Continuum spectrum of nonrelativistic multifrequency Proca stars
Phys. Rev. D 114, 023002 – Published 6 July, 2026
DOI: https://doi.org/10.1103/t8jk-v4hz
Abstract
Multifrequency Proca stars are excited self-gravitating solutions of the Schrödinger-Poisson system that generalize the conventional stationary states of a massive vector field. Unlike stationary states, which are characterized by a single oscillation frequency, multifrequency configurations exhibit a quasiperiodic dynamics involving two or three distinct frequencies. In this paper, we present a systematic study of the spectrum of spherical multifrequency Proca stars and show that, at fixed particle number, they form continuous families interpolating between discrete stationary states of constant linear polarization. Furthermore, we analyze their stability and demonstrate that a subset of these multifrequency configurations are linearly stable against general perturbations. In particular, we show that a necessary, although not sufficient, condition for stability is the presence of a non-negligible nodeless component, and that radial stability alone is not sufficient to guarantee full linear stability. Finally, we briefly discuss the potential implications of multifrequency states for proving the particle spin in ultralight dark matter models.