I was wondering if there is some kind of Einstein's field equation for orbifolds (say semi-Riemannian of Lorentz signature if this make sense).

Here, by an orbifold I mean the "stacky" quotient of, for example, a compact Lie group $G$ acting smoothly on a manifold $M$ and with finite stabilizers...hence the stacky quotient will be (the Morita equivalence class of) its translation (Lie) groupoid $[M\times G\rightrightarrows M]$, in contrast to the "coarse" orbit space $M/G$ which is an object with singularities.

For this kind of stacky objects there is a theory of connections and curvature for $S^1$-bundles (related with Maxwell's equations, I guess)...I´m just curious if there exist more "classical" notions of curvature which allow to state Einstein´s field equation in this context...of course, if this is the case it would be great to think about its meaning from the perspective of singularities as well.

This post imported from StackExchange MathOverflow at 2016-10-07 22:45 (UTC), posted by SE-user Enrique Becerra