Abstract
Phase diagrams of the boson stars and shells of the $U(1)$ gauged $\mathbb{C}{P}^{N}$ nonlinear sigma model are studied. The solutions of the model exhibit both the ball- and the shell-shaped charge density depending on $N$. There appear four independent regions of the solutions which are essentially caused from the coexistence of electromagnetism and gravity. We examine several phase diagrams of the boson stars and the shells and discuss what and how the regions are emerged. A coupling with gravity allows for harboring of the charged black holes for the $Q$-shell solutions. Some solutions are strongly affected by the presence of the black holes and they allow to be smoothly connected. As a result, the regions are integrated by the harboring black holes.
Highlights
A complex scalar field theory with some self-interactions has stationary soliton solutions called Q-balls [1,2,3,4]
In supersymmetric extensions of the standard model, Q-balls appear as the scalar superpartners of baryons or leptons forming coherent states with baryon or lepton number
As it was seen in the previous section, our boson shells exhibit distinctive behavior depending on the value of the coupling constant α
Summary
A complex scalar field theory with some self-interactions has stationary soliton solutions called Q-balls [1,2,3,4]. In supersymmetric extensions of the standard model, Q-balls appear as the scalar superpartners of baryons or leptons forming coherent states with baryon or lepton number. The gravitating boson shells can harbor a Schwarzschild and a Reissner-Nordström type black hole. For the Uð1Þ gauged model [15], we observed the signal of the bifurcation and the domain structure in the solutions These boson shells harbor a Schwarzschild and a ReissnerNordström black hole. We discuss several novel results for the phase structure of our Uð1Þ gauged gravitating boson stars and shells. We observe several bifurcations of the solutions which previously were not known and give us deeper insights for the interactions forming the boson stars/shells and for the property of the harbor of the black holes.
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