A Universal Inequality for Axisymmetric and Stationary Black Holes with Surrounding Matter in the Einstein-Maxwell Theory

We prove that in Einstein-Maxwell theory the inequality (8 pi J)(2)+(4 pi Q(2))(2) < A(2) holds for any sub-extremal axisymmetric and stationary black hole with arbitrary surrounding matter. Here J, Q, and A are angular momentum, electric charge, and horizon area of the black hole, respectively.