We study compact gravitating Q-ball, Q-shell solutions in a sigma model with the target space CP N . Models with odd integer N and suitable potential can be parameterized by N -th complex scalar fields and they support compact solutions. A coupling with gravity allows for harboring of the Schwarzschild black holes for the Q-shell solutions. The energy of the solutions behaves as E ∼ |Q| 5/6 , where Q stands for the U (1) Noether charge, for both the gravitating and the black hole solutions. Notable difference from the solutions of the flat space is that upper bound of |Q| appears when the coupling with gravity is stronger. The maximal value of |Q| quickly reduces for larger coupling constant. It may give us a useful hint of how a star forms its shape with a certain finite number of particles. *

No abstract

Phase diagrams of the boson stars and shells of the U (1) gauged CP 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 coexistence of the electromagnetism and the 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.

No abstract

Coupled multi-component ℂPN models with V-shaped potentials are analyzed. It is shown that the model has solutions being combinations of compact Q-balls and Q-shells. The compact nature of solutions permits the existence of novel harbor-type solutions having the form of Q-balls sheltered by Q-shells. The relation between the energy E and Noether charge Q is discussed both analytically and numerically. The energy of the solutions behaves as E ∼ |Q|α, α < 1, i.e., as for the standard Q-ball. Furthermore, the ratio E/Q for various configurations in the multi-component model suggests that the solutions are at least classically stable.