Abstract In the Einstein-Bardeen model coupled to a free complex scalar field, the introduction of the scalar field prevents the formation of an event horizon. When the magnetic charge q exceeds a certain critical value, a frozen Bardeen-boson star can be obtained with the frequency 0. In this paper, we extend this model by including a charged scalar field and obtain two types of solutions: the small q solution and the large q solution. For the small q solution, we find that there exists a maximum value for the charge q; the introduction of charge makes it possible to obtain frozen star solutions without requiring the frequency to approach zero. For the large q solution, the charge can tend toward infinity.
Huang et al. (Tue,) studied this question.
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