Note on reflection symmetry in stationary axisymmetric electrovacuum spacetimes

Abstract

Recently, Kordas (1995 Class. Quantum Grav. 12 2037) and Meinel and Neugebauer (1995 Class. Quantum Grav. 12 2045) studied the conditions for reflection symmetry in stationary axisymmetric spacetimes in vacuum. They found that a solution to the Einstein field equations is reflectionally symmetric if their Ernst potential (ρ = 0, z) = e(z) on a portion of the positive z-axis extending to infinity satisfies the condition e+(z)e*+(−z) = 1. In this note, we formulate analogous conditions for two complex Ernst potentials in electrovacuum. We also present the special case of rational axis potentials.