Gravitating compact $Q$-ball and $Q$-shell solutions in the $\mathbb{C}{P}^N$ nonlinear sigma model

Abstract

We study compact gravitating $Q$-ball, $Q$-shell solutions in a sigma model with the target space $\mathbb{C}{P}^N$. 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 $E\sim |Q{|}^{5/6}$, 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.

arXiv comment13 pages, 11 figures, corrected typos

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Cited by in corpus (6)

• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• Charged hairy black holes in the gauged Einstein-Friedberg-Lee-Sirlin model
• Compact, charged boson-stars, -shells in the $\mathbb{C}{P}^N$ gravitating nonlinear sigma model
• Nodal compact $Q$-ball/$Q$-shell in the $\mathbb{C}{P}^N$ nonlinear sigma model
• Phase analyses for compact, charged boson stars and shells harboring black holes in the $\mathbb{C}{P}^N$ nonlinear sigma model
• Compact Q-balls and Q-shells in a multi-component $\mathbb{C}{P}^N$ model