Study of the thermodynamics of charged rotating black holes in five-dimensional anti-de sitter spacetimes - El-Sayed, Hassan (AUC Knowledge Fountain, 2020)
Despite the success of General Relativity in the past century, a quantum description of gravity remains one of the most active areas of research in theoretical physics today. While gravity becomes dominant at large scales where classical physics is an appropriate effective theory, the study of very massive systems on a very small scale would require a quantum theory of gravity. A quantum description of gravity is also needed to have a grand unified theory of all the fundamental forces. The most prominent candidate for a theory of quantum gravity is currently String Theory. The discovery of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence shows a duality between gravity solutions from String Theory in anti-de Sitter (AdS) spacetimes and conformal field theories (CFT) that reside on its boundary. Particularly, in a certain limit, the correspondence means that the study of certain classes of Quantum Field Theory in flat spacetime can be mapped to classical black hole solutions in five-dimensional anti-de Sitter spacetimes, the latter being considered an approximation to solutions from String Theory. A strong interest in the study of five-dimensional black hole solutions in anti-de Sitter spacetimes then follows naturally from the AdS/CFT correspondence. One of the predictions of the AdS/CFT correspondence is a relation between the conformal anomaly of the CFT and the trace of the energy momentum theory of the garivational theory. Another interesting prediction is an equivalence between the AdS background energy of black hole solutions and the vacuum energy of the dual CFT on the boundary. The study of black hole thermodynamics in anti-de Sitter spacetimes presents certain challenges that do not exist in flat spacetimes. Particularly, certain isometric charges as well as the action become divergent on the boundary. Our goal here is to study the thermodynamics of the most general solution of blackholes in five-dimensional AdS spacetimes. In doing so, we will address the aforementioned difficulties and discuss the appropriate solutions for them. We will also calculate the conformal anomaly and vacuum energy of the dual CFT then calculate the corresponding quantities in the black hole solution. This will provide a test for the AdS/CFT correspondence in the most general case of black hole solutions in five dimensions AdS spacetimes.