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.Comment: 8 pages, 6 figures, final version to appear in PR

Quasinormal modes for the scattering on a naked Reissner-Nordström singularity

“…In [22], the quasi-normal modes of a scalar field in an electrically charged Vaidya background were studied using a similar numerical setup to what we are going to use here. An interesting investigation done in [22] tried to determine what would happen with the quasi-normal modes as the time-dependent background approached a naked singularity, but the numerical code used was not suitable for following the field evolution after the extremal configuration (q = m) was reached. In our present work, we have a static configuration that describes a naked a singularity in order to study the properties of the quasinormal modes.…”

Hyperboloidal slices for the wave equation of Kerr–Schild metrics and numerical applications

“…Our framework is general enough to cover metrics of the Kerr-Schild form. Thus, our approach could be applied in the numerical analysis of quasi-normal modes in Vaidya [14], and more generally, in time-dependent non-axisymmetric Kerr-Schild spacetimes.…”

Gravitational waves from scalar field accretion

“…In reference [27] the author considered a time dependent potential and showed that the tail behavior actually changes from the standard time independent potential. This phenomena was also considered in references [28] where the authors considered a Vaidya spacetime where the explicit change in the parameters of the black hole is reflected in the quasi normal frequencies of the scattered field.…”