Note on reflection symmetry in stationary axisymmetric electrovacuum spacetimes

TL;DR

This paper extends the understanding of reflection symmetry conditions from vacuum to electrovacuum stationary axisymmetric spacetimes, providing new criteria involving Ernst potentials and exploring rational axis potentials.

Contribution

It formulates analogous reflection symmetry conditions for electrovacuum solutions and analyzes the special case of rational axis potentials.

Findings

Derived symmetry conditions for Ernst potentials in electrovacuum

Established criteria for reflection symmetry on the axis

Explored properties of rational axis potentials

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 space--times in vacuum. They found that a solution to the Einstein field equations is reflectionally symmetric if their Ernst's potential ${\cal E}(\rho=0,z)= e(z)$ on a portion of the positive z-axis extending to infinity satisfies the condition $e_{+}(z){e}_{+}^{*}(-z)=1$. In this note, we formulate an analogous conditions for two complex Ernst potentials in electrovacuum. We also present the special case of rational axis potentials.