## 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.

### MSC:

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