Quasi-local gravitational angular momentum and centre of mass from generalised Witten equations

Understand

Witten's proof for the positivity of the ADM mass gives a definition of energy in terms of three-surface spinors.

• In this paper, we give a generalisation for the remaining six Poincar\'e charges at spacelike infinity, which are the angular momentum and centre of mass.
• The construction improves on certain three-surface spinor equations introduced by Shaw.
• We solve these equations asymptotically obtaining the ten Poincar\'e charges as integrals over the Nester--Witten two-form.