Constrained field theories on spherically symmetric spacetimes with horizons

TL;DR

This paper investigates how horizons in spherically symmetric black hole spacetimes modify the constraints of gauge theories, exemplified by the Maxwell field, using the Dirac-Bergmann algorithm.

Contribution

It demonstrates the horizon-induced modifications to constraints in gauge theories on black hole backgrounds, providing a detailed analysis with Maxwell theory as an example.

Findings

Constraints are altered by horizon contributions.

Horizon effects influence the dynamics of gauge fields.

Maxwell field behavior is affected by black hole horizons.

Abstract

We apply the Dirac-Bergmann algorithm for the analysis of constraints to gauge theories defined on spherically symmetric black hole backgrounds. We find that the constraints for a given theory are modified on such spacetimes through the presence of additional contributions from the horizon. As a concrete example, we consider the Maxwell field on a black hole background, and determine the role of the horizon contributions on the dynamics of the theory.