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.

We study a holographic construction of quantum rotating BTZ black holes that incorporates the exact backreaction from strongly coupled quantum conformal fields. It is based on an exact four-dimensional solution for a black hole localized on a brane in AdS₄, first discussed some years ago but never fully investigated in this manner. Besides quantum CFT effects and their backreaction, we also investigate the role of higher-curvature corrections in the effective three-dimensional theory. We obtain the quantum-corrected geometry and the renormalized stress tensor. We show that the quantum black hole entropy, which includes the entanglement of the fields outside the horizon, satisfies the first law of thermodynamics exactly, even in the presence of backreaction and with higher-curvature corrections, while the Bekenstein-Hawking-Wald entropy does not. This result, which involves a rather non-trivial bulk calculation, shows the consistency of the holographic interpretation of braneworlds. We compare our renormalized stress tensor to results derived for free conformal fields, and for a previous holographic construction without backreaction effects, which is shown to be a limit of the solutions in this article.

The connection between black hole thermodynamics and chemistry is extended to the lower-dimensional regime by considering the rotating and charged Bañados, Teitelboim, and Zanelli (BTZ) metric in the ($2+1$)-dimensional and ($1+1$)-dimensional limits of Einstein gravity. The Smarr relation is naturally upheld in both BTZ cases, where those with $Q\ne 0$ 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 $D\to 0$ 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 $(1+1)\text{−}D$ 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 $D\to 2$ black holes exhibit any interesting phase behavior.

Holographic braneworlds are used to present a higher-dimensional origin of extended black hole thermodynamics. In this framework, classical, asymptotically anti–de Sitter black holes map to quantum black holes in one dimension less, with a conformal matter sector that backreacts on the brane geometry. Varying the brane tension alone leads to a dynamical cosmological constant on the brane, and, correspondingly, a variable pressure attributed to the brane black hole. Thus, standard thermodynamics in the bulk, including a work term coming from the brane, induces extended thermodynamics on the brane, exactly, to all orders in the backreaction. A microsopic interpretation of the extended thermodynamics of specific quantum black holes is given via double holography.

We study the corrections to the Casimir effect in the classical geometry of two parallel metallic plates, separated by a distance a, due to the presence of a minimal length ($\hbar${}$\beta${}) arising from quantum mechanical models based on a generalized uncertainty principle (GUP). The approach for the quantization of the electromagnetic field is based on projecting onto the maximally localized states of a few specific GUP models and was previously developed to study the Casimir-Polder effect. For each model we compute the lowest order correction in the minimal length to the Casimir energy and find that it scales with the fifth power of the distance between the plates a-5 as opposed to the well known QED result which scales as a-3 and, contrary to previous claims, we find that it is always attractive. The various GUP models can be in principle differentiated by the strength of the correction to the Casimir energy as every model is characterized by a specific multiplicative numerical constant.