Constrained field theories on Kerr backgrounds

TL;DR

This paper studies how gauge theory constraints, like the Maxwell Gauss law, are altered on Kerr and Kerr-de Sitter black hole backgrounds, revealing horizon-induced surface charges and currents consistent with the membrane paradigm.

Contribution

It demonstrates the modification of gauge constraints on rotating black hole backgrounds, linking horizon surface terms to induced charges and currents, and impacts gauge fixing and brackets.

Findings

Surface terms modify gauge constraints at horizons.

Horizon surface charges and currents match membrane paradigm.

Gauss law constraint is altered by horizon contributions.

Abstract

We analyze the constraints of gauge theories on Kerr and Kerr-de Sitter spacetimes, which contain one or more horizons. We find that the constraints are modified on such backgrounds through the presence of additional surface terms at the horizons. As a concrete example, we consider the Maxwell field and find that the Gauss law constraint involves surface corrections at the horizons. These surface contributions correspond to induced surface charges and currents on the horizons, which agree with those found within the membrane paradigm. The modification of the Gauss law constraint also influences the gauge fixing and Dirac brackets of the theory.