The Inverse Mean Curvature Flow in Arw Spaces—transition from Big Crunch to Big Bang

We consider spacetimes N satisfying some structural conditions, which are still fairly general, and prove convergence results for the leaves of an inverse mean curvature flow. Moreover, we define a new spacetime N̂ by switching the light cone and using reflection to define a new time function, such that the two spacetimes N and N̂ can be pasted together to yield a smooth manifold having a metric singularity, which, when viewed from the region N is a big crunch, and when viewed from N̂ is a big bang. The inverse mean curvature flows in N resp. N̂ correspond to each other via reflection. Furthermore, the properly rescaled flow in N has a natural smooth extension of class C across the singularity into N̂ . With respect to this natural, globally defined diffeomorphism we speak of a transition from big crunch to big bang.