Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory

Using the recently established formalism of a worldline quantum field theory 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 the 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.

Figure 1

The three diagrams contributing to the bremsstrahlung at 2PM order, where ${\omega }_i=k·v_i$ by energy conservation at the worldline vertices. All three diagrams have the integral measure in Eq. (16); 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, while (b) and (c) do.

Figure 2

Plots of the wave memories $\mathrm{\Delta }{f}_{+,\times }$ for $v=0.2$. For a visualisation of the complete waveforms as they evolve with retarded time $u$ see the Supplemental Material [36].