Radial stability of spherical bosonic stars and critical points

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 always change at such critical points. The results are in agreement with the so-called critical point method.