Boson stars and solitons confined in a Minkowski box

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-Nordstrom 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-Nordstrom 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.