Radiation from a D-dimensional collision of shock waves: first order perturbation theory

TL;DR

This paper develops a perturbative method to analyze gravitational radiation from head-on shock wave collisions in D-dimensional spacetime, quantifying energy emission and waveforms across dimensions.

Contribution

It introduces a first-order perturbation framework for D-dimensional shock wave collisions and calculates gravitational wave energy emission, extending previous 4D results to higher dimensions.

Findings

In 4D, 25% of energy emitted as gravitational waves.

Energy emission increases with dimension, reaching 40% in D=10.

Waveforms and physical interpretation of peaks are provided.

Abstract

We study the spacetime obtained by superimposing two equal Aichelburg-Sexl shock waves in D dimensions traveling, head-on, in opposite directions. Considering the collision in a boosted frame, one shock becomes stronger than the other, and a perturbative framework to compute the metric in the future of the collision is setup. The geometry is given, in first order perturbation theory, as an integral solution, in terms of initial data on the null surface where the strong shock has support. We then extract the radiation emitted in the collision by using a D-dimensional generalisation of the Landau-Lifschitz pseudo-tensor and compute the percentage of the initial centre of mass energy epsilon emitted as gravitational waves. In D=4 we find epsilon=25.0%, in agreement with the result of D'Eath and Payne. As D increases, this percentage increases monotonically, reaching 40.0% in D=10. Our result is always within the bound obtained from apparent horizons by Penrose, in D=4, yielding 29.3%, and Eardley and Giddings, in D> 4, which also increases monotonically with dimension, reaching 41.2% in D=10. We also present the wave forms and provide a physical interpretation for the observed peaks, in terms of the null generators of the shocks.