The inverse mean curvature flow in ARW spaces--transition from big crunch to big bang
| dc.creator | Gerhardt, Claus | |
| dc.date | 2004-03-29 | |
| dc.date | 2004-03-30 | |
| dc.date.accessioned | 2026-07-07T05:06:50Z | |
| dc.date.available | 2026-07-07T05:06:50Z | |
| dc.description | 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 $\hat N$ 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.description | 39 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.identifier | https://arxiv.org/abs/math/0403485 | |
| dc.identifier | http://arxiv.org/abs/math/0403485 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70626 | |
| dc.subject | Differential Geometry | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | [2000]{35J60, 53C21, 53C44, 53C50, 58J05} | |
| dc.title | The inverse mean curvature flow in ARW spaces--transition from big crunch to big bang | |
| dc.type | text |