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with maxima
/* FLRW metric: (c) CC-BY-SA B. Roukema (2011) */
load(ctensor);
init_ctensor();
csetup();
4;
y;
[t,r,theta,phi];
1;
1;
-c^2 ; /* t */
a^2 / (1 -k*r^2) ; /* r */
a^2 * r^2 ; /* theta */
a^2 * r^2 * (cos(theta))^2; /* phi */
/* Enter functional dependencies with the DEPENDS function or 'N' if none */
/* e.g. depends([a,d],x); */
/* depends([a],t); */
depends([a],t);
y;
christof(mcs); /* 2nd kind i.e. Gamma^i_j_k is enough */
einstein(true); /* "mixed" means e.g. G_a^b */
c^2 * ein[1,1] = c^2 * 8* %pi * G /c^4 * (- rho *c^2);
c^2 * ein[2,2] - lhs(%) = c^2 * 8* %pi * G /c^4 * p - rhs(%), sumfactor;
--
BoudRoukema - 04 Mar 2011