Multiple Reentrant Phase Transitions and Triple Points in Lovelock Thermodynamics

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.Comment: 50 pages, 28 Figures v2: minor corrections, references adde

Black Holes, Equilibrium, and Cosmology

We trace the origins and development of black hole thermodynamics across the past half-century, emphasizing the framework's relation to classical thermodynamics, and the vital role played by the notions of equilibrium, stationarity, and symmetry. We discuss different interpretations of the first law of black hole mechanics, and assess the validity of its mechanical, process-based interpretation for evaporating black holes. We bring these ideas to the cosmological realm, and highlight the various difficulties that arise when formulating thermodynamics for black holes in asymptotically de Sitter backgrounds. We discuss a number of proposed solutions and the open questions that arise therein.Comment: 9 pages, 1 figure. Honorable Mention for the Gravity Research Foundation 2023 Awards for Essays on Gravitatio

Euclidean and Hamiltonian Thermodynamics for Regular Black Holes

We investigate the thermodynamic properties of the Hayward regular black hole using both Euclidean path integral and Hamiltonian methods, in asymptotically anti-de Sitter, Minkowski, and de Sitter spacetimes. With the inclusion of matter fields which act as a source for the regular black hole geometry, an effective temperature emerges that differs from the conventional definition related to the Killing surface gravity. We posit that this temperature is the appropriate choice for studying thermodynamic phenomena, by demonstrating consistency between the Euclidean and Hamiltonian formulations in the appropriate limits. We examine the thermodynamic properties and phase structure of the Hayward black hole in the canonical ensemble and show that, counter to some earlier indications, standard mean-field theory critical behaviour is observed when the cosmological constant is treated as a thermodynamic pressure. We note the absence of a Hawking-Page transition, and conjecture that quantum gravity corrections which are suitably strong to regulate the Schwarzschild singularity generically prevent the transition from occurring. We also show that the Smarr relation remains linear in all cases, despite the absence of a linearity proof for non-linear electrodynamic theories with non-symmetry inheriting fields.Comment: 19 pages, 10 figures

Gravitational Thermodynamics: From Black Holes to Holography

The subject of gravitational thermodynamics lies at the center of numerous fields of study, many of which may seem disconnected, yet have proven to be deeply entwined. This thesis examines two primary facets of this subject, the study of black hole thermodynamics, and the principle of bulk/boundary duality (or `holography') as applied to gravitating systems. In Part I of this thesis we explore thermodynamic aspects of a wide variety of black hole spacetimes. We focus on asymptotically de Sitter black holes, in an extended phase space where the cosmological constant is interpreted as a thermodynamic pressure. We begin with the prototypical classes, examining general relativistic Schwarzschild- and Reissner-Nordstr\"{o}m-de Sitter black holes. We demonstrate the consistent formulation of their thermodynamics in the extended phase space using a Euclidean path integral approach, and uncover novel compact small-large black hole transitions not seen in asymptotically AdS spacetimes. We also consider a number of extensions of Einstein-Maxwell theory: Born-Infeld electrodynamics, conformally coupled scalar fields, and Gauss-Bonnet gravity. We study the thermodynamic properties and phase structure of black hole solutions in these theories, uncovering (among other things) a unique reentrant phase transition in the grand canonical ensemble, compact reentrant phase transitions, and isolated critical points. We also examine the analogy these systems make with ordinary fluid systems, showing that in contrast to asymptotically anti-de Sitter black holes, de Sitter black holes have nonlinear equations of state which forbid such an interpretation. Part II of this thesis represents an attempt to understand the thermodynamic nature of gravity from a broader perspective. Here, we take a `holographic' approach, promoting the gravitational screen formalism to a fully covariant mapping between bulk geometric quantities and those of a relativistic dissipative fluid system on the (arbitrary, timelike) boundary. We demonstrate the projection of the field equations onto the screen boundary, derive the corresponding fluid conservation equations, and explicitly construct the dictionary relating the two systems. We show how entropy production in the fluid is tied to gravitational wave propagation in the bulk, and discuss the role of the equation of state of the fluid in the correspondence. Finally, we explicitly construct several gravitational screens in spherically symmetric spacetimes. We determine the properties of the resulting holographic fluids, and use thermodynamical laws governing the fluid to assign a notion of temperature and entropy to the bulk geometry

Exotic Black Hole Thermodynamics in Third-Order Lovelock Gravity

The generalization of Birkhoff's theorem to higher dimensions in Lovelock gravity allows for black hole solutions with horizon geometries of non-constant curvature. We investigate thermodynamic aspects of these `exotic' black hole solutions, with a particular emphasis on their phase transitions. We consider an extended phase space where the cosmological constant acts as a thermodynamic pressure, and examine both uncharged and $U(1)$ charged solutions. In $d=7$, black hole solutions are restricted to having constant-curvature horizon base manifolds. Uncharged $d=7$ black holes possess novel triple point phenomena analogous to those recently uncovered in exotic $d=6$ black holes in Gauss-Bonnet gravity, while their charged counterparts generically undergo small-large black hole phase transitions. In $d=8$, we find that both charged and uncharged black holes exhibit triple point behaviour and small-large black hole transitions. We also show that a wide range of `exotic' horizon geometries can be ruled out due to the appearance of naked singularities.Comment: 24 pages, 9 Figure

Physical black holes in cosmological spacetimes

Working in the semi-classical setting, we present an exactly solvable candidate model for astrophysical black holes, which can be embedded in a cosmological background and possess regular apparent horizons that form in finite observational time. We construct near-horizon quantities from the assumption of regularity of the renormalized expectation value of the energy-momentum tensor, and derive explicit coordinate transformations in the near-horizon region. We discuss the appropriate boundary conditions for the embedding of the model into an FRWL background, describe their evaporation in the linear regime, and highlight consequences for the laws of black hole mechanics when back-reaction is present.Comment: 6 pages, 1 figure. Comments welcome

Horizon-bound objects: Kerr-Vaidya solutions

The formation of horizons in finite time according to distant observers results in a number of remarkable properties of the objects they bound. Subject to this requirement, spherically-symmetric black holes can only decrease in mass, while white holes can only expand. We provide a detailed analysis of the latter scenario, focussing on the energy-momentum tensor near the horizon and the experiences of various observers. Kerr-Vaidya metrics are the simplest dynamical axially-symmetric solutions, all of which violate the null energy condition and thus are not excluded by the criterion of finite formation time. Of the four classes of Kerr-Vaidya metrics, two correspond to the allowed spherically-symmetric solutions: evaporating black holes and expanding white holes. We demonstrate a consistent description of accreting black holes based on the ingoing Kerr-Vaidya metric with increasing mass, and show that the model can be extended to cases where the angular momentum to mass ratio varies. Their apparent horizon is shown to be weakly singular. Pathologies are also identified in the evaporating white hole geometry which reinforce controversies arising from the classical and quantum instabilities of their static counterparts. We also describe a generalization of the equivalence between Rindler and Schwarzschild horizons to Kerr-Vaidya black holes, and describe the relevant geometric constructions.Comment: 18 pages, 5 figures. Minor edits. Comments welcome