New black hole solutions with axial symmetry in Einstein–Yang–Mills theory

Abstract

We construct new black hole solutions in Einstein-Yang-Mills theory. They are static, axially symmetric and asymptotically flat. They are characterized by their horizon radius and a pair of integers (k, n), where k is related to the polar angle and n to the azimuthal angle. The known spherically and axially symmetric EYM black holes have k = 1. For k > 1, pairs of new black hole solutions appear above a minimal value of n, that increases with k. Emerging from globally regular solutions, they form two branches, which merge and end at a maximal value of the horizon radius. The difference of their mass and their horizon mass equals the mass of the corresponding regular solution, as expected from the isolated horizon framework.

Black holes and gravitating axially symmetric non-abelian solitons in d = 3+1 and d = 4+1

“…Our solutions are akin to the static, axially symmetric EYM configurations in d = 4, studied exhaustively in [26], [27,28]. The regular and black hole solutions presented are natural generalisations of the known [10] d = 5 EYM spherically symmetric globally regular and black hole solutions.…”

“…As compared to the d = 4 case [27,28], we expect the existence of a much richer set of nonspherically symmetric EYM solutions in d = 5.…”

Rotating black holes with non-Abelian hair

“…By including an integer w.r.t. the polar angle, one obtains a further type of static EYM black holes [17]. All these configurations can be interpreted as bound states of black holes and solitonic configurations [18,19,20,21,22].…”

Scalar hairy black holes and scalarons in the isolated horizons formalism

“…Finally, the combination of the Mass formula, together with the fact that in theories such as Einstein-Yang-Mills-Higgs (EYMH) different "branches" of static solutions merge, has allowed to have a formula for the difference of soliton masses in terms of black hole quantities [5,6,7]. Many of these predictions have been confirmed in more general situations and for other matter couplings [8,9]. For a recent review on IH (including hair) see [10], and for a review of hairy black holes see [11].…”