Frozen solitonic Hayward-boson stars in Anti-de Sitter Spacetime

Abstract

We construct solitonic Hayward-boson stars (SHBSs) in Anti-de Sitter (AdS) spacetime, which consists of the Einstein-Hayward model and a complex scalar field with a soliton potential. Our results reveal a critical magnetic charge $q_c$. For $q\geq q_c$ in the limit of $\omega \rightarrow 0$, the matter field is primarily distributed within the critical radius $r_c$, beyond which it decays rapidly, while the metric components $-g_{tt}$ and $1/g_{rr}$ become very small at $r_c$. These solutions are termed ``frozen solitonic Hayward-boson stars" (FSHBSs). Continuously decreasing $\Lambda$ disrupts the frozen state. However, we did not find a frozen solution when $q<q_c$. The value of $q_c$ depends both on the cosmological constant $\Lambda$ and the self-interaction coupling $\eta$. We also found that for high frequency solutions, increasing $\eta$ can yield a pure Hayward solution. However, for low frequency solutions, increasing $\eta$ reduces both $1/g_{rr}$ and $-g_{tt}$. Furthermore, we analyzed the effective potential of SHBSs and identified an extra pair of light rings in the second solution branch.