Hi I'm new to this so please don't butcher me. I am just a enthusiastic individual with a huge interest in theoretical physics. In GR, the Einstein field equations relate energy and momentum (I think) to curvature, then to local flat geometry (I think) my question is do the EFEs physically describe something (ie: a rotating spherical object like earth or a large nebula etc...) or are they a purely mathematical tool used to describe local geometry in relation to energy and momentum. I know the geodesic equation is needed to explain the "force" of gravity which results, i'm just wondering if they also to describe the topology as well. I have always found this confusing, and can not seem to get a clear answer on it, thanks to anyone would cold help.