Radiative Classical Gravitational Observables at $\mathcal O(G^3)$ from Scattering Amplitudes

Understand

We compute classical gravitational observables for the scattering of two spinless black holes in general relativity and $\mathcal N {=} 8$ supergravity in the formalism of Kosower, Maybee, and O'Connell (KMOC).

• We focus on the gravitational impulse with radiation reaction and the radiated momentum in black hole scattering at $\mathcal O(G^3)$ to all orders in the velocity.
• These classical observables require the construction and evaluation of certain loop-level quantities which are greatly simplified by harnessing recent advances from scattering amplitudes and collider physics.
• In particular, we make use of generalized unitarity to construct the relevant loop integrands, employ reverse unitarity, the method of regions, integration-by-parts (IBP), and (canonical) differential equations to simplify and evaluate all loop and phase-space integrals to obtain the classical gravitational observables of interest to two-loop order.