A new, conserved, symmetric tensor field for a source-free Maxwell test field on a four-dimensional spacetime with a conformal Killing–Yano tensor, satisfying a certain compatibility condition, is introduced. In particular, this construction works for the Kerr spacetime.
"A new tensorial conservation law for Maxwell fields on the Kerr background." J. Differential Geom. 105 (2) 163 - 176, February 2017. https://doi.org/10.4310/jdg/1486522812