Regular and black hole solutions of Einstein-Yang-Mills dilaton theory

Do stringy corrections stabilize colored black holes?

“…The presence of the Gauss-Bonnet term means that these perturbation equations are considerably more complex than those of the EYMD system [3]. However, the gauge field does not make them particularly more complicated than for the neutral black holes with the Gauss-Bonnet term [17].…”

“…In this paper, we are concerned only with the black hole solutions, and shall not consider the particle-like solutions which exist for other values of β. However, much of our analysis applies equally well for all values of β, and in particular to the case β = 0, which corresponds to the Einstein-Yang-Mills-Dilaton (EYMD) black holes considered in [3,4]. If the coupling constant is fixed (for numerical computations the value α ′ /g 2 = 1 is convenient) then there is only one remaining parameter, namely the event horizon radius r h .…”

“…Therefore, they correspond to saddle points of the action (2.1) due to the fact that the gauge group is non-Abelian. In addition, since the sphaleronic sector perturbation equations do not depend on the Gauss-Bonnet term, and the proof of instability depends not on the details of the equilibrium solutions, but only on their global features (such as the existence of the event horizon) the analysis also applies to the EYMD black holes [3]. We emphasize that the calculations necessary to obtain the expectation value (3.11) made use only of the static equilibrium equation for w (which has the same form for both the Gauss-Bonnet and EYMD models) and not that for φ, which does involve the Gauss-Bonnet term.…”

“…Stable examples of black holes with hair are of particular interest for their physical relevance, and also in order to investigate the effects of hair on quantum processes connected with black holes. However, many of the hairy black holes currently known are unstable, particularly those involving non-Abelian gauge fields [2][3][4][5][6][7][8], where the instability is topological in nature and similar to that of the flat space sphaleron. The only exceptions to the above rule are the black hole solutions found in the framework of the Einstein-Skyrme theory [9] and the magnetically charged, non-Abelian black holes in the limit of infinitely strong coupling of the Higgs field [10] or in the presence of a negative cosmological constant [11].…”

Towards a novel no-hair theorem for black holes

“…On the other hand, Wheeler's hypothesis was proven wrong in e.g. Einstein-Yang-Mills [7] and Einstein-Skyrme [8] theory, in various combinations with dilaton [9] or Higgs [10] fields. Some, but not all, of these hairy black holes are unstable.…”