We study the spacetime obtained by superimposing two equal Aichelburg-Sexl shock waves in D dimensions traveling, head-on, in opposite directions. Considering the collision in a boosted frame, one shock becomes stronger than the other, and a perturbative framework to compute the metric in the future of the collision is setup. The geometry is given, in first order perturbation theory, as an integral solution, in terms of initial data on the null surface where the strong shock has support. We then extract the radiation emitted in the collision by using a D-dimensional generalisation of the Landau-Lifschitz pseudo-tensor and compute the percentage of the initial centre of mass energy ϵ emitted as gravitational waves. In D = 4 we find ϵ = 25.0%, in agreement with the result of D’Eath and Payne . As D increases, this percentage increases monotonically, reaching 40.0% in D = 10. Our result is always within the bound obtained from apparent horizons by Penrose, in D = 4, yielding 29.3%, and Eardley and Giddings , in D > 4, which also increases monotonically with dimension, reaching 41.2% in D = 10. We also present the wave forms and provide a physical interpretation for the observed peaks, in terms of the null generators of the shocks.
P.D. D’Eath and P.N. Payne, Gravitational radiation in high speed black hole collisions. 1. Perturbation treatment of the axisymmetric speed of light collision, Phys. Rev.D 46 (1992) 658 [SPIRES].MathSciNetADSGoogle Scholar
P.D. D’Eath and P.N. Payne, Gravitational radiation in high speed black hole collisions. 2. Reduction to two independent variables and calculation of the second order news function, Phys. Rev.D 46 (1992) 675 [SPIRES].MathSciNetADSGoogle Scholar
P.D. D’Eath and P.N. Payne, Gravitational radiation in high speed black hole collisions. 3. Results and conclusions, Phys. Rev.D 46 (1992) 694 [SPIRES].MathSciNetADSGoogle Scholar
H. Witek et al., Numerical relativity for D dimensional space-times: head-on collisions of black holes and gravitational wave extraction, Phys. Rev.D 82 (2010) 104014 [arXiv:1006.3081] [SPIRES].ADSGoogle Scholar
E. Berti, V. Cardoso and B. Kipapa, Up to eleven: radiation from particles with arbitrary energy falling into higher-dimensional black holes, Phys. Rev.D 83 (2011) 084018 [arXiv:1010.3874] [SPIRES].ADSGoogle Scholar
E. Berti, M. Cavaglia and L. Gualtieri, Gravitational energy loss in high energy particle collisions: Ultrarelativistic plunge into a multidimensional black hole, Phys. Rev.D 69 (2004) 124011 [hep-th/0309203] [SPIRES].MathSciNetADSGoogle Scholar
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