Regge poles of the Schwarzschild black hole: a WKB approach

TL;DR

This paper derives simple analytical formulas for the Regge poles of Schwarzschild black holes using third-order WKB methods, aiding the understanding of wave scattering, quasinormal modes, and gravitational lensing effects.

Contribution

It introduces new analytical expressions for Regge poles of Schwarzschild black holes using a third-order WKB approach, simplifying wave scattering and gravitational wave analysis.

Findings

Analytical expressions for Regge poles for spins 0, 1, 2.

Dispersion relations for photons near the photon sphere.

Implications for gravitational lensing and wave scattering.

Abstract

We provide simple and accurate analytical expressions for the Regge poles of the Schwarzschild black hole. This is achieved by using third-order WKB approximations to solve the radial wave equations for spins 0, 1 and 2. These results permit us to obtain analytically the dispersion relation and the damping of the "surface waves" lying on the photon sphere of the Schwarzschild black hole and which generate the weakly damped quasinormal modes of its spectrum. Our results could be helpful in order to simplify considerably the description of wave scattering from the Schwarzschild black hole as well as the analysis of the gravitational radiation created in many black hole processes. Furthermore, the existence of dispersion relations for the photons propagating close to the photon sphere could have also important consequences in the context of gravitational lensing.