Magnetic monopoles near the black hole threshold

We present new analytic and numerical results for self-gravitating SU(2)-Higgs magnetic monopoles approaching the black hole threshold. Our investigation extends to large Higgs self-coupling, λ, a regime heretofore unexplored. When λ is small, the critical solution where a horizon first appears is extremal Reissner-Nordstroem outside the horizon but has a nonsingular interior. When λ is large, the critical solution is an extremal black hole with non-Abelian hair and a mass less than the extremal Reissner-Nordstroem value. The transition between these two regimes is reminiscent of a first-order phase transition. We analyze in detail the approach to these critical solutions as the Higgs expectation value is varied, and compare this analysis with the numerical results. copyright 1999 The American Physical Society