  We obtain a characterization of the Kerr metric among stationary,
asymptotically flat, vacuum spacetimes, which extends the characterization in
terms of the Simon tensor (defined only in the manifold of trajectories) to the
whole spacetime. More precisely, we define a three index tensor on any
spacetime with a Killing field, which vanishes identically for Kerr and which
coincides in the strictly stationary region with the Simon tensor when
projected down into the manifold of trajectories. We prove that a stationary
asymptotically flat vacuum spacetime with vanishing spacetime Simon tensor is
locally isometric to Kerr. A geometrical interpretation of this
characterization in terms of the Weyl tensor is also given. Namely, a
stationary, asymptotically flat vacuum spacetime such that each principal null
direction of the Killing form is a repeated principal null direction of the
Weyl tensor is locally isometric to Kerr.
