Black Holes and Holography

In the absence of a complete quantum mechanical understanding, careful analysis of the semiclassical theory öer surprisingly deep lessons and insights into the working of gravity. Intuitions from quantum ¿eld theories in ¿xed background can often break down once we allow the geometry to ¿uctuate. A lack of understanding of these subtleties can lead to apparent inconsistencies and paradoxes, such as the black hole information paradox.One of the key results of this thesis is the holographic storage of information in a theory of quantum gravity in asymptotically ¿at spacetimes. The holographic prin-ciple refers to the proposition that in gravity the true quantum degrees of freedom in a region are encoded in its boundary. This expectation stems from the fact that the entropy of a black hole is proportional to the area [1], and not the volume, of the event horizon. The most explicit and well understood realization of the holo-graphic principle comes from string theory. The anti-de-Sitter space/conformal ¿eld theory conjecture [2, 3, 4], or AdS/CFT for short, suggests that quantum gravity in asymptotically AdS spacetimes is dual to a non-gravitational ¿eld theory in one lower dimension. Although this explicit realization is built from string theory, we would argue that we do not need detailed high energy structure of gravity to indicate holography. A semiclassical analysis is enough to show that any reasonable theory of quantum gravity must be holographic.