Dissertation/Thesis Abstract

The numerical simulation of general relativistic shock waves by a locally inertial Godunov method featuring dynamical time dilation
by Vogler, Zeke K., Ph.D., University of California, Davis, 2010, 151; 3404967
Abstract (Summary)

We introduce what we call a locally inertial Godunov method with dynamical time dilation, and use it to simulate a new one parameter family of general relativistic shock wave solutions of the Einstein equations for a perfect fluid. The forward time solutions resolve the secondary reflected wave (an incoming shock wave) in the Smoller-Temple shock wave model for an explosion into a static singular isothermal sphere. The backward time solutions indicate black hole formation from a smooth underlying solution via collapse associated with an incoming rarefaction wave. As far as we know, this is the first numerical simulation of a fluid dynamical shock wave in general relativity.

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Indexing (document details)
Advisor: Temple, John Blake
Commitee: Cheer, Angela, Hunter, John
School: University of California, Davis
Department: Applied Mathematics
School Location: United States -- California
Source: DAI-B 71/06, Dissertation Abstracts International
Subjects: Mathematics
Keywords: Conservation laws, Godunov method, Numerical PDE's, Numerical general relativity, Time dilation
Publication Number: 3404967
ISBN: 978-1-124-02655-8
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