Quasinormal modes for the charged Vaidya metric

Cecilia Chirenti and Alberto Saa

We propose a model to describe a time-dependent charged black hole, with varying mass $M(t)$ or charge $Q(t)$, using the charged Vaidya metric. The scalar wave equation is solved in this background, and the resulting time-dependent quasinormal modes are presented and analyzed. A possible astrophysical scenario is described, in which a charged black hole (whose formation we do not discuss here) could loose mass while keeping a constant amount of charge. We look for signatures in the quasinormal frequencies from the creation of a naked singularity, when the final mass of the time evolution is taken to be (asymptotically) $M_f < Q_f$. It is found that the manner in which the mass function approaches this limit is determinant for the behavior of the scattered wave.