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

Abstract

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.

References in corpus (3)

• Ultrarelativistic fluid dynamics
• On the dynamics of relativistic multi-layer spherical shell systems
• A Proof of Convergence for Numerical Approximations Generated by the Locally Inertial Godunov Method in General Relativity

Cited by in corpus (3)

• A direct Eulerian GRP scheme for spherically symmetric general relativistic hydrodynamics
• No Regularity Singularities Exist at Points of General Relativistic Shock Wave Interaction between Shocks from Different Characteristic Families
• Points of General Relativisitic Shock Wave Interaction are "Regularity Singularities" where Spacetime is Not Locally Flat