Non-Abelian black holes and catastrophe theory. II. Charged type.

We reanalyze the gravitating monopole and its black hole solutions in the EinsteinYang-Mills-Higgs system and we discuss their stabilities from the point of view of catastrophe theory. Although these non-trivial 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 non-trivial 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 . PACS numbers: 97.60.Lf, 11.15.-q, 95.30.Tg, 04.20.-q