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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|Advisor:||Temple, John Blake|
|Commitee:||Cheer, Angela, Hunter, John|
|School:||University of California, Davis|
|School Location:||United States -- California|
|Source:||DAI-B 71/06, Dissertation Abstracts International|
|Keywords:||Conservation laws, Godunov method, Numerical PDE's, Numerical general relativity, Time dilation|
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