Quantization of the Schwarzschild Black Hole

TL;DR

This paper applies the Dirac-Wheeler-DeWitt quantization to the Schwarzschild black hole, analyzing symmetries, measures, and gauge fixing to establish a consistent quantum description.

Contribution

It introduces a detailed quantization framework for the Schwarzschild black hole using the Dirac-Wheeler-DeWitt approach, including symmetry and gauge analysis.

Findings

Operators generating rigid symmetries are characterized.

Invariant measure under transformations is established.

Reduced and gauge-fixed quantizations yield the same Hilbert space.

Abstract

We quantize by the Dirac - Wheeler-DeWitt method the canonical formulation of the Schwarzschild black hole developed in a previous paper. We investigate the properties of the operators that generate rigid symmetries of the Hamiltonian, establish the form of the invariant measure under the rigid transformations, and determine the gauge fixed Hilbert space of states. We also prove that the reduced quantization method leads to the same Hilbert space for a suitable gauge fixing.