Black Holes in Magnetic Monopoles with a Dark Halo

Abstract

We study a spontaneously broken Einstein-Yang-Mills-Higgs model coupled via a Higgs portal to an uncharged scalar $χ$. We present a phase diagram of self-gravitating solutions showing that, depending on the choice of parameters of the $χ$ scalar potential and the Higgs portal coupling constant $ γ$, one can identify different regions: If $γ$ is sufficiently small a $χ$ halo is created around the monopole core which in turn surrounds a black-hole. For larger values of $γ$ no halo exists and the solution is just a black hole-monopole one. When the horizon radius grows and becomes larger than the monopole radius solely a black hole solution exists. Because of the presence of the $χ$ scalar a bound for the Higgs potential coupling constant exists and when it is not satisfied, the vacuum is unstable and no non-trivial solution exists. We briefly comment on a possible connection of our results with those found in recent dark matter axion models.