Inelastic Coupled-Channel Eikonal Scattering

TL;DR

This paper develops a formalism for inelastic scattering in black hole dynamics using coupled-channel eikonal methods, enabling analysis of mass and spin changes during inelastic processes and absorption effects.

Contribution

It introduces the inelastic coupled-channel eikonal (ICCE) framework using KMOC formalism, allowing for the inclusion of inelastic effects in classical and wave scattering on black holes.

Findings

Derived unitarity relations with inelastic effects.

Formulated a resummation approach for inelastic scattering.

Applied to mass change in binary black hole dynamics.

Abstract

Emitted radiation and absorption effects in black hole dynamics lead to inelastic scattering amplitudes. In this paper, we study how these effects introduce an inelasticity function to the $2\rightarrow2$ eikonalised $S$-matrix and how they can be described using unequal mass and spin on-shell amplitudes. To achieve this, we formulate the inelastic coupled-channel eikonal (ICCE) using the KMOC formalism and the language of quantum channels, where off-diagonal channels involve mass and spin changes. This formulation allows us to re-use usual eikonal results but also suggests a different resummation of inelastic effects. We then apply this formulation to calculate classical inelastic processes, such as the mass change in binary dynamics due to the presence of an event horizon. Additionally, we provide a complementary analysis for the case of wave scattering on a black hole, considering absorption effects. In both scenarios, we derive unitarity relations accounting for inelastic effects.