Gravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory

TL;DR

This paper addresses gravitational bremsstrahlung in the scattering of two spinless bodies within a Post-Minkowskian Effective Field Theory framework. It derives the conserved stress-energy tensor and the classical graviton-emission amplitude at leading and next-to-leading order in $G$, expressing the amplitude in terms of one-dimensional integrals of Bessel functions and using it to obtain the waveform, the radiated four-momentum, and the radiated angular momentum. The results reproduce known limits: the energy spectrum and total radiated energy agree with 2PN and recent amplitude-based calculations, and the angular momentum matches Damour's soft-limit results; the soft energy spectrum also aligns with prior work. The work provides a robust basis for connecting worldline EFT methods with PM scattering observables and sets the stage for extensions to spin and finite-size effects.

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.

Figures (1)

• Figure 1: The three Feynman diagrams needed for the computation of the stress-energy tensor up to NLO order in $G$. To compute the symmetric one, it is enough to exchange $1 \leftrightarrow 2$.