Boson stars in the $U(1)$ gauged 3+1 dimensional $O(3)$ sigma-model

Abstract

We study regular self-gravitating non-topological soliton solutions of the $U(1)$ gauged non-linear $O(3)$ sigma model with the usual kinetic term and a simple symmetry breaking potential in 3+1 dimensional asymptotically flat spacetime. Both parity-even and parity-odd configurations with an angular node of the scalar field are considered. Localized solutions are endowed with an electric charge, spinning configurations are also coupled to the toroidal flux of magnetic field. We confirm that such solutions do not exist in the flat space limit. Similar to the usual boson stars, a spiral-like frequency dependence of the mass and the Noether charge of the gauged solutions is observed. Depending on the relative strength of gravity and the electromagnetic interaction, the resulting gauged $O(3)$ boson stars at the mass threshold either possess the usual Newtonian limit, or they are linked to a regular strongly gravitating critical configuration. We explore domain of existence of the solutions and investigate some of their physical properties.