The phase transition and the Quasi-Normal Modes of black Holes

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We reexamined the argument that the quasinormal modes could be a probe of the phase transition of a topological black hole to a hairy configuration by investigating general scalar perturbations. We found further evidence in the quasinormal modes for this phase transition. For the general black hole configurations, we observed that although the quasinormal modes can present us different phases of different configurations, there is no dramatic change in the slope of quasinormal frequencies at the critical point of the phase transition. More detailed studies of quasinormal modes are needed to reveal the subtle behavior of the phase transition.