High frequency solutions in general relativity and the Burnett’s conjecture

Abstract: In this talk, I will review some works in collaboration with Jonathan Luk on the behaviour of high frequency solutions to the Einstein equations. In the eighties, the physicist Burnett conjectured that the adherence of the solutions to the Einstein equations, converging strongly at the level of the metric, and with boudedness assumptions at the level of derivative of the metric, are the solutions to the Einstein-massless Vlasov equations. I will focus on the resolution of this conjecture with the additionnal assumption of a translation symmetry, and explain how to approximate a solution to the Einstein-Vlasov equations by vacuum solutions.

general relativity and quantum cosmologymathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

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.