Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory

TL;DR

This work compute the far-field time-domain waveform of the gravitational waves produced in the encounter at leading order in the post-Minkowskian (weak field but generic velocity) expansion, and extracts the leading-order total radiated angular momentum and energy.

Abstract

Using the recently established formalism of a worldline quantum field theory (WQFT) description of the classical scattering of two spinless black holes, we compute the far-field time-domain waveform of the gravitational waves produced in the encounter at leading order in the post-Minkowskian (weak field, but generic velocity) expansion. We reproduce previous results of Kovacs and Thorne in a highly economic way. Then using the waveform we extract the leading-order total radiated angular momentum and energy (including differential results). Our work may enable crucial improvements of gravitational-wave predictions in the regime of large relative velocities.

Figures (3)

• Figure 1: The three diagrams contributing to the Bremsstrahlung at 2PM order, where $\omega_i=k\cdot v_i$ by energy conservation at the worldline vertices. All three diagrams have the integral measure in Eq. (\ref{['eq:measure']}); in the rest frame of black hole 1 diagram (a) does not contribute as soon as the outgoing graviton is contracted with a purely spatial polarization tensor.
• Figure 2: Plots of the wave memories $\Delta f_{+,\times}$ for $v=0.2$. For a visualisation of the complete waveforms as they evolve with retarded time $u$ see https://box.hu-berlin.de/f/73b510f4dae1408ba612/ and https://box.hu-berlin.de/f/6c1ff4812f7448ca913d/.
• Figure 3: The differential power spectrum (total energy radidated per unit frequency) given in Eq. (\ref{['psfinal']}) at $\mathcal{O}(G^3)$, including terms up to order $v^{4}$ in a low-velocity expansion.