On the divergence of the space-matter tensor in general relativity. (English) Zbl 1216.83008

Summary: The divergence of the space-matter tensor is studied in detail and the perfect-fluid space-times with divergence-free space-matter tensor are considered. It is seen that such space-times either satisfy a vacuum-like equation of state or represent a Friedmann-Robertson-Walker cosmological model with \((\mu - 3p)\) as constant. The space-matter tensor is also expressed in terms of projective, conformal, conharmonic and concircular curvature tensors and the relations between their divergences are obtained.


83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83F05 Relativistic cosmology
53Z05 Applications of differential geometry to physics
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