An angular momentum bound at null infinity

TL;DR

This paper establishes an inequality connecting angular momentum, mass, and other geometric quantities at null infinity, providing insights into gravitational initial data and constraints on hypersurfaces in stationary space-times.

Contribution

It introduces a new inequality relating key geometric and physical quantities at null infinity for CMC initial data sets, with applications to non-existence results.

Findings

Proved an inequality linking extrinsic curvature, angular momentum, and mass at null infinity.

Derived non-existence results for certain CMC hypersurfaces in stationary space-times.

Extended the understanding of gravitational initial data constraints.

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