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.

13 pages, 2 figures, v2: typos corrected

References in corpus (4)

• Maxwell's Equations in the Myers-Perry Geometry
• Symmetry operators and decoupled equations for linear fields on black hole spacetimes
• Principal Tensor Strikes Again: Separability of Vector Equations with Torsion
• Gauged twistor spinors and symmetry operators

Cited by in corpus (4)

• Massive vector fields in Kerr--Newman and Kerr--Sen black hole spacetimes
• An alternative to the Simon tensor
• A massless scalar particle coupled to the Wahlquist metric
• On First Order Symmetry Operators for the Field Equations of Differential Forms