Snapping swallowtails in accelerating black hole thermodynamics

Abstract

The thermodynamic behaviour of a charged and accelerating AdS black hole is studied in the context of extended phase space with variable cosmological constant. When compared to the charged AdS black hole without acceleration, a remarkable new feature of `snapping swallowtails' appears. Namely, for any black hole with charge $Q$ and any string tension $\mu$ causing the acceleration of the black hole, there exists a transition pressure $P_t=3{\mu }^2/(8\pi Q^2)$ at which the standard swallowtail `snaps', causing the branch of low temperature black holes to completely disappear, leading to a pressure induced zeroth order phase transition between small and large black holes. For intermediate values of the string tension, we also observe a reentrant phase transition, as the small black hole changes to a large one and then back to small, as the pressure decreases, crossing the coexistence line of the two phases several times. We also find a new class of `mini-entropic' black holes, whose isoperimetric ratio becomes unbounded in a certain region of parameter space.

18 pages, 8 figures. Accepted for publication in Classical and Quantum Gravity