Extreme $\ell$-boson stars

TL;DR

This paper explores a new class of scalar field objects called $oldsymbol{ ext{ extit{ extl}}}$-boson stars, analyzing their properties, structure, and stability, especially for large angular parameters, revealing shell-like morphologies and finite compactness limits.

Contribution

It provides a comprehensive analysis of $oldsymbol{ ext{ extit{ extl}}}$-boson stars, including their size, mass, anisotropy, and orbit properties, especially in the large $oldsymbol{ ext{ extit{ extl}}}$ limit, extending previous knowledge.

Findings

Shell-like structure with a 'hole' in the interior

Size grows linearly with $ ext{ extl}$, faster than thickness

Compactness approaches half the Buchdahl limit for stability

Abstract

A new class of complex scalar field objects, which generalize the well known boson stars, was recently found as solutions to the Einstein-Klein-Gordon system. The generalization consists in incorporating some of the effects of angular momentum, while still maintaining the spacetime's spherical symmetry. These new solutions depend on an (integer) angular parameter $\ell$, and hence were named $\ell$-boson stars. Like the standard $\ell=0$ boson stars these configurations admit a stable branch in the solution space; however, contrary to them they have a morphology that presents a shell-like structure with a "hole" in the internal region. In this article we perform a thorough exploration of the parameter space, concentrating particularly on the extreme cases with large values of $\ell$. We show that the shells grow in size with the angular parameter, doing so linearly for large values, with the size growing faster than the thickness. Their mass also increases with $\ell$, but in such a way that their compactness, while also growing monotonically, converges to a finite value corresponding to about one half of the Buchdahl limit for stable configurations. Furthermore, we show that $\ell$-boson stars can be highly anisotropic, with the radial pressure diminishing relative to the tangential pressure for large $\ell$, reducing asymptotically to zero, and with the maximum density also approaching zero. We show that these properties can be understood by analyzing the asymptotic limit $\ell\rightarrow\infty$ of the field equations and their solutions. We also analyze the existence and characteristics of both timelike and null circular orbits, especially for very compact solutions.