Gravitational partial-wave absorption from scattering amplitudes

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 OGNewtons+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O}\left({G}_{\textrm{Newton}}^{s+1}\right) $$\end{document}, where s is the spin of the outgoing massive state.