Non-topological soliton Bardeen boson stars and their frozen states

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Abstract We investigate a Bardeen model coupling Einstein gravity with nonlinear electromagnetic fields and non-topological soliton complex scalar fields, governed by the magnetic charge $$\tilde{q}$$ q ~ , the complex scalar field frequency $$\tilde{\omega }$$ ω ~ , and the self-interaction parameter $$\tilde{\eta }$$ η ~ . Our results reveal that the magnetic charge $$\tilde{q}$$ q ~ exhibits $$\tilde{\eta }$$ η ~ -dependent critical values $$\tilde{q}_c$$ q ~ c , beyond which ( $$\tilde{q} > \tilde{q}_c$$ q ~ > q ~ c ) Bardeen boson stars (BBSs) may transition into frozen states ( $$\tilde{\omega } \rightarrow 0$$ ω ~ → 0 ). These frozen states are characterized by a critical horizon whose radius $$\tilde{r}^\textrm{H}_{c}$$ r ~ c H satisfies $$\tilde{r}_{\text {inner}}^{\text {H,RN}}< \tilde{r}_{c} < \tilde{r}_{\text {outer}}^{\text {H,RN}}$$ r ~ inner H,RN < r ~ c < r ~ outer H,RN , where $$\tilde{r}_{\text {inner}}^{\text {H,RN}}$$ r ~ inner H,RN and $$\tilde{r}_{\text {outer}}^{\text {RN}}$$ r ~ outer RN

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