Reduced Phase Space Quantization of spherically symmetric Einstein-Maxwell-Theory including a cosmological constant

TL;DR

This paper develops a canonical quantization approach for spherically symmetric Einstein-Maxwell gravity with a cosmological constant, using reduced phase space variables that include mass and charge, providing insights relevant to full 3+1 gravity.

Contribution

It introduces a reduced phase space quantization framework for spherically symmetric Einstein-Maxwell theory with a cosmological constant, utilizing Ashtekar variables for simplification.

Findings

Reduced phase space dimension depends on topology.

Comparison with algebraic quantization highlights advantages.

Model serves as a testing ground for full 3+1 gravity.

Abstract

We present here the canonical treatment of spherically symmetric (quantum) gravity coupled to spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the reduced phase space which is coordinatized by the mass and the electric charge as well as their canonically conjugate momenta, whose geometrical interpretation is explored. The dimension of the reduced phase space depends on the topology chosen, quite similar to the case of pure (2+1) gravity. We also compare the reduced phase space quantization to the algebraic quantization. Altogether, we observe that the present model serves as an interesting testing ground for full (3+1) gravity. We use the new canonical variables introduced by Ashtekar which simplifies the analysis tremendously.