Conserved currents for electromagnetic fields in the Kerr spacetime

TL;DR

This paper develops conserved currents for electromagnetic fields in Kerr spacetime, generalizing previous results and introducing a new current with finite fluxes, aiding understanding of electromagnetic behavior near rotating black holes.

Contribution

It constructs new conserved currents for electromagnetic fields in Kerr spacetime using symmetry operators, extending previous work and ensuring finite fluxes at infinity and the horizon.

Findings

Reproduces known conserved currents by Andersson, Bäckdahl, and Blue (2015)

Introduces a new conserved current for electromagnetic fields in Kerr

Shows fluxes of the new current are finite at null infinity and the horizon

Abstract

We construct a variety of conserved currents for test electromagnetic fields on a Kerr background. Our procedure, which involves the symplectic product for electromagnetism and symmetry operators, generates the conserved currents given by Andersson, B\"ackdahl, and Blue (2015), as well as a new conserved current. These currents reduce to the sum of (positive powers of) the Carter constants of photons in the geometric optics limit, and generalize the current for scalar fields discovered by Carter (1977) involving the Killing tensor. We furthermore show that the fluxes of our new current through null infinity and the horizon are finite.