Reentrant phase transitions in rotating anti–de Sitter black holes

Abstract

We study the thermodynamics of higher-dimensional singly spinning asymptotically AdS black holes in the canonical (fixed J) ensemble of extended phase space, where the cosmological constant is treated as pressure and the corresponding conjugate quantity is interpreted as thermodynamic volume. Along with the usual small/large black hole phase transition, we find a new phenomenon of reentrant phase transitions for all d ≥ 6 dimensions, in which a monotonic variation of the temperature yields two phase transitions from large to small and back to large black holes. This situation is similar to that seen in multicomponent liquids. Introduction. In view of the AdS/CFT correspondence, phase transitions in asymptotically AdS black holes allow for a dual interpretation in the thermal conformal field theory (CFT) living on the AdS boundary-the principal example being the well known radiation/Schwarzschild-AdS black hole Hawking-Page transition [1] which can be interpreted as a confinement/deconfinement phase transition in the dual quark gluon plasma [2]. Charged [3-6] and rotating [7,8] asymptotically AdS back holes possess an interesting feature-they allow for a first order small-blackhole/large-black-hole phase (SBH/LBH) transition which is in many ways reminiscent of the liquid/gas transition of the Van der Waals fluid. This superficial analogy was recently found more intriguing [9] by considering a thermodynamic analysis in an extended phase space where the cosmological constant is identified with thermodynamic pressure and its variations are included in the first law of black hole thermodynamics. This notion emerges from geometric derivations of the Smarr formula [10] that i) imply the mass of an AdS black hole should be interpreted as the enthalpy of the spacetime and ii) allow for a computation of the conjugate thermodynamic volume. Intensive and extensive quantities are now properly identified [9] and the SBH/LBH transition can be understood as a liquid/gas phase transition by employing Maxwell's equal area law to the P − V diagram. Coexistence lines and critical exponents are then seen to match those of a Van der Waals fluid.

Analytical and exact critical phenomena ofd-dimensional singly spinning Kerr-AdS black holes

“…[50] that, when d ≥ 6, the reentrant phase transitions occur. The P -T phase diagram can be found in Fig.…”

“…The isobar behaves differently at different pressures (for details, one can see Refs. [49][50][51]). Considering that the black hole near the first critical point always has a higher Gibbs free energy than the very large black hole, the first critical point will not emerge in the phase diagram.…”

“…The authors of Ref. [50] first found the reentrant large/small/large black hole phase transition in the d = 6-dimensional singly spinning Kerr-AdS black hole system. For the d = 6-dimensional multiply spinning Kerr-AdS black hole with two fixed angular momenta J 1 and J 2 , the system has a triple point and solid/liquid/gas analogue phase transition in some parameter ranges [51], and more than one critical point was found.…”

$$P$$ P – $$V$$ V criticality of AdS black hole in the Einstein–Maxwell–power-Yang–Mills gravity

“…Until now, these critical behaviour of a lot of black hole systems in this extended phase space are under discussion in this direction [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. It is worth to noting that, in four-dimensional Born-Infeld AdS black holes [4], the impact of the nonlinearity can bring the new phenomenon of reentrant phase transition which was observed in rotating AdS holes [19,20], while this reentrant phase transition does not occur for higher dimensional Born-Infeld AdS black holes [21].…”

Phase Transitions of Regular Schwarzschild-anti-deSitter Black Holes

“…giving rise to several effects (see for example [9,10,11]). In such a case the equation of state P (V, T ) for the regular AdS black hole becomes…”