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 space--times in vacuum. They found that a solution to the Einstein field equations is reflectionally symmetric if their Ernst's potential $\mathcal{E}(\rho =0,z)=e(z)$ on a portion of the positive z-axis extending to infinity satisfies the condition $e_{+}(z)e_{+}^{\ast }(-z)=1$. 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.

6 pages, LaTex. Some minor changes in the text

References in corpus (2)

• Corrections and Comments on the Multipole Moments of Axisymmetric Electrovacuum Spacetimes
• Tracing the geometry around a massive, axisymmetric body to measure, through gravitational waves, its mass moments and electromagnetic moments

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