Department of Mathematics

This talk will discuss a recent paper by Blake Temple and me in which we demonstrate existence and consistency at the level of shock-waves by proving the existence of shock-wave solutions of the spherically symmetric Einstein equations for a perfect fluid, starting from initial density and velocity profiles that are only locally of bounded variation. For these solutions, the components of the gravitational metric tensor are only Lipschitz continuous at shock-waves, and so it follows that these solutions satisfy the Einstein equations, as well as the relativistic compressible Euler equations, only in the weak sense of the theory of distributions. The analysis introduces a locally inertial Glimm scheme that exploits the locally flat character of spacetime, and relies on special properties of the relativistic compressible Euler equations when $p=\sigma^{2}\rho$, $\sigma\equiv const$.