Gravitational Bremsstrahlung from Reverse Unitarity

TL;DR

This paper calculates gravitational wave momentum radiation during black hole scattering at third order in G, extending to bound orbits, advancing understanding of binary dynamics using quantum amplitude techniques.

Contribution

It introduces a novel application of reverse unitarity and KMOC formalism to compute gravitational radiation in black hole scattering at ${ m O}(G^3)$, including bound states.

Findings

Computed total radiated momentum at ${ m O}(G^3)$ for scattering.

Derived energy loss in elliptic orbits via analytic continuation.

Established a framework connecting quantum amplitudes to classical gravitational observables.

Abstract

We compute the total radiated momentum carried by gravitational waves during the scattering of two spinless black holes at the lowest order in Newton's constant, $\mathcal O(G^3)$, and all orders in velocity. By analytic continuation into the bound state regime, we obtain the ${\cal O}(G^3)$ energy loss in elliptic orbits. This provides an essential step towards the complete understanding of the third-post-Minkowskian binary dynamics. We employ the formalism of Kosower, Maybee, and O'Connell (KMOC) which relates classical observables to quantum scattering amplitudes and derive the relevant integrands using generalized unitarity. The subsequent phase-space integrations are performed via the reverse unitarity method familiar from collider physics, using differential equations to obtain the exact velocity dependence from near-static boundary conditions.