Can outside fields destroy black holes?

Stationary, axisymmetric, asymptotically flat space-times with a black hole surrounded by matter rings, disks, or shells are considered. A certain set of invariant functions, called local invariants, is defined which contains full information about the metric and electromagnetic field in a small electrovacuum neighborhood of the horizon. The local invariants are shown to satisfy an inequality, which is a generalization of the well-known Kerr-Newman inequality m2a2+e2, and which places an upper bound on the gravimagnetic, electric, and magnetic field strengths as measured at the surface of the black hole, independently of whether the fields are produced by the black hole itself or originate in outside sources.