00001 subroutine kerr_schild_metric_3plus1(x,y,z,psi,alph,bvu,bvd,hijd,hiju)
00002 use phys_constant, only : long
00003 implicit none
00004 real(long) :: psi, alph, bvu(3), bvd(3), hijd(3,3), hiju(3,3)
00005 real(long) :: x, y, z, r, lvu(0:3), lvd(0:3), H
00006 real(long) :: Hp1, H1pH, pp4, pm4, fij(3,3)
00007
00008 call kerr_schild_r_lv_home(x,y,z,r,lvu,lvd,H)
00009 Hp1 = 1.0d0 + H
00010 H1pH = H/Hp1
00011
00012 psi = Hp1**(1.0d0/12.0d0)
00013 alph = 1.0d0/sqrt(Hp1)
00014
00015 pp4 = Hp1**(1.0d0/3.0d0)
00016 pm4 = 1.0d0/pp4
00017
00018 bvu(1:3) = H1pH *lvu(1:3)
00019 bvd(1:3) = pm4*H*lvd(1:3)
00020
00021 fij(1:3,1:3) = 0.0d0
00022 fij(1,1) = 1.0d0 ; fij(2,2) = 1.0d0 ; fij(3,3) = 1.0d0
00023 hijd(1:3,1) = pm4*(fij(1:3,1) + H*lvd(1:3)*lvd(1)) - fij(1:3,1)
00024 hijd(1:3,2) = pm4*(fij(1:3,2) + H*lvd(1:3)*lvd(2)) - fij(1:3,2)
00025 hijd(1:3,3) = pm4*(fij(1:3,3) + H*lvd(1:3)*lvd(3)) - fij(1:3,3)
00026 hiju(1:3,1) = pp4*(fij(1:3,1) - H1pH*lvu(1:3)*lvu(1)) - fij(1:3,1)
00027 hiju(1:3,2) = pp4*(fij(1:3,2) - H1pH*lvu(1:3)*lvu(2)) - fij(1:3,2)
00028 hiju(1:3,3) = pp4*(fij(1:3,3) - H1pH*lvu(1:3)*lvu(3)) - fij(1:3,3)
00029
00030 end subroutine kerr_schild_metric_3plus1
