2004/04/30 by Claus Gerhardt
Physics and Astronomy · Mathematics · #gr-qc #hep-th #math.DG
published as Adv.Theor.Math.Phys. 8 (2004) 319-343 · 20 pages, a pdf version can also be retrieved from http://www.math.uni-heidelberg.de/studinfo/gerhardt/brane.pdf and bibtex data from http://www.math.uni-heidelberg.de/studinfo/gerhardt/bibtexcgbrane.html, v5: the results of http://arXiv.org/abs/gr-qc/0404112 have been applied to ARW branes, the introduction has been rewritten, this is the final version that will appear in Adv. Theor. Math. Physics
We consider branes N=I×\so, where \so is an n\ndash dimensional space form, not necessarily compact, in a Schwarzschild-AdS(n+2) bulk \mc N. The branes have a big crunch singularity. If a brane is an ARW space, then, under certain conditions, there exists a smooth natural transition flow through the singularity to a reflected brane N, which has a big bang singularity and which can be viewed as a brane in a reflected Schwarzschild-AdS(n+2) bulk \mc N. The joint branes N\uu N can thus be naturally embedded in R2× \so, hence there exists a second possibility of defining a smooth transition from big crunch to big bang by requiring that N\uu N forms a C^∞-hypersurface in R2× \so. This last notion of a smooth transition also applies to branes that are not ARW spaces, allowing a wide range of possible equations of state.