Null geometry and applications to existence of spacetimes

Abstract: Non-null hypersurfaces can be easily viewed as geometric objects detached from the spacetime where they are embedded. This process of "detachment" is more complicated in the case of null hypersurfaces. In this talk I will introduce the notion of "null manifold", together with related concepts such as "ruled null manifold" or "metric hypersurface data", as a way to study null hypersurfaces from a fully detached point of view. With this framework at hand, I will then discuss three applications related to existence of spacetimes. Specifically, I will present a detached version of the characteristic initial value problem, a general analysis of transverse expansions across a null hypersurface and an existence and asymptotic uniqueness result of $\Lambda$-vacuum spacetimes from data on a (detached) non-degenerate Killing horizon. The three applications are joint work with Gabriel Sánchez Pérez.

general relativity and quantum cosmologymathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

Comments: will be streamed from the GAPs conference at IMAG www.birs.ca/events/2025/5-day-workshops/25w5397

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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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