Charged scalar quasi-normal modes for linearly charged dilaton-Lifshitz solutions

Most available studies of quasi-normal modes for Lifshitz black solutions are limited to the neutral scalar perturbations. In this paper, we investigate the wave dynamics of massive charged scalar perturbation in the background of $(3+1)$-dimensional charged dilaton Lifshitz black branes/holes. We disclose the dependence of the quasi-normal modes on the model parameters, such as the Lifshitz exponent $z$, the mass and charge of the scalar perturbation field and the charge of the Lifshitz configuration. In contrast with neutral perturbations, we observe the possibility to destroy the original Lifshitz background near the extreme value of charge where the temperature is low. We find out that when the Lifshitz exponent deviates more from unity, it is more difficult to break the stability of the configuration. We also study the behavior of the real part of the quasi-normal frequencies. Unlike the neutral scalar perturbation around uncharged black branes where an overdamping was observed to start at $z=2$ and independent of the value of scalar mass, our observation discloses that the overdamping starting point is no longer at $z=2$ and depends on the mass of scalar field for charged Lifshitz black branes. For charged scalar perturbations, fixing $m_s$, the asymptotic value of $\omega_R$ for high $z$ is more away from zero when the charge of scalar perturbation $q_s$ increases. There does not appear the overdamping.