$\ell$-Boson stars in anti-de Sitter spacetime

TL;DR

This work extends the study of $\\ell$-boson stars to anti-de Sitter spacetimes by constructing static, spherically symmetric solutions of the Einstein-Klein-Gordon equations with an AdS cosmological constant. The model uses an odd number of complex scalars with equal mass and an ansatz that yields a common radial profile but nontrivial angular dependence, preserving spherical symmetry in the metric. A detailed boundary-value analysis reveals a discrete spectrum $\\omega_{\\ell,n}$ and two equivalent formulations (non-compact and compact) to facilitate numerical shooting, with a low-mass analytic spectrum $L \,\\omega_{\\ell,n}^{(0)} = 2n + \\ell + \\frac{3}{2} + \\frac{1}{2} \\\sqrt{4 (L \\mu)^2 + 9}$ agreeing with full solutions. Numerically, ground-state solutions up to $\\ell=15$ show thick-shell density profiles, mass increasing with $\\ell$, and a growing compactness; notably, for $\\ell \\ge 6$ light rings appear in the first region, enabling zones without circular orbits bounded by light rings. The results highlight distinctive AdS features, including enhanced compactness and light-ring structure, while leaving a full stability analysis for future work.

Abstract

In previous work, we introduced the $\ell$-boson stars, a generalization of standard boson stars, which are parameterized by an angular momentum number $\ell$, while still preserving the spacetime's spherical symmetry. In this article, we present and study the properties of $\ell$-boson stars in spacetimes with a negative cosmological constant, such that they are asymptotically anti-de Sitter.

Figures (5)

• Figure 1: Field profiles for $\mu=0$ in the maximum mass cases.
• Figure 2: Density profiles for $\mu=0$ in the maximum mass cases.
• Figure 3: Total mass $M$ vs frequency $\omega_\ell$ for $\mu=0$ and $L \mu=1$.
• Figure 4: Compactness of maximum mass solutions vs. $\ell$.
• Figure 5: Types of circular orbits for solutions with $\mu=0$ and $\ell=10$.