Conserved currents for electromagnetic fields in the Kerr spacetime

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.