The Numerical Simulation of General Relativistic Shock Waves by a Locally Inertial Godunov Method Featuring Dynamical Time Dilation
This work provides the first numerical simulation of general relativistic shock waves, addressing a fundamental problem in relativistic astrophysics for researchers studying gravitational collapse and explosions.
The authors introduce a locally inertial Godunov method with dynamical time dilation to simulate general relativistic shock waves, resolving secondary reflected waves in the Smoller-Temple model and indicating black hole formation from smooth initial data. This is the first numerical simulation of a fluid dynamical shock wave in general relativity.
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.