Quantum Thermodynamics of Black Hole Horizons

Exploiting results recently proved in a technical paper (and some of them are reviewed herein in the language of theoretical physicists) we focus on quantization of the metric of a black hole restricted to the Killing horizon with universal radius r0. The metric is represented in a suitable manner after imposing spherical symmetry and, after restriction to the Killing horizon, it is quantized employing chiral currents. Two components of the metric" are in fact quantized: one behaves as an affine scalar fields under changes of coordinates and the other is a proper scalar field. The symplectic group acts on both fields as subgroup of diffeomorphisms of the horizon and this action