On the Ernst electro-vacuum equations and ergosurfaces

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".