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

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 Schrödinger 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.

arXiv comment23, pages, 8 figures

References in corpus (12)

• TOPICAL REVIEW: General relativistic boson stars
• Dynamical Boson Stars
• Formation of Solitonic Stars Through Gravitational Cooling
• Gravitational Wave Signatures of Highly Compact Boson Star Binaries
• Gravitational Stability of Boson Stars
• Dynamical Evolution of Boson Stars II: Excited States and Self-Interacting Fields
• Non-linear dynamics of spinning bosonic stars: formation and stability
• Boson stars driven to the brink of black hole formation
• $\ell$-Boson stars
• Dynamical evolutions of $\ell$-boson stars in spherical symmetry
• Critical Behavior in the Gravitational Collapse of a Scalar Field with Angular Momentum in Spherical Symmetry
• Dynamical $\ell$-boson stars: generic stability and evidence for non-spherical solutions

Cited by in corpus (11)

• Dynamical Boson Stars
• Boson Stars and Oscillatons: A Review
• Head-on collisions of $\ell$-boson stars
• Boson stars and their relatives in semiclassical gravity
• Extreme $\ell$-boson stars
• Bayesian analysis for rotational curves with $\ell$-boson stars as a dark matter component
• On the radial linear stability of nonrelativistic $\ell$-boson stars
• Are nonrelativistic ground state $\ell$-boson stars only stable for $\ell =0$ and $\ell =1$?
• Assessing the stability of ultracompact spinning boson stars with nonlinear evolutions
• Noble gravitational atoms: Self-gravitating black hole scalar wigs with angular momentum number
• $\ell$-Boson stars in anti-de Sitter spacetime