Einstein-Yang-Mills isolated horizons: Phase space, mechanics, hair, and conjectures - art. no. 044046

The concept of an "isolated horizon" has been recently used to provide a fu ll Hamiltonian treatment of black holes. It has been applied successfully t o the cases of nonrotating, nondistorted black holes in the Einstein vacuum , Einstein-Maxwell, and Einstein-Maxwell-dilaton theories. In this paper, t he extent to which the framework can be generalized to the case of non-Abel ian gauge theories is investigated in which "hairy black holes" are known t o exist. It is found that this extension is indeed possible, despite the fa ct that, in general, there is no "canonical normalization" yielding a prefe rred horizon mass. In particular the zeroth and first laws are established for all normalizations. Colored static spherically symmetric black hole sol utions to the Einstein-Yang-Mills equations are considered from this perspe ctive. A canonical formula for the horizon mass of such black holes is foun d. This analysis is used to obtain nontrivial relations between the masses of the colored black holes and the regular solitonic solutions in Einstein- Yang-Mills theory. A general testing bed for the instability of hairy black holes in general nonlinear theories is suggested. As an example, the embed ded Abelian magnetic solutions are considered. It is shown that, within thi s framework, the total energy is also positive and thus the solutions are p otentially unstable. Finally, it is discussed which elements would be neede d to place the isolated horizon framework for Einstein-Yang-Mills theory on the same footing as the previously analyzed cases. Motivated by these cons iderations and using the fact that the isolated horizon framework seems to be the appropriate language to state uniqueness and completeness conjecture s for the EYM equations, in terms of the horizon charges, two such conjectu res are put forward.