Statistics – Computation
Scientific paper
Feb 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cqgra...6l...7m&link_type=abstract
Classical and Quantum Gravity (ISSN 0264-9381), vol. 6, Feb. 1, 1989, p. L7-L13. Research supported by NSF.
Statistics
Computation
14
Gravitational Effects, Hamiltonian Functions, Space-Time Functions, Vector Spaces, Angular Momentum, Mass, Minkowski Space, Tensors
Scientific paper
A connection is established between Penrose's definition of quasi-local mass and the more conventional notions of mass, momentum etc., arising from the canonical formalism of general relativity (which exist at least asymptotically). It is shown that each component of the 'angular momentum' twistor can be thought of as the value of a Hamiltonian which generates motions of regions of the spacetime which tend towards one of a collection of 'quasi-Killing vectors' on the bounding 2-surface on which the computations take place. The quasi-Killing vectors are obtained from solutions of the twistor equation, and essential use is made of the spinorial version of the gravitational Hamiltonian first employed in Witten's simplified proof of positive energy in general relativity. These ideas are then used to suggest a variation on Penrose's quasi-local mass definition using 'quasi-conformal Killing vectors' rather than quasi-Killing vectors. This has the advantage that there are only sixteen real quantities rather than the twenty real (ten complex) ones from Penrose's original definition.
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