Tensor calculus for general relativity question.

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Use the metic that Einstein proposed in the first cosmological model based on general relativity.

ds2 = -dt2 + (dr2) / (1 - Kr2) + r2(dθ2 + sin2θd[itex]\phi[/itex]2) where K > 0

Show that the stress energy tensor is that of a static, spatially uniform perfect fluid and determine ρ and p in terms of G and K. If the universe contains only cold matter (denoted by subscript m, with pm << ρm) and vaccum energy (denoted by subscript v, with pv = -ρv), what is the ratio of ρv / ρm?

could someone help me out? its something I've been working on for a while now and end up in some weird mess.
 
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stevendaryl
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Use the metic that Einstein proposed in the first cosmological model based on general relativity.

ds2 = -dt2 + (dr2) / (1 - Kr2) + r2(dθ2 + sin2θd[itex]\phi[/itex]2) where K > 0

Show that the stress energy tensor is that of a static, spatially uniform perfect fluid and determine ρ and p in terms of G and K. If the universe contains only cold matter (denoted by subscript m, with pm << ρm) and vaccum energy (denoted by subscript v, with pv = -ρv), what is the ratio of ρv / ρm?

could someone help me out? its something I've been working on for a while now and end up in some weird mess.
Every time I try to compute the curvature tensor, I end up with pages of mathematics that always has an error.
 
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which part do you get up to ?
 

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