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

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.