Numerical Analysis of a Canonical Shock Wave Interaction Problem in General Relativity
by Blake Temple   Zeke Vogler  

Vol. 11 No. 1 (2016) P.217~P.234

ABSTRACT

We present the analysis of convergence of the locally inertial Godunov method with dynamical time dilation applied to a canonical initial data set which is arguably the simplest initial data that creates a point of shock wave interaction in General Relativity. New applications include the analysis of convergence in the presence of new boundary conditions which enables one to test the validity of the Einstein constraint equations numerically in new Lipschitz continuous space-time metrics. The numerical method, introduced in [14, 15], is an algorithm for simulating general relativistic shock-waves in spherically symmetric spacetimes, and the analysis here rigorously establishes claims made in authors’ PRSA article [15].

KEYWORDS
General Relativity, Shock Wave Interactions, Numerical Relativity, Godunov Method, Locally Inertial.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 83C10, 76L05, 35L65, 32D20.

MILESTONES

Received: 2015-04-28
Revised : 2015-09-30
Accepted: 2015-10-01

Download Full Content