Abstract:
(Smooth) Null hypersurfaces of spacetimes play a prevalent role in General Relativity, where they describe various kinds of horizons. When it comes to studying the geometry of null submanifolds in general, the degeneracy of the metric causes technical difficulties that must be properly addressed. The goal of the talk is to give an introduction to the geometry of null hypersurfaces and to develop the necessary tools to handle their degenerate structure. In particular, this will be applied by presenting a proof of the Penrose Incompleteness Theorem which makes heavy use of the structure of achronal boundaries. We will closely follow ideas by Prof. Dr. Gregory J. Galloway; see especially "https://www.math.miami.edu/~galloway/vienna-course-notes.pdf".
Null Geometry
31.10.2025 09:45 - 11:15
Organiser:
M. Kunzinger, R. Steinbauer
Location: