The Einstein-Euler system with a physical vacuum boundary in spherical symmetry.

We establish local well-posedness for the Einstein-Euler system with a physical vacuum boundary in spherical symmetry. Our proof relies on a new way of thinking about Einstein’s equations in spherical symmetry that is well-adapted to the fluid’s characteristics on the free boundary. We also exploit the Einstein constraint

equations in spherical symmetry in a new way, as a tool to understand the

evolution problem. This is joint work with Jared Speck.