A Harmonic Space Approach to Spherically Symmetric Quantum Gravity

Details A Harmonic Space Approach to Spherically Symmetric Quantum Gravity A Harmonic Space Approach to Spherically Symmetric Quantum Gravity

1996-10-18

arxiv.org/abs/gr-qc/9610042v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

30 pages, Latex

Scientific paper

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 $-\infty$ to $\infty$. The Hilbert space is constructed explicitely using a harmonic space approach.

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