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

TL;DR

This paper extends perturbation theory for D-dimensional shock wave collisions to higher orders, deriving a non-perturbative inelasticity expression and analyzing the limitations of perturbative methods in charged particle collisions.

Contribution

It develops a higher-order perturbation framework and a non-perturbative expression for inelasticity in shock wave collisions, and investigates the breakdown of perturbation theory with charged particles.

Findings

First-order inelasticity is 1/2 - 1/D.

Higher-order perturbation theory can be formulated and validated.

Perturbation theory fails in charged particle collisions due to additional radiation artifacts.

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.