Black holes and string theory : selected topics

Abstract

This thesis is divided into three parts. In Part I the concept of holography in the context of the Maldacena conjecture and the three-dimensional black hole of Banados, Teitelboim and Zanelli (BTZ) is studied. In particular, it is shown how a theorem of Sullivan provides a precise mathematical statement of a three-dimensional kinematic holographic principle, that is, the hyperbolic structure of a geometrically finite Kleinian manifold is completely determined in terms of the corresponding Teichmuller space of the boundary. It is shown that the Euclidean BTZ black hole is a geometrically finite Kleinian manifold and some consequences of the theorem for this space-time are explored.