Asymptotically flat solutions to the Ernst equation with reflection symmetry

TL;DR

This paper characterizes a class of asymptotically flat, axisymmetric, stationary vacuum solutions to Einstein's equations with reflection symmetry, using a simple relation for the Ernst potential on the symmetry axis, generalizing potential theory.

Contribution

It introduces a unique characterization of these solutions via a relation for the Ernst potential, extending known potential theory results.

Findings

Solutions are uniquely determined by the Ernst potential relation.

The relation simplifies the classification of such solutions.

Generalizes classical potential theory to Einstein's equations.

Abstract

It is shown that the class of asymptotically flat solutions to the axisymmetric and stationary vacuum Einstein equations with reflection symmetry of the metric is uniquely characterized by a simple relation for the Ernst potential on the upper part of the symmetry axis. This result generalizes a well-known fact from potential theory.