Magnetic Monopoles Near the Black Hole Threshold

TL;DR

This paper investigates the behavior of self-gravitating SU(2)-Higgs magnetic monopoles near the black hole formation threshold, revealing a transition from extremal Reissner-Nordstrom solutions to black holes with non-Abelian hair as the Higgs self-coupling varies.

Contribution

It provides new analytic and numerical insights into monopole solutions approaching black hole thresholds, especially in the large Higgs self-coupling regime.

Findings

Critical solutions differ for small and large Higgs self-coupling.

Transition between regimes resembles a first-order phase transition.

Detailed analysis of approach to critical solutions as Higgs expectation varies.

Abstract

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-Nordstrom 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-Nordstrom 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.