Explorations of Black Hole Thermodynamics in de Sitter Spacetime
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Date
2019-01-23
Authors
Mbarek, Saoussen
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
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.
Description
Keywords
Black Holes, Thermodynamics, de Sitter spacetime, AdS/CFT, Quantum Gravity, Gravity