Book by Cox, J. T., Dawson, Donald Andrew, Greven, Andreas, Groah, Jeff, Temple, Blake

Mutually Catalytic Super Branching Random Walks: Large Finite Systems And Renormalization Analysis;Memoirs of the American Mathematical Society

Science & Math

Groah, Jeff

Temple, Blake

Cox, J. T.

Dawson, Donald Andrew

Greven, Andreas

Mathematics

Amer Mathematical Society

We demonstrate the consistency of the Einstein equations 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 total 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 $p=\sigma^2\rho$, $\sigma\equiv const$.

Shock-Wave Solutions Of The Einstein Equations With Perfect Fluid Sources: Existence And Consistency By A Locally Inertial Glimm Scheme (Memoirs of the American Mathematical Society)

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