Group theoretical quantization of Schwarzschild and Taub-NUT

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.