Absorptive Effects in Black Hole Scattering

TL;DR

This paper introduces absorptive Compton amplitudes to quantify wave absorption in black hole scattering, enabling calculation of mass changes due to various field interactions, and reproduces known power loss results.

Contribution

It defines new absorptive amplitudes in black hole perturbation theory and applies them to compute mass changes, extending previous results to generic spins and mass ratios.

Findings

Reproduced power loss in black hole scattering.

Calculated mass change due to absorption of different fields.

Extended analysis to generic spin orientations.

Abstract

In this paper we define absorptive Compton amplitudes, which captures the absorption factor for waves of spin-weight-$s$ scattering in black hole perturbation theory. At the leading order, in the $G M \omega$ expansion, such amplitudes are purely imaginary and expressible as contact terms. Equipped with these amplitudes we compute the mass change in black hole scattering events via Kosower-Maybee-O'Connell formalism, where the rest mass of Schwarzschild/Kerr black hole is modified due to absorption of gravitational, electromagnetic, or scalar fields sourced by other compact object. We reproduced the power loss previously computed in the post-Newtonian expansion. The results presented here hold for similar mass ratios and generic spin orientation, while keeping the Kerr spin parameter to lie in the physical region $\chi \le 1$.