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arXiv · 1703.08654

Universal ratios of critical physical quantities of charged AdS black holes

Jie-Xiong Mo·Gu-Qiang Li·Xiao-Bao Xu
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Abstract

We investigate the ratios of critical physical quantities related to the $T-S$ criticality of charged AdS black holes. It is shown that the ratio $\frac{T_cS_c}{Q_c}$ is universal while $\frac{T_cr_c}{Q_c}$ is not. This finding is quite interesting considering the former observation that both the $T-S$ graph and $T-r_+$ graph exhibit reverse van der Waals behavior. It is also worth noting that the value of $\frac{T_cS_c}{Q_c}$ differs from that of $\frac{P_cv_c}{T_c}$ for $P-V$ criticality. Moreover, we discuss universal ratios for the $P-V$ criticality and $Q-Φ$ criticality. We successfully interpret the former finding that the ratio $\frac{Φ_cQ_c}{T_c}$ is not universal and construct two universal ratios for the $Q-Φ$ criticality instead. To the best of our knowledge, we are the first to introduce the dimensional analysis technique to study the ratios of critical physical quantities. It is expected that this technique can be generalized to probe the universal ratios for $Y-X$ criticality in future research.

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Jie-Xiong Mo, Gu-Qiang Li, Xiao-Bao Xu. 2017-03-25. Universal ratios of critical physical quantities of charged AdS black holes. https://doi.org/10.1088/1475-7516%2F2018%2F07%2F017

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