When is spacetime homogenous and isotropic?
For example, some metric $g_{\mu \nu}$ is homogeneous and isotropic. We now construct effective metric
$$n_{\mu \nu} ~\rightarrow~ g_{\mu \nu} + f(x^\mu)v_\mu v_\nu.$$
where $v_\mu$ is 4-vector, and $f$ is scalar. Is the effective metric $n_{\mu \nu}$ homogeneous and isotropic as well?
\thetaresults $\theta$,\omegainserts $\omega$, etc. It's quite interesting. You can revise your post if you can ;-) – Waffle's Crazy Peanut Apr 19 '13 at 13:18