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

TL;DR

This paper investigates the hidden symmetries of the Wahlquist spacetime and demonstrates how these symmetries enable the separation of Maxwell's equations into scalar equations, facilitating their solution.

Contribution

The study reveals the existence of gauged conformal Killing-Yano tensors in Wahlquist spacetime and shows how they lead to the separability of Maxwell's equations.

Findings

Wahlquist spacetime admits three GCKY tensors.

Maxwell equations reduce to three Debye scalar equations.

Two Debye equations are separable and solvable by separation of variables.

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.