- #1
ramparts
- 45
- 0
The stress-energy tensor is usually defined in standard GR treatments as
[tex]T_{\mu\nu} = -\frac{2}{\sqrt{-g}}\frac{\delta(\sqrt{g}L_m)}{\delta g^{\mu\nu}})[/tex]
with the Lm the matter Lagrangian.
I'm curious what Lm 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.
[tex]T_{\mu\nu} = -\frac{2}{\sqrt{-g}}\frac{\delta(\sqrt{g}L_m)}{\delta g^{\mu\nu}})[/tex]
with the Lm the matter Lagrangian.
I'm curious what Lm 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.