Nonstationary regime for quasinormal modes of the charged Vaidya metric

Abstract: We consider non-stationary spherically symmetric $n$-dimensional charged black holes with varying mass $m(v)$ and/or electric charge $q(v)$, described by generic charged Vaidya metrics with cosmological constant $\Lambda$ in double null coordinates, and perform a comprehensive numerical analysis of the fundamental quasinormal modes (QNM) for minimally coupled scalar fields. We show that the "instantaneous" quasinormal frequencies exhibit the same sort of non-stationary behavior reported previously for the four-dimensional uncharged case with $\Lambda=0$. Such property seems to be very robust, independent of the spacetime dimension and of the metric parameters, provided they be consistent with the existence of an event horizon. The study of time dependent Reissner-Nordstr\"om black holes allows us to go a step further and quantify the deviation of the stationary regime for QNM with respect to charge variations as well. We also look for signatures in the quasinormal frequencies from the creation of a Reissner-Nordstr\"om naked spacetime singularity. Even though one should expect the breakdown of our approach in the presence of naked singularities, we show that it is possible, in principle, to obtain some information about the naked singularity from the QNM frequencies, in agreement with the previous results of Ishibashi and Hosoya showing that it would be indeed possible to have regular scattering from naked singularities.