Explorations of Black Hole Thermodynamics in de Sitter Spacetime

In this thesis I map out two approaches that are foundational to studying black hole thermodynamics in de Sitter spacetime. The first is to understand the "thermodynamic volume" of cosmological horizons in isolation. Fortunately a broad class of exact solutions having only a cosmological horizon exists: Eguchi-Hanson de Sitter solitons. I carried out the first study of thermodynamic volume associated with the cosmological horizon for Eguchi-Hanson de Sitter solitons in general dimensions. This work illustrated that the cosmological volume is a well-defined concept, and that cosmological horizons indeed have meaningful thermodynamic properties. The second approach is to move on and include black hole horizons. My first step along this path is to understand the phase transitions of thermalons: objects that describe a transition from a black hole in Anti de Sitter spacetime to one in de Sitter spacetime. This indicated that asymptotically de Sitter black holes do have phase transitions which inspired my second project where I exploit a class of exact hairy black hole solutions to Einstein gravity with conformally coupled scalar fields to overcome the two-horizon problem. By adding hair to the black hole, the thermodynamic equilibrium could be maintained between the two horizons. These solutions make it possible to explore a range of black hole phase transitions in de Sitter spacetime. I found that this hairy charge black hole system, and the de Sitter space surrounding it, undergo a "Reverse" Hawking-Page phase transition within the grand-canonical ensemble. This is the first approach that successfully addressed the two-horizon problem whilst including all contributions of energy from every part of the system