Gravitational partial-wave absorption from scattering amplitudes

TL;DR

This paper develops a new framework using scattering amplitudes to analyze gravitational absorption by black holes, connecting quantum amplitudes with classical absorption effects and matching general relativity results.

Contribution

It introduces an in-in probability framework with partial-wave states for gravitational absorption, linking quantum amplitudes to classical cross-sections and deriving effective couplings.

Findings

Derived covariant spin-weighted spherical harmonics for amplitudes

Matched quantum amplitude results with classical GR cross-sections

Found absorption couplings scale as ${ m O}(G_ ext{Newton}^{s+1})$

Abstract

We study gravitational absorption effects using effective on-shell scattering amplitudes. We develop an in-in probability-based framework involving plane- and partial-wave coherent states for the incoming wave to describe the interaction of the wave with a black hole or another compact object. We connect this framework to a simplified single-quantum analysis. The basic ingredients are mass-changing three-point amplitudes, which model the leading absorption effects and a spectral-density function of the black hole. As an application, we consider a non-spinning black hole that may start spinning as a consequence of the dynamics. The corresponding amplitudes are found to correspond to covariant spin-weighted spherical harmonics, the properties of which we formulate and make use of. We perform a matching calculation to general-relativity results at the cross-section level and derive the effective absorptive three-point couplings. They are found to behave as ${\cal O}(G_\text{Newton}^{s+1})$, where $s$ is the spin of the outgoing massive state.