$\ell$-Boson stars

Abstract: We present new, fully nonlinear numerical solutions to the static, spherically symmetric Einstein-Klein-Gordon system for a collection of an arbitrary odd number $N$ of complex scalar fields with an internal $U(N)$ symmetry and no self-interactions. These solutions, which we dub $\ell$-boson stars, are parametrized by an angular momentum number $\ell=(N-1)/2$, an excitation number $n$, and a continuous parameter representing the amplitude of the fields. They are regular at every point and possess a finite total mass. For $\ell = 0$ the standard spherically symmetric boson stars are recovered. We determine their generalizations for $\ell > 0$, and show that they give rise to a large class of new static configurations which might have a much larger compactness ratio than $\ell=0$ stars.

• The paper extends known boson star solutions by incorporating non-zero angular momentum ℓ configurations that yield higher compactness than conventional ℓ = 0 models.
• The paper derives and numerically solves the spherically symmetric Einstein-Klein-Gordon field equations for multiple scalar fields, ensuring regular solutions across space.
• The paper reveals that ℓ-boson stars could mimic black holes or underpin galactic halos, motivating further studies on stability, dynamics, and astrophysical implications.

Overview of $\ell$-Boson Stars

The paper introduces a new, fully nonlinear numerical solution for the static, spherically symmetric Einstein-Klein-Gordon (EKG) system as applied to a collection of an arbitrary odd number $N$ of complex scalar fields. These configurations of boson stars are labeled by an angular momentum number $\ell=(N-1)/2$, as well as an excitation number $n$, and a continuous variable representing the amplitude of the fields. The motivation for this study stems from the potential astrophysical significance of boson stars as hypothetical objects that might exist in the universe and could mimic black holes or form the core of galactic halos.

Key Findings and Methodology

1. Generalized Solutions: The authors extended the known boson star solutions to include configurations with a non-zero angular momentum number $\ell$, resulting in what are termed $\ell$-boson stars. This generalization yields a broader class of static configurations, which possess larger compactness ratios than the traditional $\ell = 0$ boson stars.
2. Field Equations: The authors derived the spherically symmetric field equations for an ensemble of scalar fields within a fixed angular momentum number $\ell$, showcasing how these fields' stress energy-momentum tensors maintain spherical symmetry across the spacetime.
3. Numerical Analysis: Using a combination of local and global analyses, the authors employed numerical methods to solve for these $\ell$-boson stars. They demonstrated the existence of regular solutions at every point in space and compared different configurations' mass and spatial extent based on the angular momentum number.
4. Configuration Characteristics: For different values of $\ell$, the paper provides detailed data on mass and effective radius, comparing compactness across configurations. The higher the angular momentum number, the more compact the configuration becomes, leading to potentially more massive objects than $\ell = 0$ configurations.
5. Stability and Dynamics: The analysis suggests that $\ell > 0$ configurations exhibit similar features to $\ell = 0$ boson stars. Configurations with masses beneath the identified peak are generally stable under perturbations, while more massive states could lead to collapse or oscillation.

Implications and Future Directions

The introduction of $\ell$-boson stars significantly enhances the landscape of static boson star solutions, providing new routes for exploring their physical characteristics and stability conditions. This work suggests that the space of viable boson star solutions could be significantly more intricate when considering collections of scalar fields. The findings motivate further investigation into multi-state configurations involving various modes simultaneously and exploring their potential implications in astrophysical contexts and dark matter models.

Future work might extend these considerations into time-dependent settings and analyze the effect of angular momentum mediation in scalar field collapse or the formation of boson stars under dynamical conditions. Furthermore, given the role such models could play in understanding exotic astrophysical phenomena, further scrutiny into these solutions' observational signatures would be beneficial. The expansion to include interactions or the incorporation of additional symmetries could also provide more sophisticated models for boson star behavior in diverse cosmic environments.