A harmonic space approach to quantum gravity of stationary space–times with SO(3) symmetry

Abstract

After dimensional reduction the stationary sector of SO(3) symmetric Einstein’s gravity is identified with an SL(2,R)/SO(2) Sigma model coupled to a one-dimensional gravitational remnant. The space of classical solutions consists of the Schwarzschild and Taub–NUT family. A Dirac quantization of this system is performed and the observables—the mass and the charge operator—are shown to be self-adjoint operators with a continuous spectrum ranging from −∞ to ∞. The Hilbert space is constructed explicitly using a harmonic space approach.