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Black holes in magnetic monopoles. (English) Zbl 1232.81033
Summary: 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-field vacuum expectation value \(v\) is less than or equal to a critical value \(v_{\mathrm{cr}}\), 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-Nordström solution. For \(v<v_{\mathrm{cr}}\), 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-Nordström solutions are discussed.

MSC:
81T13 Yang-Mills and other gauge theories in quantum field theory
83C57 Black holes
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