On the linear stability of $\ell$-boson stars with respect to radial perturbations

TL;DR

This paper analyzes the linear stability of $ ext{l}$-boson stars, showing that for each angular momentum number $ ext{l}$, there are stable and unstable families, with stability determined by the maximum mass configuration.

Contribution

It generalizes previous stability analyses of boson stars to include angular momentum, deriving pulsation equations and identifying stable configurations for $ ext{l}$-boson stars.

Findings

Existence of stable $ ext{l}$-boson star families for each angular momentum $ ext{l}$.

Stable configurations oscillate with characteristic frequencies matching nonlinear simulations.

Maximum mass configuration separates stable and unstable families.

Abstract

In previous work we constructed new boson star solutions consisting of a family of massive complex scalar fields minimally coupled to gravity in which the individual fields have angular momentum, yet the configuration as a whole is static and spherically symmetric. In the present article we study the linear stability of these $\ell$-boson stars with respect to time-dependent, radial perturbations. The pulsation equations, governing the dynamics of such perturbations are derived, generalizing previous work initiated by M. Gleiser, and shown to give rise to a two-channel Schr\"odinger operator. Using standard tools from the literature, we show that for each fixed value $\ell$ of the angular momentum number, there exists a family of $\ell$-boson stars which are linearly stable with respect to radial fluctuations; in this case the perturbations oscillate in time with given characteristic frequencies which are computed and compared with the results from a nonlinear numerical simulation. Further, there is also a family of $\ell$-boson stars which are linearly unstable. The two families are separated by the configuration with maximum mass. These results are qualitatively similar to the corresponding stability results of the standard boson stars with $\ell=0$, and they imply the existence of new stable configurations that are more massive and compact than usual boson stars.