Black Hole Phase Transitions and Magnetic AdS Black Branes in N=2 Supergravity
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The first part of this thesis will focus on black hole phase transitions. Using the Hawking-Page phase transition as a starting point, we obtain the framework that can generally be applied to the study of black hole phase transitions. We will review the phase structure of different black hole solutions, pointing out the influence of the addition of new fields to the theory. Furthermore, we study the similarities between the phase structure of Minkoswki spacetimes in a finite cavity and that of asymptotically anti-de Sitter theories. Finally, we point out the influence of the black hole topology on the phase diagram. Using the knowledge of the black hole solutions in the first part, the second part describes the search for a new magnetic AdS black brane solution in $N=2$ supergravity, generalizing the one that has recently been found. After a review of this known solution, we will show the difficulties which arise in finding an analytical solution. We then proceed describe asymptotic magnetic black brane solutions, which can be used as a starting point for the method used to find numerical solutions.