This has come up in a few threads that I have participated in, so it seems convenient to post here for reference some general equations relating to the metric and the Einstein Field Equation for static, spherically symmetric spacetimes.

First, we are talking about spacetimes which can be described by the following line element, written in standard Schwarzschild coordinates (i.e., coordinates in which a 2-sphere at radial coordinate [itex]r[/itex] has area [itex]4 \pi r^2[/itex]):...