In this thesis I map out two approaches that are foundational to studying black holethermodynamics in de Sitter spacetime. The first is to understand the ;;thermodynamicvolume;; of cosmological horizons in isolation. Fortunately a broad class of exact solutionshaving only a cosmological horizon exists: Eguchi-Hanson de Sitter solitons. I carriedout the first study of thermodynamic volume associated with the cosmological horizon forEguchi-Hanson de Sitter solitons in general dimensions. This work illustrated that thecosmological volume is a well-defined concept, and that cosmological horizons indeed havemeaningful thermodynamic properties.The second approach is to move on and include black hole horizons. My first stepalong this path is to understand the phase transitions of thermalons: objects that describea transition from a black hole in Anti de Sitter spacetime to one in de Sitter spacetime. Thisindicated that asymptotically de Sitter black holes do have phase transitions which inspiredmy second project where I exploit a class of exact hairy black hole solutions to Einsteingravity with conformally coupled scalar fields to overcome the two-horizon problem. Byadding hair to the black hole, the thermodynamic equilibrium could be maintained betweenthe two horizons. These solutions make it possible to explore a range of black hole phasetransitions in de Sitter spacetime. I found that this hairy charge black hole system, andthe de Sitter space surrounding it, undergo a ;;Reverse;; Hawking-Page phase transitionwithin the grand-canonical ensemble. This is the first approach that successfully addressedthe two-horizon problem whilst including all contributions of energy from every part of thesystem.
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Explorations of Black Hole Thermodynamics in de Sitter Spacetime
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