The reduced phase space of spherically symmetric Einstein-Maxwell theory including a cosmological constant

TL;DR

This paper extends the canonical quantization of spherically symmetric gravity to include Maxwell fields and a cosmological constant, exploring the reduced phase space with new variables that simplify the analysis.

Contribution

It introduces a canonical framework for spherically symmetric Einstein-Maxwell theory with a cosmological constant using Ashtekar variables, detailing the phase space structure and geometrical interpretation.

Findings

Reduced phase space depends on topology, similar to (2+1) gravity.

New canonical variables simplify the analysis.

Explores geometrical interpretation of conjugate momenta.

Abstract

We extend here the canonical treatment of spherically symmetric (quantum) gravity to the most simple matter coupling, namely 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 investigate several conceptual and technical details that might be of interest for full (3+1) gravity. We use the new canonical variables introduced by Ashtekar, which simplifies the analysis tremendously.