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1997 Class. Quantum Grav. 14 1927-1936 doi: 10.1088/0264-9381/14/7/025
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School of Mathematical Studies, Portsmouth University, Portsmouth PO1 2EG, UK Department of Mathematics and Applied Mathematics, University of Cape Town, Cape Town 7700, South AfricaAbstract.
In a cosmological context, the electric and magnetic parts of the Weyl tensor, 
and 
, represent the locally free curvature, i.e. they are not pointwise determined by the matter fields. By performing a complete covariant decomposition of 
and 
, we show that the parts of the derivative of the curvature which are locally free (i.e. not pointwise determined by the matter via the Bianchi identities) are exactly the symmetrized trace-free spatial derivatives of and together with their spatial curls. These parts of the derivatives are shown to be crucial for the existence of gravitational waves.
PACS numbers: 0420, 9880, 9530
Print publication: Issue 7 (July 1997) |
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