2004/03/29 by Claus Gerhardt, Gerhardt, Claus · 1 citation
Mathematics · Physics and Astronomy · #53C21 #53C44 #53C50 #58J05} #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th) #[2000]{35J60 #gr-qc #hep-th #math.DG #msc:53C21 #msc:53C44 #msc:53C50
paper · pdf · doi:10.48550/arxiv.math/0403485
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
openalex publication_date 2004/03/29 · arxiv created 2004/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 N by switching the light cone and using reflection to define a new time function, such that the two spacetimes N and 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 N is a big bang. The inverse mean curvature flows in N \resp N correspond to each other via reflection. Furthermore, the properly rescaled flow in N has a natural smooth extension of class C3 across the singularity into N. With respect to this natural, globally defined diffeomorphism we speak of a transition from big crunch to big bang.