg(mm(a)) * mm(b) * nabla_nn(a,b)
qlm_nplambda (i,j,hn) = qlm_nplambda (i,j,hn) + conjg(mm(a)) * conjg(mm(b)) * nabla_nn(a,b)
end do
end do
end do
end do
call set_boundary (CCTK_PASS_FTOF, hn, qlm_npkappa (:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_nptau (:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_npsigma (:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_nprho (:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_npepsilon(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_npgamma (:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_npbeta (:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_npalpha (:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_nppi (:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_npnu (:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_npmu (:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_nplambda (:,:,hn), +1)
end subroutine qlm_calc_newman_penrose
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