BHI Colloquium


Monday, October 25, 2021, 11:00am to 12:00pm

Martin LeSourd (Mathematics) - BHI

Title: Extending beyond Cauchy horizons in Low Regularity

Abstract: In a spacetime that develops from initial data, there can come a point where the initial data no longer determines the spacetime. The boundary of the spacetime up to that point is called a ''Cauchy horizon''. Whether spacetimes that arise from generic (i.e., non-special) initial data produce Cauchy horizons, and, if they do, whether such spacetimes are extendible beyond their Cauchy horizons is the content of the famous conjecture of Strong Cosmic Censorship (the conjecture claims that they cannot be extended, at least in some given regularity class). In recent work with E.Minguzzi, we proved a theorem which describes what these Cauchy horizons imply for the global structure of the spacetime. Our methods accommodate the widest possible class of spacetimes under the purview of Strong Cosmic Censorship, and the result clarifies some questions posed four decades ago. It also leads to a new problem - a new conjecture ? - concerning the location of Cauchy horizons within black hole interiors. 

Bio: Martin Lesourd completed his undergraduate and graduate studies in Mathematics, Physics and Philosophy at (Trinity) Cambridge University and (Linacre) Oxford University.  He is a mathematician whose research lies in two disciplines: general relativity and geometric analysis. Broadly speaking, his aim is to better understand a space - this could be a spacetime (which contains a black hole for instance) or a Riemannian Manifold - by studying Partial Differential Equations that can be associated to that space. With regards to general relativity, he studies both the Einstein equations and the Constraint equations, and most recently has been trying to describe the formation of black holes from a purely mathematical standpoint.