Non-Topological Soliton Bardeen Boson Stars and Their Frozen States

TL;DR

This paper explores non-topological soliton boson stars in a Bardeen model, revealing critical magnetic charges for frozen states, their properties, and universal light ring solutions, with implications for black hole mimickers.

Contribution

It introduces the concept of frozen states in Bardeen boson stars and analyzes their properties, including critical charges, horizon characteristics, and light ring solutions, expanding understanding of non-topological soliton configurations.

Findings

Frozen states occur beyond critical magnetic charge values.

Frozen BBSs have a critical horizon radius between RN black hole horizons.

All frozen BBSs exhibit universal light ring solutions.

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 $\tilde{q}$, the complex scalar field frequency $\tilde{\omega}$, and the self-interaction parameter $\tilde{\eta}$. Our results reveal that the magnetic charge $\tilde{q}$ exhibits $\tilde{\eta}$-dependent critical values $\tilde{q}_c$, beyond which ($\tilde{q} > \tilde{q}_c$) Bardeen boson stars (BBSs) may transition into frozen states ($\tilde{\omega} \to 0$). These frozen states are characterized by a critical horizon whose radius $\tilde r^\mathrm{H}_{c}$ satisfies $\tilde r_{\text{inner}}^{\text{H,RN}} < \tilde r_{c} < \tilde r_{\text{outer}}^{\text{H,RN}}$, where $\tilde r_{\text{inner}}^{\text{H,RN}}$ and $\tilde r_{\text{outer}}^{\text{RN}}$ denote the inner and outer horizons of magnetic Reissner-Nordstr\"{o}m (RN) black holes with equivalent mass and magnetic charge. Notably, the ADM mass of frozen BBSs is independent of $\tilde{\eta}$. Furthermore, light ring (LR) solutions exist universally across all tested combinations of $\tilde{q}$ and $\tilde{\eta}$, with all frozen BBSs exhibiting LRs whose outer radius $\tilde r_{\text{outer}}^{\text{LR}}$ is independent of $\tilde{\eta}$. Compared to magnetic RN black holes, frozen BBSs possess a smaller outer LR radius ($\tilde r_{\text{outer}}^{\text{LR}} < \tilde r_{\text{outer}}^{\text{LR, RN}}$).