Abstract:We investigate the effects of higher curvature corrections from Lovelock gravity on the phase structure of asymptotically AdS black holes, treating the cosmological constant as a thermodynamic pressure. We examine how various thermodynamic phenomena, such as Van der Waals behaviour, reentrant phase transitions (RPT), and tricritical points are manifest for U(1) charged black holes in Gauss-Bonnet and 3rd-order Lovelock gravities. We furthermore observe a new phenomenon of 'multiple RPT' behaviour, in which for fixed pressure the small/large/small/large black hole phase transition occurs as the temperature of the system increases. We also find that when the higher-order Lovelock couplings are related in a particular way, a peculiar isolated critical point emerges for hyperbolic black holes and is characterized by non-standard critical exponents.

The connection between black hole thermodynamics and chemistry is extended to the lowerdimensional regime by considering the rotating and charged BTZ metric in the (2 + 1)-D and a (1 + 1)-D limits of Einstein gravity. The Smarr relation is naturally upheld in both BTZ cases, where those with Q = 0 violate the Reverse Isoperimetric Inequality and are thus superentropic. The inequality can be maintained, however, with the addition of a new thermodynamic work term associated with the mass renormalization scale. The D → 0 limit of a generic D + 2-dimensional Einstein gravity theory is also considered to derive the Smarr and Komar relations, although the opposite sign definitions of the cosmological constant and thermodynamic pressure from the D > 2 cases must be adopted in order to satisfy the relation. The requirement of positive entropy implies an upper bound on the mass of a (1 + 1)-D black hole. Promoting an associated constant of integration to a thermodynamic variable allows one to define a "rotation" in one spatial dimension. Neither the D = 3 nor the D → 2 black holes exhibit any interesting phase behaviour.

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