On the Ernst electro-vacuum equations and ergosurfaces

TL;DR

This paper investigates the smoothness of ergosurfaces in solutions to the Ernst electro-vacuum equations, proving smoothness under certain conditions and providing examples of singularities in other cases.

Contribution

It establishes conditions for smooth ergosurfaces in electro-vacuum solutions and presents examples of singular ergocircles, advancing understanding of spacetime geometry in this context.

Findings

Proves smoothness of ergosurfaces when Re(E) dominates at the zero-level-set of f.

Provides examples of solutions with singular ergocircles.

Partial results on ergosurfaces in remaining cases.

Abstract

The question of smoothness at the ergosurface of the space-time metric constructed out of solutions (E,phi) of the Ernst electro-vacuum equations is considered. We prove smoothness of those ergosurfaces at which Re(E) provides the dominant contribution to f=-(Re(E)+|phi|^2) at the zero-level-set of f. Some partial results are obtained in the remaining cases: in particular we give examples of leading-order solutions with singular isolated "ergocircles".