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We consider stationary, axially and equatorially symmetric systems consistingof 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 ofspacetimes can be identified, leading from the Kerr-Newman solution inelectrovacuum to the solution in question. The quantity $a=J/M$ is the blackhole's intrinsic angular momentum per unit mass, $Q$ its electric charge and$M$ the well known black hole mass parameter introduced by Christodoulou andRuffini.

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