Use the metic that Einstein proposed in the first cosmological model based on general relativity.(adsbygoogle = window.adsbygoogle || []).push({});

ds^{2}= -dt^{2}+ (dr^{2}) / (1 - Kr^{2}) + r^{2}(dθ^{2}+ sin^{2}θd[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 p_{m}<< ρ_{m}) and vaccum energy (denoted by subscript v, with p_{v}= -ρ_{v}), what is the ratio of ρ_{v}/ ρ_{m}?

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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# Tensor calculus for general relativity question.

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