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.

13 pages, 11 figures, corrected typos

References in corpus (7)

• Compact Q-balls and Q-shells in a scalar electrodynamics
• Some stationary properties of a $Q$-ball in arbitrary space dimensions
• Compact Q-balls in the complex signum-Gordon model
• Stability of Q-balls and Catastrophe
• Unified picture of Q-balls and boson stars via catastrophe theory
• Boson Shells Harbouring Charged Black Holes
• Charged Compact Boson Stars and Shells in the Presence of a Cosmological Constant

Cited by in corpus (4)

• 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
• Compact Q-balls and Q-shells in a multi-component $\mathbb{C}{P}^N$ model