Nonlocal Ernst Equations

TL;DR

This paper introduces new nonlocal Ernst equations derived from Einstein-Maxwell and Einstein-N-abelian Yang-Mills field equations, highlighting their reductions and symmetries, including cases without asymptotic flatness.

Contribution

It presents the discovery of nonlocal Ernst equations and analyzes their local and nonlocal reductions, expanding the understanding of symmetries in these field equations.

Findings

Nonlocal Ernst equations are newly identified.

Certain field equations admit reflection symmetry.

Symmetries exist without asymptotic flatness.

Abstract

We show that the Ernst equations for stationary axially symmetric Einstein-Maxwell and Einstein - N-abelian Yang-Mills field equations have local and nonlocal reductions. Among these reduced equations the nonlocal Ernst equations are new. We show that a class of these field equations admit reflection symmetry without requiring the asymptotical flatness.