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 $C^3$.
Publié le : 2006-03-14
Classification:
Lorentzian manifold,
transition from big crunch to big bang,
cyclic universe,
general relativity,
inverse mean curvature flow,
ARW spacetimes,
35J60,
53C21,
53C44,
53C50,
58J05
@article{1175797479,
author = {Gerhardt, Claus},
title = {The Inverse Mean Curvature Flow in Robertson-Walker Spaces and its Application},
journal = {Methods Appl. Anal.},
volume = {13},
number = {1},
year = {2006},
pages = { 19-28},
language = {en},
url = {http://dml.mathdoc.fr/item/1175797479}
}
Gerhardt, Claus. The Inverse Mean Curvature Flow in Robertson-Walker Spaces and its Application. Methods Appl. Anal., Tome 13 (2006) no. 1, pp. 19-28. http://gdmltest.u-ga.fr/item/1175797479/