Topological Black Holes with Some Applications in AdS/CFT Correspondence

Abstract

In this thesis, we attempt to review and understand the properties of topological black holes in asymptotically Anti-de Sitter (AdS) space. These black holes have the property that the horizon is an Einstein manifold of positive, zero or negative curvature. We then study Maldacena's conjecture in string theory, called the AdS/CFT correspondence, which says that gravity in AdS bulk corresponds to conformal fi eld theory (CFT) defi ned on its boundary. That is, the string theory under discussion lives not in our (3+1)- spacetime, but in the corresponding 5-dimensional AdS bulk. We study the geometry of stringy black holes in the bulk and uses it to understand the physics of quark gluon plasma. Since black holes in string theory can have scalar hair in addition to electrical charges, it is only natural that we also study stringy black holes with dilaton charge and their possible applications in AdS/CFT correspondence.