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Two types of self-gravitating particle solutions found in several theories with non-Abelian fields are smoothly connected by a family of nontrivial black holes. There exists a maximum point of the black hole entropy where the stability of solutions changes. This criterion is universal, and the changes in stability follow from a catastrophe-theoretic analysis of the potential function defined by black hole entropy.
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Maeda et al. (1994) studied this question.
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