(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A space-time has metric [tex] ds^2=-dt^2+R^2(dx^2+dy^2+dz^2) [/tex], where R is a function of t only. Assume that the space-time is filled with an ideal gas, with energy-momentum tensor [tex]T_{\mu\nu} = pg_{\mu\nu}+ (p+\rho)u_{\mu}u_{\nu}[/tex], where u is the four-vector of gas particles vector, and p and [tex]\rho[/tex] are functions of t. If [tex]R(t) = \sqrt{t/t_0}[/tex] where t_0 is a constant, prove that p = [tex]\rho[/tex] /3.

3. The attempt at a solution

I can only show this when the second derivative of R is zero. What should I do to prove this under the circumstances described in the problem statement?

Thanks,

AB

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# Homework Help: P=(\rho)/3 in the RW universe

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