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

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## 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 EYMH 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-Nordstroem metric on the one hand and the hairy black hole solutions which are described by a metric which is not of Reissner-Nordstroem form on the other hand.) One can experimentally distinguish such black holes with 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 to distinguish magnetically charged black holes with 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 EYMH equations with a Higgs triplett 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 same asymptotic characteristics. We find in particular that the characteristic glory peaks in the cross sections are located at different scattering angles.