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 field 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.

Gravitating dyons with large electric charge

“…For monopoles and dyons, in the case of vanishing Higgs potential, this second branch reaches a critical value of α, where it bifurcates with the branch of extremal Reissner-Nordström black holes with the same charge(s) [7,16,17]. For monopole-antimonopole pair solutions and other composite solutions, in contrast, the second branch extends back to α = 0, where a pure Einstein-Yang-Mills solution is reached (after scaling w.r.t.…”

“…For each type of solution, a branch of gravitating solutions emerges smoothly from the corresponding flat space solution and extends up to a maximal value of α, beyond which the size of the core of the solution would be smaller than its Schwarzschild radius [16]. At the maximal value of α this fundamental branch bifurcates with a second branch of solutions.…”

“…dyon branch reaches the critical value of the coupling constant α, and merges with the extremal Reissner-Nordström branch, the spacetime splits into two regions [16]. The exterior spacetime of the critical solution, corresponds to the one of an extremal Reissner-Nordström black hole [16], while the interior spacetime retains regularity at the center, due to the influence of the non-Abelian fields present.…”

“…When gravity is coupled to Yang-Mills-Higgs theory, gravitating monopoles [16,17], dyons [18], monopoleantimonopole pairs [19,20,21,22], and further configurations arise [23]. These solutions depend on a dimensionless coupling constant α, which is proportional to the square root of Newton's constant and the Higgs vacuum expectation value.…”

Six-dimensional Yang black holes in dilaton gravity

“…But when the gauge group is spontaneously broken, there are non-singular 't Hooft-Polyakov monopoles [4,5]. Adding gravity, one can place a small Schwarzschild black hole at the centre of one of these, to produce one of Weinberg's hairy black holes [6,7,8]. These can have identical mass and charge to the RN solutions, which still exist in the larger theory, hence forming classical hair.…”