UC Santa Barbara

This thesis is divided into three Parts. In Part I the general theory of black holes in higher dimensions is discussed. In addition to an introductory essay, two studies of linear perturbations of Myers-Perry black holes are presented. These black holes are the higher dimensional generalization of the Kerr black hole, and their analysis reveals numerous instabilities. Threshold unstable modes provide the connection between the Myers-Perry black holes and novel stationary black hole solutions such as black rings or black Saturns, as well as other non-stationary solutions known as single Killing vector field black holes.

In Part II gauge/gravity duality is briefly reviewed and two aspects are studied in detail. First, the problem of finding a holographic dual to a superconductor with d-wave order parameter is investigated, and second, we examine the problem of holographic thermalization in field theories dual to rotating black holes.

Lastly, in Part III the role of de Sitter solutions in string theory is discussed. A recent puzzle surrounding the fate of the de Sitter landscape is reviewed, and it is shown how the study of black holes in certain flux backgrounds can provide insight into this puzzle. We then present a theorem ruling out the addition of black holes to a certain class of flux backgrounds. Finally, a study is presented which shows that black holes can be added to the flux backgrounds relevant for the de Sitter landscape in string theory, thereby providing strong evidence for the resolution of the puzzle.