Radiation from a D-Dimensional Collision of Shock Waves: A Summary of the First Order Results

We describe how to set up a perturbative framework to compute the metric in the future of a D-dimensional collision of two high speed black holes, by superimposing two equal Aichelburg–Sexl shock waves traveling, head-on, in opposite directions. We then estimate the radiation emitted in the collision using a D-dimensional generalisation of the Landau–Lifschitz pseudo-tensor—workable in a first order approach—and compute the percentage of the initial centre of mass energy emitted as gravitational waves. We shall see that our first order results are always within the bound obtained from apparent horizons computations.