# (Scalar) Ricci flatness of a metric

What is the physical meaning to vanishing Ricci scalar $R=0$ of a metric in general relativity? Note that this is not the same questions as the geometric meaning of $R_{\mu\nu}=0$ which has been asked before.

• First sentence correct, but your last sentence is only true for two dimensions, when the scalar curvature wholly defines the Ricci tensor. But in higher dimensions a nonzero Ricci tensor can have zero trace (and the OP was at pains to state he/she wasn't asking about $R_{\mu\,\nu}=0$). Admittedly, the case of two dimensions is quite an important one historically and conceptually and fun to think about too. You could add a little detail to your first sentence, which, although perfectly true, is a little dense for someone coming across this notion for the first time. – Selene Routley Nov 23 '16 at 11:37