Radiation from a D-dimensional collision of shock waves: higher order set up and perturbation theory validity

Abstract

The collision of two D-dimensional, ultra-relativistic particles, described in General Relativity as Aichelberg-Sexl shock waves, is inelastic. In first order perturbation theory, the fraction of the initial centre of mass energy radiated away was recently shown to be 1/2 - 1/D. Here, we extend the formalism to higher orders in perturbation theory, and derive a general expression to extract the inelasticity, valid non-perturbatively, based on the Bondi mass loss formula. Then, to clarify why perturbation theory captures relevant physics of a strong field process in this problem, we provide one variation of the problem where the perturbative framework breaks down: the collision of ultra-relativistic charged particles. The addition of charge, and the associated repulsive nature of the source, originates an extra radiation burst, which we argue to be an artifact of the perturbative framework, veiling the relevant physics.

21 pages, 3 figures; v2: matches version to Appear in Phys. Rev. D

References in corpus (5)

• The high-energy collision of two black holes
• Ultrarelativistic black hole formation
• Black hole formation in the head-on collision of ultrarelativistic charges
• Radiation from a D-dimensional collision of shock waves: first order perturbation theory
• Ultrarelativistic boost of spinning and charged black rings