Radiation from a D-dimensional collision of shock waves: numerical methods

TL;DR

This paper introduces numerical and perturbative methods for analyzing gravitational radiation resulting from the collision of shock waves in higher-dimensional spacetimes, providing detailed setup, solution techniques, and initial results.

Contribution

It offers a pedagogical framework combining perturbative and numerical approaches for D-dimensional shock wave collisions, including radiation extraction methods.

Findings

Development of numerical strategies for integral solutions

Initial results on gravitational radiation emission

Methodological insights for higher-dimensional shock collisions

Abstract

We present a pedagogical introduction to the problem of evolving a head on collision of two Aichelburg-Sexl gravitational shock waves in D-dimensions, using perturbative techniques. We follow a constructive approach with examples, going in some detail through: the set up of the exact initial conditions and their properties; perturbative methods in flat space-time with Green function solutions; and numerical strategies to evaluate the integral solutions. We also discuss, briefly, radiation extraction methods adapted to this problem, together with some of the results for this system.