Black Holes in Magnetic Monopoles

Abstract

We study magnetically charged classical solutions of a spontaneously broken gauge theory interacting with gravity. We show that nonsingular monopole solutions exist only if the Higgs vacuum expectation value $v$ is less than or equal to a critical value $v_{cr}$, which is of the order of the Planck mass. In the limiting case the monopole becomes a black hole, with the region outside the horizon described by the critical Reissner-Nordstrom solution. For $v<v_{cr}$, we find additional solutions which are singular at $r=0$, but which have this singularity hidden within a horizon. These have nontrivial matter fields outside the horizon, and may be interpreted as small black holes lying within a magnetic monopole. The nature of these solutions as a function of $v$ and of the total mass $M$ and their relation to the Reissner-Nordstrom solutions is discussed.