María Jesús Pareja and Malcolm A H MacCallum 2006 Class. Quantum Grav. 23 5039 doi:10.1088/0264-9381/23/15/019
Local freedom in the gravitational field revisited
María Jesús Pareja1 and Malcolm A H MacCallum2
Show affiliationsMaartens et al (1997 Class. Quantum Grav. 14 1927) gave a covariant characterization, in a (1 + 3) formalism based on a perfect fluid's velocity, of the parts of the first derivatives of the curvature tensor in general relativity which are 'locally free', i.e. not pointwise determined by the fluid energy–momentum and its derivative. The full decomposition of independent curvature derivative components given in earlier work on the spinor approach to the equivalence problem enables analogous general results to be stated for any order: the independent matter terms can also be characterized. Explicit relations between the two sets of results are obtained. The 24 Maartens et al locally free data are shown to correspond to the ∇Ψ quantities in the spinor approach, and the fluid terms are similarly related to the remaining 16 independent quantities in the first derivatives of the curvature.
- PACS
- MSC
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83D05 Relativistic gravitational theories other than Einstein's, including asymmetric field theories
83C60 Spinor and twistor methods; Newman-Penrose formalism
15A72 Vector and tensor algebra, theory of invariants (See also 13A50, 14L24)
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
- Subjects
- Dates
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Issue 15 (7 August 2006)
Received 26 May 2006
Published 19 July 2006
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Local freedom in the gravitational field revisited
María Jesús Pareja and Malcolm A H MacCallum 2006 Class. Quantum Grav. 23 5039
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Yuri M Pis'mak et al 2009 J. Phys. A: Math. Theor. 42 095003
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Rigid-unit modes in tetrahedral crystals
Franz Wegner 2007 J. Phys.: Condens. Matter 19 406218
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An independent brain–computer interface using covert non-spatial visual selective attention
Dan Zhang et al 2010 J. Neural Eng. 7 016010
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