Radiation from a D-dimensional collision of shock waves: first order perturbation theory

  • Carlos Herdeiro
  • Marco O. P. SampaioEmail author
  • Carmen Rebelo
Open Access


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 [12]. 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 [16], 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.


Large Extra Dimensions Black Holes 


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Copyright information

© The Author(s) 2011

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Carlos Herdeiro
    • 1
  • Marco O. P. Sampaio
    • 1
    • 2
    Email author
  • Carmen Rebelo
    • 1
  1. 1.Departamento de Física da Universidade de Aveiro and I3NAveiroPortugal
  2. 2.CERN, Physics Department, Theory DivisionGeneva 23Switzerland

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