Lorentzian Manifolds: A characterization with semiconformal curvature tensor
Commun. Korean Math. Soc. 2019 Vol. 34, No. 3, 911-920
https://doi.org/10.4134/CKMS.c180248
Published online July 31, 2019
Uday Chand De, Chiranjib Dey
35, Ballygaunge Circular Road; Vill-Dhamla, P.O.-Kedarpur
Abstract : In this paper we characterize semiconformally flat spacetimes and a spacetime with harmonic semiconformal curvature tensor. At first in a semiconformally flat perfect fluid spacetime we obtain a state equation and prove that in particular for dimension $n=4$, the spacetime represents a model for incoherent radiation. Next we prove that perfect fluid spacetime with harmonic semiconformal curvature tensor is of Petrov type $I$, $D$ or $O$ and the spacetime is a GRW spacetime. As a consequence we obtain several corollaries.
Keywords : Lorentzian manifolds, conformal curvature tensor, semiconformal curvature tensor
MSC numbers : 53B30, 53C25, 53C50, 53C80
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