The hydrogen problem of quantum gravity: quantizing Schwarzschild black holes

by Hans KASTRUP (CERN - TH and RWTH Aachen)

Thursday 22 Feb 2001, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

Starting from a Dirac-type symplectic reduction of pure spherically symmetric (Einstein-Schwarzschild) gravity in D > 3 space-time dimensions, followed by a quantization in terms of the group SU(1,1), yields a universal spectrum of the horizon area A_D-2 and, as the area is a function of the mass M, an associated spectrum of M. Assigning the Z(2)-valued geometrical degree of freedom 'orientation' to each elementary area quantum yields degeneracies of the levels which, together with the mass spectrum, imply the Bekenstein entropy and the Hawking temperature. The canonical quantum partition function of the system has the same form as the grand canonical potential of the classical droplet nucleation model for 1st order phase transitions in D-2 space dimensions.