Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-09-07
Gen.Rel.Grav.39:2125-2147,2007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
23 pages, to appear in GRG
Scientific paper
10.1007/s10714-007-0509-0
Penrose's twistorial approach to the definition of angular momentum at null infinity is developed so that angular momenta at different cuts can be meaningfully compared. This is done by showing that the twistor spaces associated with different cuts of scri can be identified as manifolds (but not as vector spaces). The result is a well-defined, Bondi-Metzner-Sachs-invariant notion of angular momentum in a radiating space-time; the difficulties and ambiguities previously encountered are attached to attempts to express this in special-relativistic terms, and in particular to attempts to identify a single Minkowski space of origins. Unlike the special-relativistic case, the angular momentum cannot be represented by a purely j=1 quantity M_{ab}, but has higher-j contributions as well. Applying standard kinematic prescriptions, these higher-j contributions are shown to correspond precisely to the shear. Thus it appears that shear and angular momentum should be regarded as different aspects of a single unified concept.
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