Aspects of Skyrmion Black Hole Hair

Abstract

In this short article, prepared for the proceedings of the Corfu Meeting 2016, I review three aspects of skyrmion/baryon black hole hair which have been investigated recently [1,2] and which I presented in my talk in Corfu. First, I will argue that one can detect the classical skyrmion/baryon hair which, as it is well-known [8], a small enough black hole can carry in classical scattering experiments of waves. Second, I will show that, under certain assumptions which I will point out, a black hole can not only carry the known classical skyrmion/baryon hair but also a quantum skyrmion/baryon hair which can be detected in Aharonov-Bohm type experiments in which a probe string encloses the black hole. In contrast to the known classical skyrmion/baryon hair, the Aharonov-Bohm type quantum skyrmion/baryon hair can be carried by black holes of arbitrary size. Third, I will argue that from the point of view of a low-energy observer who can measure the Aharonov-Bohm type skyrmion/baryon hair of a black hole, black holes respect Skyrme topological charge/baryon number.

Extensions of the generalized hedgehog ansatz for the Einstein-nonlinear σ-model system: black holes with NUT, black strings and time-dependent solutions

“…The extra assumptions (i), (ii) or (iii) imply ∇H · ∇Φ ± = 0, so that the field equations (19) and (20) become identities. In case (ii) also (18) is identically satisfied, while in case (i) it simplifies since H = 0.…”

“…Nevertheless, having in mind a specific physical system, the choice of a good ansatz for the matter field and the spacetime metric may reduce the complexity of the problem. A well-known example is given by the hedgehog ansatz in the presence of spherical symmetry, considered in this context (without backreaction) in [3,16] and further used (also with backreaction) in a number of works, see, e.g., [17][18][19] for reviews and more references. A generalizations of the hedgehog ansatz for the Skyrme-Einstein system beyond spherical symmetry has been constructed in [20] and applied to spacetimes which possess plane or hyperbolic symmetry or are stationary and axisymmetric (see [21] for earlier results for the SU (2) nonlinear σ-model).…”