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

TL;DR

This paper constructs and analyzes frozen solitonic Hayward-boson stars in Anti-de Sitter spacetime, revealing critical charge effects, solution behaviors, and unique light ring structures, advancing understanding of scalar field configurations in curved spacetime.

Contribution

It introduces the concept of frozen solitonic Hayward-boson stars in AdS spacetime, exploring their properties, critical parameters, and solution branches, which is a novel addition to scalar field star models.

Findings

Existence of a critical magnetic charge $q_c$ affecting solution structure.

Disruption of frozen states with decreasing cosmological constant $ abla$.

Identification of an extra light ring in the second solution branch.

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.