Radiation from a D-dimensional collision of shock waves: a remarkably simple fit formula
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.
Keywords
Cite
@article{arxiv.1203.5355,
title = {Radiation from a D-dimensional collision of shock waves: a remarkably simple fit formula},
author = {Flávio S. Coelho and Carlos Herdeiro and Marco O. P. Sampaio},
journal= {arXiv preprint arXiv:1203.5355},
year = {2015}
}
Comments
3 pages, 3 figures, Accepted in Physical Review Letters