Radiation from a D-dimensional collision of shock waves: a remarkably simple fit formula

TL;DR

This paper extends previous work on shock wave collisions in higher dimensions by deriving solutions for odd D and finds a simple, universal pattern for the radiated energy fraction, matching an analytic formula across multiple dimensions.

Contribution

It provides the first solution for odd D in shock wave collision energy radiation and reveals a simple pattern for the radiated energy fraction across dimensions.

Findings

Estimated radiated energy fraction matches 1/2 - 1/D for D=5,7,9,11.

Both the fit and horizon bound approach 1/2 as D increases.

The pattern holds with less than 0.1% numerical error.

Abstract

Recently, in arXiv:1105.2298 [hep-th], we have estimated the energy radiated in the head-on collision of two equal D-dimensional Aichelburg-Sexl shock waves, for even D, by solving perturbatively, to first order, the Einstein equations in the future of the collision. Here, we report on the solution for the odd D case. After finding the wave forms, we extract the estimated radiated energy for D=5,7,9 and 11 and unveil a remarkably simple pattern, given the complexity of the framework: (for all D) the estimated fraction of radiated energy matches the analytic expression 1/2-1/D, within the numerical error (less than 0.1%). Both this fit and the apparent horizon bound converge to 1/2 as D goes to infinity.