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29 March 2024
 
  » arxiv » math.DG/0403485

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The inverse mean curvature flow in ARW spaces--transition from big crunch to big bang
Claus Gerhardt ;
Date 29 Mar 2004
Subject Differential Geometry MSC-class: [2000]{35J60, 53C21, 53C44, 53C50, 58J05} | math.DG gr-qc hep-th
AbstractWe 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 $hat N$ by switching the light cone and using reflection to define a new time function, such that the two spacetimes $N$ and $hat N$ 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 $hat N$ is a big bang. The inverse mean curvature flows in $N$ esp $hat N$ correspond to each other via reflection. Furthermore, the properly rescaled flow in $N$ has a natural smooth extension of class $C^3$ across the singularity into $hat N$. With respect to this natural, globally defined diffeomorphism we speak of a transition from big crunch to big bang.
Source arXiv, math.DG/0403485
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