Journal
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
Volume 11, Issue 4, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219887814500303
Keywords
W-2-curvature tensor; Einstein space; perfect fluid spacetime; Einstein's field equation; energy-momentum tensor
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The object of this paper is to study spacetimes admitting W-2-curvature tensor. At first we prove that a W-2-flat spacetime is conformally flat and hence it is of Petrov type O. Next, we prove that if the perfect fluid spacetime with vanishing W-2-curvature tensor obeys Einstein's field equation without cosmological constant, then the spacetime has vanishing acceleration vector and expansion scalar and the perfect fluid always behaves as a cosmological constant. It is also shown that in a perfect fluid spacetime of constant scalar curvature with divergence-free W-2-curvature tensor, the energy-momentum tensor is of Codazzi type and the possible local cosmological structure of such a spacetime is of type I, D or O.
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