On Lifshitz rotating black holes and black branes in light of AdS/CFT

Abstract

One of the many things the Anti-de-Sitter/Conformal Field Theory (AdS/CFT) correspondence tells us is that there is a correspondence between black holes and condensed matter systems with a finite temperature. The aim of this thesis was to find the metric of a rotating Lifshitz black hole in 2+1 dimensions. When this metric is known we can use it to gain more information about or solve problems in strongly coupled condensed matter systems at a critical point. To get at this, we first reviewed metrics of Schwarzschild and Reissner-Nordström black holes and black branes in 3+1 dimensions. Then we calculated the metric of a rotating black disk in Anti-de-Sitter spacetime. After that we looked at a non-rotating Lifshitz black hole and a BTZ black hole in 2+1 dimensions. Finally, we combined the knowledge of these to try to calculate the metric of the rotating Lifshitz black hole.