Orbiting phenomena in black hole scattering

TL;DR

This paper investigates orbiting phenomena in black hole scattering, revealing a critical angular momentum associated with unstable circular orbits and offering new interpretations of the Regge-Wheeler potential through numerical and semi-analytical methods.

Contribution

It introduces a novel characterization of orbiting scattering via a sharp rise in reflection coefficient and interprets the Regge-Wheeler potential with quantum corrections for massless particles.

Findings

Identification of a critical angular momentum $l_C$ for orbiting scattering.

Good agreement between semi-analytical, numerical, and exact results.

Discussion of limitations of previous approximation methods.

Abstract

Rainbow, glory and orbiting scattering are usually described by the properties of the classical deflection function related to the real part of the quantum mechanical scattering phase shift or by the diffractive pattern of the quantum mechanical cross sections. Here we show that the case of orbiting scattering of massless spin 0, 1 and 2 particles from Schwarzschild black holes can be characterized by a sudden rise in $|R_l|^2$ at a critical angular momentum $l_C$, which we show corresponds to the unstable circular orbits of these particles. For the cases, $s =0, 2$, we attempt a new interpretation of the Regge-Wheeler potential by identifying the quantum mechanical corrections to the effective potential of massless particles. We probe into the black hole scattering by using numerical and semi-analytical methods which give very good agreements with the exact numerical results. The limitations of previously used approximations as compared to the exact and semi-analytical results are discussed.