A universal constraint between charge and rotation rate for degenerate black holes surrounded by matter

We consider stationary, axially and equatorially symmetric systems consisting of a central rotating and charged degenerate black hole and surrounding matter. We show that a(2) + Q(2) = M-2 always holds provided that a continuous sequence of spacetimes can be identified, leading from the Kerr-Newman solution in electrovacuum to the solution in question. The quantity a = J/M is the black hole's intrinsic angular momentum per unit mass, Q its electric charge and M is the well-known black hole mass parameter introduced by Christodoulou and Ruffini.