  In this article we construct a geometric invariant for initial data sets for
the vacuum Einstein field equations $(\mathcal{S},h_{ab},K_{ab})$, such that
$\mathcal{S}$ is a 3-dimensional manifold with an asymptotically Euclidean end
and an inner boundary $\partial \mathcal{S}$ with the topology of the 2-sphere.
The hypersurface $\mathcal{S}$ 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 $(\mathcal{S},h_{ab},K_{ab})$ 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.
