Methods and Applications of Analysis

Volume 13 (2006)

Number 1

The Inverse Mean Curvature Flow in Robertson-Walker Spaces and its Application

Pages: 19 – 28

DOI: http://dx.doi.org/10.4310/MAA.2006.v13.n1.a2

Author

Claus Gerhardt

Abstract

We consider the inverse mean curvature flow in Robertson-Walker spacetimes that satisfy the Einstein equations and have a big crunch singularity and prove that under natural conditions the rescaled inverse mean curvature flow provides a smooth transition from big crunch to big bang. We also construct an example showing that in general the transition flow is only of class $C^3$.

Keywords

Lorentzian manifold; transition from big crunch to big bang; cyclic universe; general relativity; inverse mean curvature flow; ARW spacetimes

2010 Mathematics Subject Classification

35J60, 53C21, 53C44, 53C50, 58J05

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