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Group Theoretical Quantization of Schwarzschild and Taub-NUT

Helia Hollmann
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Abstract

Stationary spherically symmetric gravity is equivalent to a nonlinear coset sigma model on SL(2,R)/SO(2) coupled to a gravitational remnant. Classically there are stationary solutions besides the static Schwarzschild metric labeled by the Schwarzschild mass $m$ and the Taub-NUT charge $l$. Imposing the SL(2,R) symmetry at the quantum level the Wheeler-DeWitt equation becomes related to the Casimir operator on the coset, which makes the system amenable to exact quantization.

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Helia Hollmann. 1996-09-24. Group Theoretical Quantization of Schwarzschild and Taub-NUT. https://doi.org/10.1016/s0370-2693(96)01221-x

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