Radiation from a D-Dimensional Collision of Shock Waves: A Remarkably Simple Fit Formula

Recently we 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 ->infinity.