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TitleCharacterizing the curvature and its first derivative for imperfect fluids
Author(s)Ramos, M. P. Machado
Keywords(1+3) formalism
Riemann tensor
Imperfect fluids
Issue dateApr-2017
PublisherSpringer Verlag
JournalGeneral Relativity and Gravitation
CitationRamos M. P. M., "Characterizing the curvature and its first derivative", Gen. Relativ. Gravit., Vol. 49, 4, 60-78, (2017)
Abstract(s)The curvature tensor and its derivatives up to any order can be covariantly characterized by a minimal set of spinor quantities. On the other hand it might be useful, particularly in cosmology, to describe the geometry of a spacetime in a (1+3) formalism, based on an invariantly defined fluid velocity. In this work, we consider an imperfect fluid possessing both isotropic and anisotropic pressure. For these fluids, we determine the (1+3) matter terms of the curvature as well as the parts of the first order covariant derivative of the curvature (∇R) determined pointwise by the matter via the Bianchi identities. Explicit relations between the set of such terms obtained from the (1+3) and spinor decomposition of ∇R are given. We show that in both sets there are 36 independent terms.
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Appears in Collections:DMA - Artigos (Papers)

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