Local freedom in the gravitational field revisited

Details Local freedom in the gravitational field revisited Local freedom in the gravitational field revisited

2006-05-12

arxiv.org/abs/gr-qc/0605075v1

Class.Quant.Grav. 23 (2006) 5039-5048

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX. 13 pp. To be submitted to Class. Quant. Grav

Scientific paper

10.1088/0264-9381/23/15/019

Maartens {\it et al.}\@ 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 {\it et al.} locally free data are shown to correspond to the $\nabla \Psi$ 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.

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