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arXiv · 2302.00717

On the radial linear stability of nonrelativistic $\ell$-boson stars

Armando A. Roque·Emmanuel Chávez Nambo·Olivier Sarbach
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Abstract

We study the linear stability of nonrelativistic $\ell$-boson stars, describing static, spherically symmetric configurations of the Schr\"odinger-Poisson system with multiple wave functions having the same value of the angular momentum $\ell$. In this work we restrict our analysis to time-dependent perturbations of the radial profiles of the $2\ell+1$ wave functions, keeping their angular dependency fixed. Based on a combination of analytic and numerical methods, we find that for each $\ell$, the ground state is linearly stable, whereas the $n$'th excited states possess $2n$ unstable (exponentially in time growing) modes. Our results also indicate that all excited states correspond to saddle points of the conserved energy functional of the theory.

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Armando A. Roque, Emmanuel Chávez Nambo, Olivier Sarbach. 2023-02-01. On the radial linear stability of nonrelativistic $\ell$-boson stars. https://doi.org/10.1103/physrevd.107.084001

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