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

TL;DR

This paper calculates classical gravitational observables for black hole scattering at third order in the gravitational constant, incorporating radiation effects and using advanced amplitude techniques to evaluate loop integrals.

Contribution

It introduces a novel computation of gravitational observables at $ ext{O}(G^3)$ using scattering amplitudes, including radiation reaction effects beyond conservative dynamics.

Findings

Computed impulse and radiated momentum at $ ext{O}(G^3)$

Extracted scattering angle and radiated energy from observables

Discussed universality and high-energy behavior of the impulse

Abstract

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. The KMOC formalism naturally incorporates radiation effects which enables us to explore these classical quantities beyond the conservative two-body dynamics. From the impulse and the radiated momentum, we extract the scattering angle and the radiated energy. Finally, we discuss universality of the impulse in the high-energy limit and the relation to the eikonal phase.