  Self-gravitating SU(2) Higgs magnetic monopoles exist up to a critical value
of the ratio of the vector meson mass to the Planck mass, which depends on the
Higgs boson mass. At the critical value a critical solution with a degenerate
horizon is reached. As pointed out by Lue and Weinberg, there are two types of
critical solutions, with a transition at an intermediate Higgs boson mass. Here
we investigate this transition for black holes, and reconsider it for the case
of gravitating monopoles.
