We reanalyze the gravitating monopole and its black hole solutions in the Einstein-Yang-Mills-Higgs system and we discuss their stabilities from the point of view of catastrophe theory. Although these nontrivial solutions exhibit fine and complicated structures, we find that stability is systematically understood via a swallow tail catastrophe. The Reissner-Nordström trivial solution becomes unstable from the point where the nontrivial monopole black hole appears. We also find that, within a very small parameter range, the specific heat of a monopole black hole changes its sign.
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