# Dynamical evolutions of $\ell$-boson stars in spherical symmetry

## TL;DR

This paper investigates the stability and evolution of $ ext{l}$-boson stars, a generalization of boson stars with angular momentum, through non-linear simulations, revealing stable and unstable regimes and their possible outcomes.

## Contribution

It introduces $ ext{l}$-boson stars with fixed angular momentum and analyzes their stability and dynamical behavior via fully non-linear simulations.

## Key findings

- Stable configurations oscillate and slowly return to equilibrium.
- Unstable configurations can collapse, migrate, or explode.
- The maximum mass configuration separates stable and unstable regions.

## Abstract

In previous work, we have found new static, spherically symmetric boson star solutions which generalize the standard boson stars by allowing a particular superposition of scalar fields in which each of the fields is characterized by a fixed value of its non-vanishing angular momentum number $\ell$. We call such solutions "$\ell$-boson stars". Here, we perform a series of fully non-linear dynamical simulations of perturbed $\ell$-boson stars in order to study their stability, and the final fate of unstable configurations. We show that for each value of $\ell$, the configuration of maximum mass separates the parameter space into stable and unstable regions. Stable configurations, when perturbed, oscillate around the unperturbed solution and very slowly return to a stationary configuration. Unstable configurations, in contrast, can have three different final states: collapse to a black hole, migration to the stable branch, or explosion (dissipation) to infinity. Just as it happens with $\ell=0$ boson stars, migration to the stable branch or dissipation to infinity depends on the sign of the total binding energy of the star: bound unstable stars collapse to black holes or migrate to the stable branch, whereas unbound unstable stars either collapse to a black hole or explode to infinity. Thus, the parameter $\ell$ allows us to construct a new set of stable configurations. All our simulations are performed in spherical symmetry, leaving a more detailed stability analysis including non-spherical perturbations for future work.