# Shock-Wave Solutions of the Einstein Equations with Perfect Fluid Sources: Existence and Consistency by a Locally Inertial Glimm Scheme

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$50.00 Seller since 2007 Feedback rating: (441) Condition: New — never opened or used in original packaging. Like New — packaging may have been opened. A "Like New" item is suitable to give as a gift. Very Good — may have minor signs of wear on packaging but item works perfectly and has no damage. Good — item is in good condition but packaging may have signs of shelf wear/aging or torn packaging. All specific defects should be noted in the Comments section associated with each item. Acceptable — item is in working order but may show signs of wear such as scratches or torn packaging. All specific defects should be noted in the Comments section associated with each item. Used — An item that has been opened and may show signs of wear. All specific defects should be noted in the Comments section associated with each item. Refurbished — A used item that has been renewed or updated and verified to be in proper working condition. Not necessarily completed by the original manufacturer. New Brand new. We distribute directly for the publisher. We demonstrate the consistency of the Einstein equations at the level of shock-waves by proving the existence of shock wave ... solutions of the spherically symmetric Einstein equations for a perfect fluid, starting from initial density and velocity profiles that are only locally of bounded total variation. For these solutions, the components of the gravitational metric tensor are only Lipschitz continuous at shock waves, and so it follows that these solutions satisfy the Einstein equations, as well as the relativistic compressible Euler equations, only in the weak sense of the theory of distributions. The analysis introduces a locally inertial Glimm scheme that exploits the locally flat character of spacetime, and relies on special properties of the relativistic compressible Euler equations when$p=\sigma^2\rho$,$\sigma\equiv const$.We demonstrate the consistency of the Einstein equations at the level of shock-waves by proving the existence of shock wave solutions of the spherically symmetric Einstein equations for a perfect fluid, starting from initial density and velocity profiles that are only locally of bounded total variation. For these solutions, the components of the gravitational metric tensor are only Lipschitz continuous at shock waves, and so it follows that these solutions satisfy the Einstein equations, as well as the relativistic compressible Euler equations, only in the weak sense of the theory of distributions. The analysis introduces a locally inertial Glimm scheme that exploits the locally flat character of spacetime, and relies on special properties of the relativistic compressible Euler equations when$p=\sigma^2\rho$,$\sigma\equiv const$. Read more Show Less Ships from: Boonsboro, MD Usually ships in 1-2 business days • Canadian • International • Standard, 48 States • Standard (AK, HI) • Express, 48 States • Express (AK, HI)$132.35
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### Overview

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 $p=\sigma^2\rho$, $\sigma\equiv const$. 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 $p=\sigma^2\rho$, $\sigma\equiv const$.

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