An angular momentum bound at null infinity

We prove an inequality relating the trace of the extrinsic curvature, the
total angular momentum, the centre of mass, and the Trautman-Bondi mass for a
class of gravitational initial data sets with constant mean curvature extending
to null infinity. As an application we obtain non-existence results for the
asymptotic Dirichlet problem for CMC hypersurfaces in stationary space-times.