Fingerprinting the Fractional Order Phase Transitions in AdS Black Holes

Abstract

In this paper, we have extended and deepened the study on fractional order phase transition (FPT) of a charged AdS black hole. We have carried out a detailed analysis of FPT for several AdS black hole prototypes: black hole surrounded by quintessence background, 5D Gauss-Bonnet, D dimensional RN-AdS BH, and lastly Kerr black holes. We have shown that the 4/3 order FPT at critical points holds for the first three black holes systems, while for Kerr black holes, the fractional order is rather 1/3. These results suggest two remarkable features: Firstly 4/3 order phase transition can be assumed for asymptotically AdS black holes spherical solutions; secondly the fractional order is not universal and can be affected by the geometric symmetry.

Fractional phase transitions of RN-AdS black holes at their Davies points*

“…However, using fractional derivatives, we determine that at the first type of Davies point, the phase transition is of the order of . At the second type of Davies point, a -order phase transition is observed, which is the same as the result obtained in the extended phase space [31]. Therefore, this generalized classification can indeed offer additional details on the critical behaviors of black holes.…”

“…Hilfer proposed a type of generalized Ehrenfest classification that classified the phase transition according to the continuity of the fractional derivatives of free energy [29,30]. Inspired by Hilfer's research, we reanalyze the phase transition of the RN-AdS black hole using the gen-eralized Ehrenfest classification and determine that the order of phase transition at the critical point should be and not [31]. At present, the generalized Ehrenfest classification is primarily used to deal with the phase transition at critical (Davies) points; hence, these do not affect the original phase structure of black holes.…”

Demystifying the fractional order phase transitions in AdS black holes

“…Indeed, the electric charge plays a primordial role which gives rise to a small/large BH phase transition analogous to that usually found in ordinary thermodynamic systems [6]. Since then, many similar thermodynamical studies for other solutions of black holes have been performed [7,8,1].…”

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In this work, we performed a detailed study of the fractional order phase transition (FPT) for several AdS black hole prototypes [1]. Our objective is to see whether the FPT 4/3 order at critical points reported in [2] is universal.

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Fractional order phase transition based on Q − Φ criticality of RN-AdS black hole

“…Indeed, based on the P − V criticality, it was found that the order of phase transition of RN-AdS black hole at the critical point is in fact 4/3, but not 2. Chabab and Iraoui [31] found that the order of phase transition is 1/3 for Kerr-AdS black holes. That means the GEC can indeed refine the types of phase transition of thermodynamic systems.…”