Boson stars and solitons confined in a Minkowski box

Abstract

We consider the static charged black hole bomb system, originally designed for a (uncharged) rotating superradiant system by Press and Teukolsky. A charged scalar field confined in a Minkowski cavity with a Maxwell gauge field has a quantized spectrum of normal modes that can fit inside the box. Back-reacting non-linearly these normal modes, we find the hairy solitons, a.k.a boson stars (depending on the chosen U(1) gauge), of the theory. The scalar condensate is totally confined inside the box and, outside it, we have the Reissner-Nordström solution. The Israel junction conditions at the box surface layer determine the stress tensor that the box must have to confine the scalar hair. Some of these horizonless hairy solutions exist for any value of the scalar field charge and not only above the natural critical charges of the theory (namely, the critical charges for the onset of the near-horizon and superradiant instabilities of the Reissner-Nordström black hole). However, the ground state solutions have a non-trivial intricate phase diagram with a main and a secondary family of solitons (some with a Chandrasekhar mass limit but others without) and there are a third and a fourth critical scalar field charges where the soliton spectra changes radically. Most of these intricate properties are not captured by a higher order perturbative analysis of the problem where we simply back-react a normal mode of the system.

Phase diagram of the charged black hole bomb system

“…This perturbative analysis is bound to capture only small mass/charge boson stars. But a full numerical nonlinear analysis can identify the whole phase space of boson stars [28]. This analysis further reveals that the phase diagram of boson stars is quite elaborate with distinct boson star families.…”

“…The discussion only includes aspects that guarantee that our exposition is self-contained and more details can be found in [26]. In section 4 we explicitly construct the hairy black hole solutions in the four relevant windows of scalar charge that, together with the boson star study of [28], allow us to arrive to the conclusions summarized in section 2. Finally, in section 5 we explain how data of the hairy solution inside the box can be used to find the Israel stress tensor of the cavity surface layer and be matched with the exterior Reissner-Nordstöm solution.…”

“…This task was completed in detail in the companion paper [28]. A phase diagram that summarizes the relevant properties for the present study is displayed in the right panel of figure 1 [28]. Note that it stores in a single plot the solitons for different theories, i.e.…”

“…for several distinct values of e. Two families of ground state boson stars (i.e. with smallest energy for a given charge) where found in [28]. One is the main or perturbative boson star family which can be found within perturbation theory if we back-react a normal mode of a Minkowski cavity to higher orders.…”

“…From the left panel of figure 1, one concludes that RN is stable for e < e NH and thus no hairy BHs exist. The only non-trivial solutions of the theory are the RN BH and the main/perturbative boson star which has a Chandrasekhar limit (see details in [28]).…”