Speaker
Description
The talk introduces a framework for studying the geometry of lightlike (null) hypersurfaces in spacetimes that may be singular or lack a smooth structure. Building on tools from optimal transport and modern Lorentzian geometry, we develop a flexible, synthetic approach to describing such hypersurfaces without relying on the usual smoothness assumptions.
Within this framework, we propose a synthetic formulation of the Null Energy Condition, a fundamental principle in general relativity governing how matter and energy influence the geometry and causal structure of spacetime. This condition plays a central role in Penrose's singularity theorem, which predicts the formation of spacetime singularities associated with gravitational collapse and was recognized by the 2020 Nobel Prize in Physics. It is also a key ingredient in Hawking's area theorem, which provides one of the foundations of black hole thermodynamics.
Joint work with Fabio Cavalletti (Milan) and Davide Manini (Vienna).