Quasilocal gravitational angular momentum and centre of mass from generalised Witten equations
Abstract
Witten's proof for the positivity of the ADM mass gives a definition of energy in terms of threesurface spinors. In this paper, we give a generalisation for the remaining six Poincaré charges at spacelike infinity, which are the angular momentum and centre of mass. The construction improves on certain threesurface spinor equations introduced by Shaw. We solve these equations asymptotically obtaining the ten Poincaré charges as integrals over the NesterWitten twoform. We point out that the defining differential equations can be extended to threesurfaces of arbitrary signature and we study them on the entire boundary of a compact fourdimensional region of spacetime. The resulting quasilocal expressions for energy and angular momentum are integrals over a twodimensional crosssection of the boundary. For any two consecutive such crosssections, conservation laws are derived that determine the influx (outflow) of matter and gravitational radiation.
 Publication:

General Relativity and Gravitation
 Pub Date:
 March 2017
 DOI:
 10.1007/s1071401722004
 arXiv:
 arXiv:1604.07428
 Bibcode:
 2017GReGr..49...38W
 Keywords:

 Spacetime topology;
 Causal structure;
 Spinor structure;
 Quasilocal energy;
 Angular momentum;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 26 pages, one figure