Abstract: We extend a singularity theorem by Galloway & Ling for spacetimes with expanding Cauchy surface (positive definite second fundamental form) to those with positive semi-definite second fundamental form. Although a seemingly minor loss of restriction it allows for a broader topological class of spacetimes to be complete. Using results from the topological study of 3-manifolds, minimal surface theory as well as Penrose's classical singularity theorem, we will determine a connection between the topology of the Cauchy surfaces and the completeness of spacetime.
A topological rigidity result for Penrose's singularity theorem
13.12.2024 09:45 - 10:45
Organiser:
M. Kunzinger (U Wien), R. Steinbauer (U Wien)
Location: