Black holes in static electrovac space-times

Abstract

The theorem of Israel which characterizes the Reissner-Nordstrom solutions as the only well behaved asymptotically flat electrovac spaces with a simple regular horizon is extended by weakening the assumptions. Critical points of the gravitational potential are not a priori excluded and the topology of the eguipotential surfaces is not restricted. The regularity of the horizon is formulated in terms of bounds for certain geometrical quantities and the assumption of existence, in some extension, of a bifurcation surface for the horizons is not made. The possibilities of non-static or non-conservative electromagnetic fields in a static space-time are discussed and excluded by physical arguments.