In this article we construct a geometric invariant for initial data sets for
the vacuum Einstein field equations (S,hab,Kab), such that
S is a 3-dimensional manifold with an asymptotically Euclidean end
and an inner boundary ∂S with the topology of the 2-sphere.
The hypersurface S can be though of being in the domain of outer
communication of a black hole or in the exterior of a star. The geometric
invariant vanishes if and only if (S,hab,Kab) is an initial
data set for the Kerr spacetime. The construction makes use of the notion of
Killing spinors and of an expression for a \emph{Killing spinor candidate}
which can be constructed out of concomitants of the Weyl tensor.Comment: 13 page