Radiation from a D-Dimensional Collision of Shock Waves: Numerics and a Charged Case
We describe the generalisation to higher orders, of a perturbative framework to find the metric after the collision of two Aichelburg–Sexl gravitational shock waves in D-dimensions. A central challenge is to estimate the amount of gravitational radiation emitted in the collision, at higher orders. We present an adaptation of the Bondi mass loss formula in D-dimensions which is valid non-perturbatively, for axially symmetric asymptotically flat space-times. This is shown to coincide with the Landau–Lifshitz pseudo tensor result at first order in perturbation theory. We also discuss the validity of the method with a collision of charged shocks.
KeywordsShock Wave Apparent Horizon Flat Space Neutral Case Null Generator
This work was supported by the grants NRHEP–295189, FP7-PEOPLE-2011-IRSES and PTDC/FIS/116625/2010. F.C., C.R and M.S. are funded respectively by the grants SFRH/BD/60272/2009, SFRH/BPD/77223/2011 and SFRH/BPD/69971/2010.