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On the structure and strength of singularities: Inextendibility results for Lorentzian manifolds

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If you have a question about this talk, please contact Renato Velozo.

Given a solution of the Einstein equations a fundamental question is whether one can extend the solution or whether the solution is maximal. If the solution is inextendible in a certain regularity class due to the geometry becoming singular, a further question is whether the strength of the singularity is such that it terminates classical time-evolution.

In this talk we give an overview of low-regularity inextendibility results for Lorentzian manifolds. We briefly recall the obstructions to continuous extensions of the Minkowski and Schwarzschild spacetimes and then discuss new results showing the locally Lipschitz inextendibility of FLRW models with particle horizons and spherically symmetric weak null singularities. The latter in particular apply to the spherically symmetric spacetimes constructed by Luk and Oh, improving their C^2-formulation of strong cosmic censorship to a locally Lipschitz formulation.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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