Holography, gravity-gauge theory link and black hole entropy

I'll begin with a very brief review of what black holes are and whether they can appear in Newtonian gravity. We shall then go on to Einstein's General Relativity and briefly see how black holes appear in this theory. Next we begin with Bekenstein's postulation of Black Holes having an entropy of their own and how that and other black hole properties force us to think about a quantum version of General Relativity. We discuss possible reasons as to why black hole entropy is not an extensive quantity like standard thermodynamic entropy, deriving a heuristic version of the notion of holography. This enables us to derive a rather general criterion for the thermal stability of black holes, whereby the instability of most common black holes becomes apparent.  We then turn to the microscopic description of the horizon degrees of freedom, and how they must be described by a topological gauge theory - Chern Simons theory, whose coupling parameter is determined in terms of the horizon area. This is an explicit `gravity-gauge theory connection'. Quantizing the bulk spacetime using Loop Quantum Gravity, and the horizon Chern Simons theory using its connection with the 2d WZW conformal field theory living on its boundary two sphere, we show how that leads us to an ab initio derivation of Bekenstein's postulation of black hole entropy for isolated black holes, but with a whole slew of quantum corrections.