Abstract:

In this talk, I hope to describe elements of proving a certain stable singularity formation result for the Einstein--Euler system which is the topic of work in progress with Jonathan Luk. I will first describe some of the motivating phenomena and what this singularity formation result has to do with shocks in gas dynamics. Then, I will describe some of the main mathematical difficulties that arise when studying the formation of shocks outside of symmetry for gas dynamics in general. I hope to end with some of the main difficulties in the case of Einstein--Euler which arise from the fact that the speed of sound is less than the speed of light.