Singularity theorems in low regularity

Abstract: The singularity theorems of R. Penrose and S. Hawking from the 1960s show that a spacetime satisfying certain physically reasonable curvature and causality conditions cannot be causal geodesically complete. Despite their great success these classical theorems still have some drawbacks, one of them being that they require smoothness of the metric while in many physical models the metric is less regular. In my talk I will present work on singularity theorems based on distributional energy conditions for metrics that are merely continuously differentiable – a regularity where one still has existence but not uniqueness for solutions of the geodesic equation. We will see that an approximation-based approach to the low-regularity issue is closely linked to establishing singularity theorems under weakened energy conditions and while the improvements necessary are still entirely straightforward in the present case, attempting to lower the regularity further would require some new methods.

general relativity and quantum cosmologymathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

( video )

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JoMaReC - Joint Online Mathematical Relativity Colloquium

Series comments: This monthly online colloquium is meant to be accessible to and informative for mathematicians and mathematical physicists with a background in General Relativity, widely interpreted to include Lorentzian Geometry, and Geometric Analysis of various Partial Differential Equations related to General Relativity.

It is aimed to present motivation and applications of particular results and/or introduce specific subfields, while refraining from too much technicalities.

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