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Conharmonic curvature tensor and the spacetime of general relativity. (English) Zbl 1202.83015

Summary: The significance of the conharmonic curvature tensor is very well known in the differential geometry of certain F-structures (e.g., complex, almost complex, Kähler, almost Kähler, Hermitian, almost Hermitian structures, etc.). In this paper, a study of the conharmonic curvature tensor has been made on the four dimensional space-time of general relativity.

The space-time satisfying Einstein’s field equations and having vanishing conharmonic tensor is considered and the existence of Killing and conformal Killing vectors on such space-time have been established. Perfect fluid cosmological models have also been studied.

MSC:
83C05Einstein’s equations (general structure, canonical formalism, Cauchy problems)
53C50Lorentz manifolds, manifolds with indefinite metrics
53C80Applications of global differential geometry to physics
83E05Geometrodynamics
53B35Hermitian and Kählerian structures (local differential geometry)
83F05Relativistic cosmology
83C55Macroscopic interaction of the gravitational field with matter (general relativity)