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We derive two new integral mass formulas for stationary black holes inEinstein-Yang-Mills theory. From these we derive a formula for $ \J \Omega -Q V$, from which it follows immediately that any stationary, nonrotating,uncharged black hole is static and has vanishing electric field on the staticslices. In the Einstein-Maxwell case, we have, in addition, the ``generalizedSmarr mass formula", for which we provide a new, simple derivation. Whencombined with the other two formulas, we obtain a simple proof that nonrotatingEinstein-Maxwell black holes must be static and have vanishing magnetic fieldon the static slices. Our mass formulas also can be generalized to cases withother types of matter fields, and we describe the nature of thesegeneralizations.Comment: 8 page

Mass formulas for stationary Einstein-Yang-Mills black holes and a simple proof of two staticity theorems