Ricci tensor in FRW metrics

1. Jan 26, 2013

Hi does anyone know a formal definition for why off diagonal ricci tensors are equal to zero in a symmetric standard FRW metric?

2. Jan 26, 2013

bcrowell

Staff Emeritus
Is this in a particular set of coordinates?

3. Jan 26, 2013

I think it follows from symmetry. For instance, $R_{\theta t}$ flips signs under a change of coordinates $\theta\rightarrow \pi-\theta$, so if it was nonzero it would violate isotropy. Under the same transformation $R_{\theta\theta}$ stays the same.