  We prove that any asymptotically flat static spacetime in higher dimensional
Einstein-Maxwell theory must have no magnetic field. This implies that there
are no static soliton spacetimes and completes the classification of static
non-extremal black holes in this theory. In particular, these results establish
that there are no asymptotically flat static spacetimes with non-trivial
topology, with or without a black hole, in Einstein-Maxwell theory.
