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- Title
Quasi-local gravitational angular momentum and centre of mass from generalised Witten equations.
- Authors
Wieland, Wolfgang
- Abstract
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 Poincaré 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 Poincaré charges as integrals over the Nester-Witten two-form. We point out that the defining differential equations can be extended to three-surfaces of arbitrary signature and we study them on the entire boundary of a compact four-dimensional region of spacetime. The resulting quasi-local expressions for energy and angular momentum are integrals over a two-dimensional cross-section of the boundary. For any two consecutive such cross-sections, conservation laws are derived that determine the influx (outflow) of matter and gravitational radiation.
- Subjects
ANGULAR momentum (Nuclear physics); GRAVITATIONAL mass; POINCARE series; CONSERVATION laws (Physics); INTEGRALS
- Publication
General Relativity & Gravitation, 2017, Vol 49, Issue 3, p1
- ISSN
0001-7701
- Publication type
Article
- DOI
10.1007/s10714-017-2200-4