The Ernst equation and ergosurfaces

TL;DR

This paper investigates the conditions under which solutions to the Ernst equation produce smooth ergosurfaces in spacetime, linking the smoothness of the metric to the properties of the Ernst potential near zero-level-sets.

Contribution

It establishes a precise criterion connecting the smoothness of Ernst solutions to the regularity of the resulting ergosurfaces in spacetime.

Findings

Smooth ergosurfaces occur when the Ernst potential is smooth and has no zeros of infinite order near the ergosurface.

The metric's smoothness near an ergosurface is equivalent to the Ernst potential's smoothness near the zero-level-set.

The paper provides conditions ensuring the physical regularity of spacetime metrics derived from Ernst solutions.

Abstract

We show that analytic solutions $\mcE$ of the Ernst equation with non-empty zero-level-set of $\Re \mcE$ lead to smooth ergosurfaces in space-time. In fact, the space-time metric is smooth near a "Ernst ergosurface" $E_f$ if and only if $\mcE$ is smooth near $E_f$ and does not have zeros of infinite order there.