Scattering by regular black holes: Planar massless scalar waves impinging upon a Bardeen black hole

TL;DR

This paper investigates how planar massless scalar waves scatter off a Bardeen regular black hole, comparing different computational methods and revealing similarities with Reissner-Nordström black hole scattering patterns.

Contribution

It provides a detailed analysis of scalar wave scattering by a Bardeen black hole, including comparisons with classical and semi-classical approaches, highlighting the effects of black hole charge.

Findings

Scattering cross section shows interference patterns similar to Reissner-Nordström black holes for certain charges.

Comparison between partial-wave, geodesic, and glory approximations validates the scattering analysis.

Regular black holes can produce scattering signatures akin to singular black holes under specific conditions.

Abstract

Singularities are common features of general relativity black holes. However, within general relativity, one can construct black holes that present no singularities. These regular black hole solutions can be achieved by, for instance, relaxing one of the energy conditions on the stress energy tensor sourcing the black hole. Some regular black hole solutions were found in the context of non-linear electrodynamics, the Bardeen black hole being the first one proposed. In this paper, we consider a planar massless scalar wave scattered by a Bardeen black hole. We compare the scattering cross section computed using a partial-wave description with the classical geodesic scattering of a stream of null geodesics, as well as with the semi-classical glory approximation. We obtain that, for some values of the corresponding black hole charge, the scattering cross section of a Bardeen black hole has a similar interference pattern of a Reissner-Nordstr\"om black hole.