diff options
Diffstat (limited to 'src/ricci4.F90')
| -rw-r--r-- | src/ricci4.F90 | 37 |
1 files changed, 36 insertions, 1 deletions
diff --git a/src/ricci4.F90 b/src/ricci4.F90 index ac3ad3a..162817a 100644 --- a/src/ricci4.F90 +++ b/src/ricci4.F90 @@ -98,9 +98,13 @@ contains CCTK_REAL :: nrm, cnt #endif integer :: i,j,k,l,m - ! R^i_jkl = Gamma^i_jl,k - Gamma^i_jk,l +#if 1 + ! R^i_jkl = + Gamma^i_jl,k - Gamma^i_jk,l ! + Gamma^m_jl Gamma^i_mk - Gamma^m_jk Gamma^i_ml ! (Wald, 3.4, eqn. (3.4.4), p. 48) + ! Note that Wald writes R_lkj^i, i.e., we have the order of the + ! indices exactly reversed. Due to the Riemann tensor's various + ! symmetries, this does not change anything. do i=1,4 do j=1,4 do k=1,4 @@ -127,6 +131,37 @@ contains end do end do end do +#else + ! R_ijk^l = + Gamma^l_ik,j - Gamma^l_jk,i + ! + Gamma^m_ik Gamma^l_mj - Gamma^m_jk Gamma^l_mi + ! (Wald, 3.4, eqn. (3.4.4), p. 48) + do i=1,4 + do j=1,4 + do k=1,4 + do l=1,4 + rmu(i,j,k,l) = + dgamma(l,i,k,j) - dgamma(l,j,k,i) + do m=1,4 + rmu(i,j,k,l) = rmu(i,j,k,l) & + + gamma(m,i,k) * gamma(l,m,j) & + - gamma(m,j,k) * gamma(l,m,i) + end do + end do + end do + end do + end do + do i=1,4 + do j=1,4 + do k=1,4 + do l=1,4 + rm(i,j,k,l) = 0 + do m=1,4 + rm(i,j,k,l) = rm(i,j,k,l) + rmu(i,j,k,m) * gg(m,l) + end do + end do + end do + end do + end do +#endif #ifdef DEBUG ! check symmetries nrm = 0 |