Formation of shocks for the Einstein-Euler system

John Anderson, Stanford University
Fine Hall 314

In this talk, I hope to describe elements of proving stable shock formation for the Einstein-Euler system in the setting of potential flow. This involves proving that the fluid variables blow up in a specific way while the gravitational metric remains comparatively smooth. I'll first describe where this fits into the study of shocks, and why it is appropriate to call this singularity formation result a shock formation result. Then, I will go through some of the most important parts of Christodoulou's landmark proof of shock formation for potential flow on a fixed background, as well as followup breakthrough works by Luk-Speck allowing for vorticity. This will show the main difficulty present in proving that the gravitational metric remains comparatively smooth in the case of Einstien-Euler. It essentially arises from the fact that the speed of sound is less than the speed of light. In the remaining time, I will try to give the main idea in overcoming this difficulty.

This is work in progress with Jonathan Luk.