Abstract
In this work we use the quasinormal frequencies of a massless scalar perturbation to probe the phase transition of the high dimension charged-AdS black hole. The signature of the critical behavior of this black hole solution is detected in the isobaric as well as in isothermal process. This paper is a natural generalization of \cite{base} to higher dimensional spacetime. More precisely our study shows a clear signal for any dimension $d$ in the isobaric process. As to the isothermal case, we find out that this signature can be affected by other parameters like the pressure and the horizon radius. We conclude that the quasinormal modes can be an efficient tool to investigate the first order phase transition, but fail to disclose the signature of the second order phase transition.
Highlights
The properties of quasinormal modes have been tested in the context of the AdS/CFT correspondence [11,12,13], the investigation of the stability of AdS black holes becomes more appealing
The quasinormal modes (QNMs) can be used as a powerful tool to detect the extra dimensions of spacetime, in other words the brane-world scenarios assume the existence of extra dimensions, so that multidimensional black holes can be formed in a laboratory [21,22,23,24]
In [1] the authors established a link between the Reissner-Nordström AdS black hole critical behavior and the quasinormal modes in d = 4, showing that QNM can be a dynamic probe of the thermodynamic phase transition
Summary
The properties of quasinormal modes have been tested in the context of the AdS/CFT correspondence [11,12,13], the investigation of the stability of AdS black holes becomes more appealing. In [1] the authors established a link between the Reissner-Nordström AdS black hole critical behavior and the quasinormal modes in d = 4, showing that QNM can be a dynamic probe of the thermodynamic phase transition. P–V criticality for scalar perturbations in a class of dRGT massive gravity around Black Holes Motivated by these results we find it crucial and well justified to generalize these studies to high dimensional spacetime, since a higher dimension RN–AdS black hole presents a Van der Waals like phase transition [35,37]. After having briefly introduced the main thermodynamical quantities and related phase transition, let us focus our attention on the derivation of the quasinormal frequencies of a scalar perturbation around a charged AdS black hole in high dimension spacetime
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