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

TL;DR

We construct and analyze solitonic Hayward boson stars (SHBSs) in Anti-de Sitter spacetime by coupling Einstein gravity to a nonlinear electromagnetic field and a complex scalar with a solitonic potential. A critical magnetic charge $q_c$ governs frozen behavior as $ω\to0$, with $q_c$ depending on the cosmological constant $Λ$ and the self-interaction $η$, and frozen interiors occurring for $q\ge q_c$ only within a finite parameter window; decreasing $Λ$ can destroy the frozen state. For $q<q_c$ the solutions exhibit spiraling $M$–$ω$ relations and a rich light-ring structure, while for $q\ge q_c$ extreme ($ω\to0$) solutions appear, accompanied by an additional pair of light rings on the second branch; increasing $η$ can move high-frequency solutions toward pure Hayward geometry, or suppress freezing at low frequencies. Overall, the work maps out the interplay of magnetic charge, AdS curvature, and self-interaction in shaping SHBSs, their horizon-like features, and photon orbits, with potential implications for holographic duals and extensions to higher dimensions.

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 $ω\rightarrow 0$, 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 $Λ$ 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 $Λ$ and the self-interaction coupling $η$. We also found that for high frequency solutions, increasing $η$ can yield a pure Hayward solution. However, for low frequency solutions, increasing $η$ 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.

Figures (15)

• Figure 1: The ADM mass $M$ (solid line) and Noether charge $Q$ (dashed line) as a function of frequency $\omega$ with $q<q_c$ at $\eta^2 = \{1,2,5\}$. The left panels corresponds to $\Lambda=0$, the right panels corresponds to $\Lambda=-0.5$.
• Figure 2: The ADM mass $M$ (solid line) and Noether charge $Q$ (dashed line) as a function of $\omega$ with different $\Lambda$ at $q=0.3,\ \eta^2 = 1$.
• Figure 3: The scalar field $\phi$, metric functions $-g_{tt}=N\,\sigma^2$ and $1/g_{rr}=N$ as functions of $x$ with $q=0.46$. The left (right) panels corresponds to $\Lambda = 0$ ($\Lambda = -0.5)$.
• Figure 4: The effective potential $V_{eff}$ as a function of $r$ with different $\omega$ at $q=0.3,\ \eta^2 = 1$ and $\Lambda=-0.1$. The left and right panels correspond to the first and second branch solutions of SHBSs, respectively.
• Figure 5: The position of light ring $R_{LR}$ as a function of frequency $\omega$ for different parameters. The solid and dashed lines correspond to the first and second branch solutions, respectively.