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Singularity Theorems with an emphasis on the interplay of low regularity and energy conditions.

The presented thesis aims to give a biased overview of the singularity theorems in general relativity. It will emphasise in particular the interplay between low regularity spacetimes (that is for us mostly \(C^1\)) and the formulation of physically reasonable energy conditions. Nevertheless it tries to give a mostly self-contained proof for the classical singularity theorems by R.Penrose and S.W.Hawking. Those results will then lie the foundation on which we will explore some possible generalizations. While generalizations of the energy conditions can be formulated quite directly, to handle low regularity we will need to introduce new tools. In particular we will give a brief overview of distributions on manifolds which allows us to construct the Ricci-tensor even in \(C^1\)-spacetimes. This distributional language will then provide a natural formulation of some important prior discussed energy conditions. Finally we aim to formulate a \(C^1\)-singularity theorem assuming only a weakened distributional strong energy condition.

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Year: 2020

Author : Jonas von Berg

Gabriele Benedetti, Matthias Bartelmann