The Numerical Simulation of General Relativistic Shock Waves by a Locally Inertial Godunov Method Featuring Dynamical Time Dilation

摘要

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