General Theory of Vacuum Ergospheres

A general definition of ergosphere is given abstracting this sort of energy source from any particular solution of Einstein's equations. A classification of ergosphere boundary points is performed according to their local properties. Points of both classes are shown to be present on the boundary of a large subfamily of ergospheres called weakly bounded. This implies existence of a singularity or a black hole inside these ergospheres. Both known ergospheres, that for $v=Hr$ and that for $r$ in the Kerr solution, are weakly bounded.