Abstract

In General Relativity, an impulsive gravitational wave is an idealisation of gravitational waves produced by a strongly gravitating source. In the presence of multiple sources, the impulsive waves eventually interact, and it is interesting to study this interaction. From the perspectives of PDEs, impulsive gravitational waves are low regularity solutions of the Einstein equations, seen as a system of non-linear wave equations; thus even well-posedness of the initial value problem is not clear a priori.

Tremendous progress has been recently made in the understanding of low regularity solutions of the Einstein equations. It is remarkable that similar techniques can be applied to very different problems, such as the formation of Black Holes, the behaviour of high-frequency space-times or the interaction of impulsive gravitational waves.

In this talk, I will survey several low-regularity physical phenomena and explain the underlying techniques from the perspective of PDEs. I will then discuss impulsive gravitational waves and present a new local existence result for solutions featuring three gravitational waves or more.

The talk will mainly emphasise PDE -related aspects, and no prior exposure to General Relativity will be assumed. This is joint work with Jonathan Luk.