  We show that if an asymptotically flat manifold with horizon boundary admits
a global static potential, then the static potential must be zero on the
boundary. We also show that if an asymptotically flat manifold with horizon
boundary admits an unbounded static potential in the exterior region, then the
manifold must contain a complete non-compact area minimizing hypersurface. Some
results related to the Riemannian positive mass theorem and Bartnik's
quasi-local mass are obtained.
