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, which we will also refer to as "magnetic monopole black hole solutions", 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-Nordström metric on the one hand and the hairy magnetic monopole black hole solutions 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 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.

arXiv comment11 pages, 7 figures, v2: some clarifications and some references added, introduction and outlook extended

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