Equatorial symmetry/antisymmetry of stationary axisymmetric electrovac spacetimes

TL;DR

This paper proves two theorems that characterize equatorially symmetric or antisymmetric stationary axisymmetric electrovac spacetimes using Ernst potentials and axis-data.

Contribution

It provides a rigorous mathematical characterization of symmetric and antisymmetric electrovac spacetimes in terms of Ernst potentials and axis-data.

Findings

Two theorems established for spacetime symmetry characterization

Characterization in terms of Ernst potentials and axis-data

Clarification of symmetry properties in electrovac spacetimes

Abstract

Two theorems are proved concerning how stationary axisymmetric electrovac spacetimes that are equatorially symmetric or equatorially antisymmetric can be characterized correctly in terms of the Ernst potentials $\E$ and $\Phi$ or in terms of axis-data.