Universal ratios of critical physical quantities of charged AdS black holes

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 TcSc Qc is universal while Tcrc Qc 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 TcSc Qc differs from that of Pcvc Tc 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 ΦcQc Tc 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.

Ratio of critical quantities related to Hawking temperature–entanglement entropy criticality

“…With the increasing of l, the critical quantities Q c , S c and δS c increase while T c decreases. The ratio TcSc Qc is almost unchanged, just as the analytic result we obtained before showed [19]. The ratio TcδSc Qc changes slightly.…”

“…Comparing the results of this paper with those of the ratio TcSc Qc [19], one can find that both the similarities and differences exist. These two ratios are independent of the characteristic length scale l and dependent on the dimension d. These similarities further enhance the relation between the entanglement entropy and the Bekenstein-Hawking entropy.…”

“…In our recent work [19], we studied the T − S criticality of these black holes and probed the possible universal ratio for T − S criticality. Here, we listed the results for the d-dimensional (d > 3) charged AdS black hole.…”

“…They argued that the ratio ΦcQc Tc depends on both Λ and n and is not universal. In our recent work [19], we construct two ratios for the Q − Φ criticality as follows…”