Explorations in black hole chemistry and higher curvature gravity

Abstract

This thesis has two goals. The primary goal is to communicate two results within the framework of black hole chemistry, while the secondary goal is concerned with higher curvature theories of gravity.

Super-entropic black holes will be introduced and discussed. These are new rotating black hole solutions that are asymptotically (locally) anti de Sitter with horizons that are topologically spheres with punctures at the north and south poles. The basic properties of the solutions are discussed, including an analysis of the geometry, geodesics, and black hole thermodynamics. It is found that these are the first black hole solutions to violate the reverse isoperimetric inequality, which was conjectured to bound the entropy of anti de Sitter black holes in terms of the thermodynamic volume. Implications of this result for the inequality are discussed.

The second main result is a new phase transition in black hole thermodynamics: the $\lambda$-line. This is a line of second order (continuous) phase transitions with no associated first order phase transition. The result is illustrated for black holes in higher curvature gravity --- cubic Lovelock theory coupled to real scalar fields. The properties of the black holes exhibiting the transition are discussed and it is shown that there are no obvious pathologies associated with the solutions. The features of the theory that allow for the transition are analyzed and then applied to obtain a further example in cubic quasi-topological gravity.

The secondary goal of the thesis is to discuss higher curvature theories of gravity. This serves as a transition between the discussion of super-entropic black holes and $\lambda$-lines but also provides an opportunity to discuss recent work in the area. Higher curvature theories are introduced through a study of general theories on static and spherically symmetric spacetimes. It is found that there are three classes of theories that have a single independent field equation under this restriction: Lovelock gravity, quasi-topological gravity, and generalized quasi-topological gravity, the latter being previously unknown. These theories admit natural generalizations of the Schwarzschild solution, a feature that turns out to be equivalent to a number of other remarkable properties of the field equations and their black hole solutions. The properties of these theories are discussed and their applicability as toy models in gravity and holography is suggested, with emphasis on the previously unknown generalized quasi-topological theories.