New results pertaining to colored static black hole solutions to the Einstein-Yang-Mills equations are obtained. The isolated horizons framework is used to define the concept of the Hamiltonian horizon mass of the black hole. An unexpected relation between the Arnowitt-Deser-Misner (ADM) and horizon masses of the black hole solution and the ADM mass of the corresponding Bartnik-McKinnon soliton is found. These results can be generalized to other nonlinear theories and they suggest a general testing bed for the instability of the corresponding hairy black holes.
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Corichi et al. (2000) studied this question.
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