An angular momentum bound at null infinity

Abstract

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 (CMC) extending to null infinity. As an application we obtain non-existence results for the asymptotic Dirichlet problem for CMC hypersurfaces in stationary space–times.