Analytic Investigation of the Branch Cut of the Green Function in Schwarzschild Space-time

TL;DR

This paper introduces a novel analytic method to study the branch cut of the Green function in Schwarzschild space-time, enabling comprehensive analysis of the modes along the cut and their physical implications.

Contribution

The authors develop a new analytic approach to evaluate the branch cut of the Green function for all frequencies, extending understanding beyond previous asymptotic analyses.

Findings

Calculated the modes along the branch cut for general-spin fields.

Analyzed the properties and connection of these modes with quasinormal modes.

Investigated the impact of branch cut modes on the self-force in Schwarzschild space-time.

Abstract

The retarded Green function for linear field perturbations in Schwarzschild black hole space-time possesses a branch cut in the complex-frequency plane. This branch cut has remained largely unexplored: only asymptotic analyses either for small-frequency (yielding the known tail decay at late times of an initial perturbation of the black hole) or for large-frequency (quasinormal modes close to the branch cut in this regime have been linked to quantum properties of black holes) have been carried out in the literature. The regime along the cut inaccessible to these asymptotic analyses has so far remained essentially unreachable. We present a new method for the analytic calculation of the branch cut directly on the cut for general-spin fields in Schwarzschild space-time. This method is valid for any values of the frequency on the cut and so it provides analytic access to the whole branch cut for the first time. We calculate the modes along the cut and investigate their properties and connection with quasinormal modes. We also investigate the contribution from these branch cut modes to the self-force acting on a point particle on a Schwarzschild background space-time.