The inverse mean curvature flow in ARW spaces--transition from big crunch to big bang

dc.creatorGerhardt, Claus
dc.date2004-03-29
dc.date2004-03-30
dc.date.accessioned2026-07-07T05:06:50Z
dc.date.available2026-07-07T05:06:50Z
dc.descriptionWe 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 $N$ \resp $\hat N$ 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.
dc.description39 pages, a pdf version can also be retrieved from http://www.math.uni-heidelberg.de/studinfo/gerhardt/imcf-arw.pdf and bibtex data from http://www.math.uni-heidelberg.de/studinfo/gerhardt/bibtexcgimcf-arw.html, v2: minor changes in Section 9: assumptions clarified
dc.identifierhttps://arxiv.org/abs/math/0403485
dc.identifierhttp://arxiv.org/abs/math/0403485
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70626
dc.subjectDifferential Geometry
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.subject[2000]{35J60, 53C21, 53C44, 53C50, 58J05}
dc.titleThe inverse mean curvature flow in ARW spaces--transition from big crunch to big bang
dc.typetext

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