Holography, CFT and Black Hole Entropy

Aspects of holography or dimensional reduction in gravitational physics are discussed with reference to black hole thermodynamics. Degrees of freedom living on Isolated Horizons (as a model for macroscopic, generic, eternal black hole horizons) are argued to be topological in nature and counted, using their relation to two dimensional conformal field theories. This leads to the microcanonical entropy of these black holes having the Bekenstein-Hawking form together with finite, unambigious {\it quantum spacetime} corrections. Another aspect of holography ensues for radiant black holes treated as a standard canonical ensemble with Isolated Horizons as the mean (equilibrium) configuration. This is shown to yield a universal criterion for thermal stability of generic radiant black holes, as a lower bound on the mass of the equilibrium isolated horizon in terms of its microcanonical entropy. Saturation of the bound occurs at a phase boundary separating thermally stable and unstable phases with symptoms of a first order phase transition.