diff options
Diffstat (limited to 'setup.mac')
| -rw-r--r-- | setup.mac | 34 |
1 files changed, 22 insertions, 12 deletions
@@ -78,18 +78,6 @@ uh_AB[4,4] : exp(2*γ)*sin(θ)^-2$ uh_AB[3,4] : 0$ uh_AB[4,3] : 0$ -/* 2-sphere metric */ -q_AB[3,3] : 1$ -q_AB[4,4] : sin(θ)^2$ -q_AB[3,4] : 0$ -q_AB[4,3] : 0$ - -/* 2-sphere inverse metric */ -uq_AB[3,3] : 1$ -uq_AB[4,4] : sin(θ)^-2$ -uq_AB[3,4] : 0$ -uq_AB[4,3] : 0$ - /* Christoffel symbols of 2-sphere */ for i : 3 thru 4 do for j : 3 thru 4 do for k : 3 thru 4 do ( h_mcs[i, j, k] : sum(uh_AB[k,C]*( @@ -111,4 +99,26 @@ for i : 3 thru 4 do for j : 3 thru 4 do ( /* Ricci scalar of 2-sphere */ h_ric_s : expand(sum(sum(uh_AB[i,j]*h_ric[i,j], i, 3, 4), j, 3, 4)); + +/* 2-sphere */ + +/* 2-sphere metric */ +q_AB[3,3] : 1$ +q_AB[4,4] : sin(θ)^2$ +q_AB[3,4] : 0$ +q_AB[4,3] : 0$ + +/* 2-sphere inverse metric */ +uq_AB[3,3] : 1$ +uq_AB[4,4] : sin(θ)^-2$ +uq_AB[3,4] : 0$ +uq_AB[4,3] : 0$ + +/* Christoffel symbols of 2-sphere */ +for i : 3 thru 4 do for j : 3 thru 4 do for k : 3 thru 4 do ( + q_mcs[i, j, k] : sum(uq_AB[k,C]*( + cdiff(q_AB[j, C], i) + + cdiff(q_AB[i, C], j) + + cdiff(q_AB[i, j], C))/2, C, 3, 4)); + print("Setup done!"); |