Lorentz-covariant perturbation theory for relativistic gravitational bremsstrahlung

TL;DR

This paper develops a Lorentz-covariant perturbation theory in momentum space to analyze relativistic gravitational bremsstrahlung, providing closed-form radiation spectra and clarifying the limitations of the equivalent graviton method.

Contribution

It introduces a novel Lorentz-covariant approach using momentum space for gravitational bremsstrahlung calculations, improving upon previous methods.

Findings

Derived closed-form spectra for scalar, electromagnetic, and gravitational radiation.

Total emitted energy results align with previous studies by Thorne and Kovacs.

Identified limitations of the equivalent graviton method in spectral-angular distribution analysis.

Abstract

We formulate Lorentz-covariant classical perturbation theory to deal with relativistic bremsstrahlung under gravitational scattering. Our approach is a version of the fast motion approximation scheme, the main novelty being the use of the momentum space representation. Using it we calculate in a closed form the spectrum of scalar, electromagnetic and gravitational radiation. Our results for the total emitted energy agree with those by Thorne and Kovacs. We also explain why the method of equivalent gravitons fails to produce the correct result for the spectral-angular distribution of emitted radiation under gravitational scattering, contrary to the case of Weizs\"acker-Williams approximation in quantum electrodynamics.