Gravitational radiation in massless-particle collisions

TL;DR

This paper analyzes gravitational radiation emitted during collisions of massless particles using perturbative classical General Relativity, revealing how radiation efficiency depends on impact parameters and reproducing quantum results in specific limits.

Contribution

It provides a detailed perturbative analysis of gravitational radiation in massless-particle collisions, including nonlinear effects and frequency characteristics, extending previous quantum results.

Findings

Radiation efficiency scales as the square of the impact parameter ratio, ^2.

Dominant radiation frequency is on the order of the inverse Schwarzschild radius.

Quantum results are recovered in the zero-frequency limit.

Abstract

The angular and frequency characteristics of the gravitational radiation emitted in collisions of massless particles is studied perturbatively in the context of classical General Relativity for small values of the ratio $\alpha\equiv 2 r_S/b$ of the Schwarzschild radius over the impact parameter. The particles are described with their trajectories, while the contribution of the leading nonlinear terms of the gravitational action is also taken into account. The old quantum results are reproduced in the zero frequency limit $\omega\ll 1/b$. The radiation efficiency $\epsilon \equiv E_{\rm rad}/2E$ outside a narrow cone of angle $\alpha$ in the forward and backward directions with respect to the initial particle trajectories is given by $\epsilon \sim \alpha^2$ and is dominated by radiation with characteristic frequency $\omega \sim {\mathcal O}(1/r_S)$.