Explain how our indices differ from Wald.

Add (disabled) code that uses Wald's index convention.


git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinUtils/TGRtensor/trunk@28 b716e942-a2de-43ad-8f52-f3dfe468e4e7

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