Session S19 - Geometric and Analytic Aspects of General Relativity

Thursday, July 15, 17:00 ~ 18:00 UTC-3

Causality on coverings and the Gannon-Lee theorem

Ivan Costa e Silva

Federal University of Santa Catarina, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

A number of techniques in Lorentzian geometry, such as those used in the proofs of singularity theorems, depend on certain smooth coverings retaining interesting global geometric properties, including causal ones. We briefly review this prolem and give explicit examples showing that, unlike some of the more commonly adopted rungs of the causal ladder such as strong causality or global hyperbolicity, less-utilized conditions such as causal continuity or causal simplicity {\em do not} in general pass to coverings, as already speculated by E. Minguzzi. As a consequence, any result which relies on these causality conditions transferring to coverings must be revised accordingly. In particular, we show concrete applications of these ideas to the Gannon-Lee singularity theorem.

Joint work with Ettore Minguzzi (University of Florence, Italy).

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