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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
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Topic revision: r1 - 04 Mar 2011, BoudRoukema
 
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