Mathematical Physics: I am trying to peel away what are the minimal requirements to get GR in an unique way, similar to how this is done in category theory and I am wondering I have heard that if you demand 3 things, that all curvature, ie acceleration (without Electromagnetism, etc.) is gravity and vice versa(Equivalence Principle), Mach Principle, the distribution of mass is what controls this curvature, and that the Hilbert action be preserved you get General Relativity.
So I am asking, what would be the action, corresponding Lie Group and geometry if there is no c? Ie, no speed that is fixed under the Lie Group? Let's call this GR without c, GRnc for short
If you take this group and you modify it, maybe some kind of compactification, a way to treat an infinite speed as a finite one, do you get back GR? How would black holes look like then? if you take GRnc and insert and object of infinite energy density? Or rather how do this black holes look like?
