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.
Highlights
AdS black hole phase transitions [1]
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
Summary
Lovelock gravity [44] is a higher derivative theory that has received a lot of attention in recent years. General relativity is recovered upon setting α(k) = 0 for k ≥ 2.2 The vacuum equations of motion for Lovelock gravity, following from the Lagrangian density (2.1), are kmax. Using the Hamiltonian formalism it is possible to derive the expression for gravitational entropy in Lovelock gravity and the corresponding first law of black hole thermodynamics [57]. Both the first law and the associated Smarr formula in an extended phase space were obtained exploiting the Killing potential formalism [58]. In the extended thermodynamic phase space, all Lovelock coupling constants (including the cosmological constant α(0)) are considered as thermodynamic variables and allowed to vary in the first law of black hole thermodynamics. The physical meaning of these variables along with their conjugates, apart from the cosmological constant which has an interpretation of pressure and its conjugate variable is an associated volume, remains to be explored.
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