Roy Maartens et al 1997 Class. Quantum Grav. 14 1927 doi:10.1088/0264-9381/14/7/025
Local freedom in the gravitational field
Roy Maartens
, George F R Ellis
and Stephen T C Siklos§
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
- MSC
- Subjects
- Dates
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Issue 7 (July 1997)
Received 5 November 1996, in final form 6 March 1997
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Local freedom in the gravitational field
Roy Maartens et al 1997 Class. Quantum Grav. 14 1927
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