Radial stability of spherical bosonic stars and critical points

Abstract

We study radial perturbations of spherically symmetric spin-$0$ and spin-$1$ bosonic stars, computing numerically the squared frequency of the fundamental mode. We find that not all critical points $-$ where the Arnowitt-Deser-Misner mass attains an extremum $-$ correspond to zero modes. Thus, radial stability does not $\text{always}$ change at such critical points. The results are in agreement with the so-called critical point method.

23 pages, 8 figures and 6 tables

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