Abstract
In this work, we investigate the time evolution of a massless scalar perturbation around small and large \(\text{RN-AdS}_{4}\) black holes for the purpose of probing the thermodynamic phase transition. We show that below the critical point the scalar perturbation decays faster with increasing of the black hole size, both for small and large black hole phases. Our analysis of the time profile of quasinormal mode reveals a sharp distinction between the behaviors of both phases, providing a reliable tool to probe the black hole phase transition. However at the critical point \(P=P_{c}\), as the black hole size extends, we note that the damping time increases and the perturbation decays faster, the oscillation frequencies raise either in small and large black hole phase. In this case the time evolution approach fails to track the \(\text{AdS}_{4}\) black hole phase.
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Acknowledgements
The authors are grateful to Prof. Victor Santos for useful discussion and comments. This work is supported in part by the Groupement de recherche international (GDRI): Physique de l’infiniment petit et de l’infiniment grand—P2IM.
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Chabab, M., El Moumni, H., Iraoui, S. et al. Phase transition of charged-AdS black holes and quasinormal modes: A time domain analysis. Astrophys Space Sci 362, 192 (2017). https://doi.org/10.1007/s10509-017-3175-z
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DOI: https://doi.org/10.1007/s10509-017-3175-z