Memoirs of the American Mathematical Society 2004; 84 pp; softcover Volume: 172 ISBN10: 082183553X ISBN13: 9780821835531 List Price: US$57 Individual Members: US$34.20 Institutional Members: US$45.60 Order Code: MEMO/172/813
 We demonstrate the consistency of the Einstein equations at the level of shockwaves 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 \(p=\sigma^2\rho\), \(\sigma\equiv const\). We demonstrate the consistency of the Einstein equations at the level of shockwaves 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 \(p=\sigma^2\rho\), \(\sigma\equiv const\). Readership Graduate students and research mathematicians interested in partial differential equations, relativity, and gravitational theory. Table of Contents  Introduction
 Preliminaries
 The fractional step scheme
 The Riemann problem step
 The ODE step
 Estimates for the ODE step
 Analysis of the approximate solutions
 The elimination of assumptions
 Convergence
