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A Harmonic Space Approach to Spherically Symmetric Quantum Gravity

Helia Hollmann
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Abstract

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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Helia Hollmann. 1996-10-18. A Harmonic Space Approach to Spherically Symmetric Quantum Gravity. https://arxiv.org/abs/gr-qc/9610042

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