Classical Yang–Mills Black Hole Hair in Anti-de Sitter Space

Abstract

The properties of hairy black holes in Einstein-Yang-Mills (EYM) theory are reviewed, focusing on spherically symmetric solutions. In particular, in asymptotically anti-de Sitter space (adS) stable black hole hair is known to exist for su(2) EYM. We review recent work in which it is shown that stable hair also exists in su(N) EYM for arbitrary N, so that there is no upper limit on how much stable hair a black hole in adS can possess.

A modulated shear to entropy ratio

“…In this language table 1 lists only the smaller, λ 0 , eigenvalues and eigenfunctions. All the solutions for which λ i < 0 with i ≥ 1 will necessarily lie inside the critical curve described in the left panel of figure 1 and are expected to be unstable due to their higher free energy (see e.g., [65]). …”

No-go on strictly stationary spacetimes in four/higher dimensions

“…But, we know that there is the static nontrivial solution for the Einstein-Yang-Mills systems [5] (see Ref. [6] and references therein). Holographic argument of condensed matters relied on nontrivial self-gravitating configurations in asymptotically anti-deSitter spacetimes (see Ref.…”

On the existence of soliton and hairy black hole solutions of {\mathfrak {su}}(N) Einstein–Yang–Mills theory with a negative cosmological constant

“…Introducing a negative cosmological constant changes the picture completely (see [8] for a recent review). In asymptotically flat space, soliton and black hole solutions exist at discrete points in the parameter space, but in four-dimensional asymptotically anti-de Sitter (adS) space, su(2) EYM solutions are found in continuous open sets of the parameter space [9,10,11].…”

“…Recently soliton and black hole solutions of four-dimensional su(N) EYM theory with a negative cosmological constant have been found [8,14,15]. For purely magnetic solutions, the gauge field is described by N − 1 gauge field functions ω j .…”