The stress-energy tensor is usually defined in standard GR treatments as(adsbygoogle = window.adsbygoogle || []).push({});

[tex]T_{\mu\nu} = -\frac{2}{\sqrt{-g}}\frac{\delta(\sqrt{g}L_m)}{\delta g^{\mu\nu}})[/tex]

with the L_{m}the matter Lagrangian.

I'm curious what L_{m}is for a perfect fluid with density ρ and pressure P that would lead to the standard stress-energy tensor

[tex]T_{\mu\nu} = (\rho+P)u^\mu u^\nu + Pg_{\mu\nu}[/tex]

in an FRW metric.

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# Matter Lagrangian for perfect fluid

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