Group Theoretical Quantization of Schwarzschild and Taub-NUT

TL;DR

This paper applies group theoretical methods to quantize spherically symmetric gravity, revealing exact solutions and quantum properties of Schwarzschild and Taub-NUT spacetimes through symmetry-based techniques.

Contribution

It introduces a novel group theoretical quantization approach for stationary spherically symmetric gravity using SL(2,R)/SO(2) coset models, enabling exact solutions.

Findings

Exact quantization of the Wheeler-DeWitt equation via Casimir operators

Identification of quantum states corresponding to Schwarzschild and Taub-NUT solutions

Demonstration of symmetry-based quantization in gravitational models

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.