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, $\lambda ,$ a regime heretofore unexplored. When $\lambda$ is small, the critical solution where a horizon first appears is extremal Reissner-Nordström outside the horizon but has a nonsingular interior. When $\lambda$ is large, the critical solution is an extremal black hole with non-Abelian hair and a mass less than the extremal Reissner-Nordström 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.