Scattering of massless scalar waves by magnetically charged black holes in Einstein–Yang–Mills–Higgs theory

Abstract

The existence of the classical black hole solutions of the Einstein–Yang–Mills–Higgs equations with non-Abelian Yang–Mills–Higgs hair implies that not all classical stationary magnetically charged black holes can be uniquely described by their asymptotic characteristics. In fact, in a certain domain of parameters, there exist different spherically-symmetric, non-rotating and asymptotically-flat classical black hole solutions of the Einstein–Yang–Mills–Higgs equations which have the same ADM mass and the same magnetic charge but significantly different geometries in the near-horizon regions. (These are black hole solutions which are described by a Reissner–Nordström metric on the one hand and the black hole solutions with non-Abelian Yang–Mills–Higgs hair which are described by a metric which is not of Reissner–Nordström form on the other hand). One can experimentally distinguish such black holes with the same asymptotic characteristics but different near-horizon geometries classically by probing the near-horizon regions of the black holes. We argue that one way to probe the near-horizon region of a black hole which allows one to distinguish magnetically charged black holes with the same asymptotic characteristics but different near-horizon geometries is by classical scattering of waves. Using the example of a minimally-coupled massless probe scalar field scattered by magnetically charged black holes which can be obtained as solutions of the Einstein–Yang–Mills–Higgs equations with a Higgs triplet and gauge group SU(2) in the limit of an infinite Higgs self-coupling constant we show how, in this case, the scattering cross sections differ for the magnetically charged black holes with different near-horizon geometries but the same asymptotic characteristics. We find in particular that the characteristic glory peaks in the cross sections are located at different scattering angles.