Thermodynamics and Universality in Anisotropic Higher Curvature Spacetimes

Abstract

In my thesis, I describe new results in the thermodynamics of black holes in two gravitational scenarios: spacetime anisotropy and higher curvature gravity. I focus on classifying the critical point of "Large Black Hole / Small Black Hole" phase transitions in higher curvature gravity in various dimensions, for both numerical and analytic black hole solutions. Special emphasis will be placed on five-dimensional cubic and quartic quasitopological gravity. I cover the motivation and document a number of higher curvature black hole solutions as well as the thermodynamic behaviour of these black holes when they are asymptotically Lifshitz symmetric (a form of anisotropy). I describe the methodology used to construct the set of thermodynamic potentials for black holes with general asymptotics from a collection of well-justified conjectures, followed by the development of procedures to numerically and analytically determine unknown quantities such as mass and thermodynamic volume from these conjectures. I will complete this thesis by extracting the critical exponents and thereby finding the universality class of the critical behaviour for a number of black hole solutions. This work has implications for the study of the gauge/gravity duality as well as for the dynamical behaviour of black holes.