Hidden symmetry and the separability of the Maxwell equation on the Wahlquist spacetime

Abstract

We examine hidden symmetry and its relation to the separability of the Maxwell equation on the Wahlquist spacetime. After seeing that the Wahlquist spacetime is a type-D spacetime whose repeated principal null directions are shear-free and geodesic, we show that the spacetime admits three gauged conformal Killing–Yano (GCKY) tensors which are in a relation with torsional conformal Killing–Yano tensors. As a by-product, we obtain an ordinary CKY tensor. We also show that thanks to the GCKY tensors, the Maxwell equation reduces to three Debye equations, which are scalar-type equations, and two of them can be solved by separation of variables.