Gravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory

TL;DR

This paper analyzes gravitational radiation during two-body scattering using post-Minkowskian effective field theory, deriving key quantities and confirming results with scattering amplitude methods, including energy spectrum behavior at zero frequency.

Contribution

It introduces a new approach to compute gravitational radiation in two-body scattering using EFT, deriving the stress-energy tensor and emission amplitudes at higher orders.

Findings

Derived the conserved stress-energy tensor coupled to gravity.

Computed the graviton emission amplitude at leading and next-to-leading order.

Confirmed agreement with scattering amplitude methods for radiated momentum.

Abstract

We study the gravitational radiation emitted during the scattering of two spinless bodies in the post-Minkowskian Effective Field Theory approach. We derive the conserved stress-energy tensor linearly coupled to gravity and the classical probability amplitude of graviton emission at leading and next-to-leading order in the Newton's constant $G$. The amplitude can be expressed in compact form as one-dimensional integrals over a Feynman parameter involving Bessel functions. We use it to recover the leading-order radiated angular momentum expression. Upon expanding it in the relative velocity between the two bodies $v$, we compute the total four-momentum radiated into gravitational waves at leading-order in $G$ and up to an order $v^8$, finding agreement with what was recently computed using scattering amplitude methods. Our results also allow us to investigate the zero frequency limit of the emitted energy spectrum.