1996/10/18 by Helia Hollmann, Hollmann, Helia
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/9610042
30 pages, Latex
arxiv created 1996/10/18 · arxiv updated 2009/11/30
After dimensional reduction the stationary spherically symmetric sector of 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 a one parameter family interpolating between the Schwarzschild and the Taub-NUT solution. A Dirac Quantization of this system is performed and the observables -- the Schwarzschild mass and the Taub-NUT charge operator -- are shown to be self-adjoint operators with a continuous spectrum ranging from -∞ to ∞. The Hilbert space is constructed explicitely using a harmonic space approach.