Black Hole S-matrix for a scalar field

TL;DR

This paper constructs a unitary S-matrix for scalar particle scattering on a Schwarzschild black hole, combining near-horizon and far-region dynamics, and explores gravitational echoes during black hole relaxation.

Contribution

It introduces a novel approach to unify near-horizon and far-region scattering processes into a single unitary S-matrix for black hole physics.

Findings

Successfully formulated a manifestly unitary S-matrix for black hole scattering.

Identified gravitational echoes as a signature of black hole relaxation.

Analyzed the emergence of quasi-normal modes in the scattering process.

Abstract

We describe a unitary scattering process, as observed from spatial infinity, of massless scalar particles on an asymptotically flat Schwarzschild black hole background. In order to do so, we split the problem in two different regimes governing the dynamics of the scattering process. The first describes the evolution of the modes in the region away from the horizon and can be analysed in terms of the effective Regge-Wheeler potential. In the near horizon region, where the Regge-Wheeler potential becomes insignificant, the WKB geometric optics approximation of Hawking's is replaced by the near-horizon gravitational scattering matrix that captures non-perturbative soft graviton exchanges near the horizon. We perform an appropriate matching for the scattering solutions of these two dynamical problems and compute the resulting Bogoliubov relations, that combines both dynamics. This allows us to formulate an S-matrix for the scattering process that is manifestly unitary. We discuss the analogue of the (quasi)-normal modes in this setup and the emergence of gravitational echoes that follow an original burst of radiation as the excited black hole relaxes to equilibrium.