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Spacetimes admitting W2-curvature tensor
Sahanous Mallick,Uday Chand De +1 more
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In this article, it was shown that a W2-flat spacetime is conformally flat and hence it is of Petrov type O, and 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 ideal fluid always behaves as a cosmologically constant.Abstract:
The object of this paper is to study spacetimes admitting W2-curvature tensor. At first we prove that a W2-flat spacetime is conformally flat and hence it is of Petrov type O. Next, we prove that if the perfect fluid spacetime with vanishing W2-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 W2-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.read more
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The W2-curvature tensor on warped product manifolds and applications
Sameh Shenawy,Bülent Ünal +1 more
TL;DR: In this paper, the W2-curvature tensor on warped product manifolds and on generalized Robertson-Walker and standard static space-times has been studied and the geometry of the base and fiber of these warped product space-time models has been investigated.
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Spacetimes with different forms of energy-momentum tensor
TL;DR: In this article, a necessary and sufficient condition for a spacetime with pseudo symmetric energy-momentum tensor to be a pseudo Ricci symmetric spacetime was given, and several interesting results were obtained.
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On pseudo H-symmetric Lorentzian manifolds with applications to relativity
TL;DR: In this paper, a new type of curvature tensor called H-curvature tensors of type (1, 3) was introduced, which is a linear combination of conformal and projective curvatures.
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Characterizations of mixed quasi-Einstein manifolds
TL;DR: In this article, mixed quasi-Einstein manifolds have been studied and some geometric properties of mixed QE2Einstein manifold have been discussed, and M(QE)4 spacetime with spac...
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On generalized projective P-curvature tensor
TL;DR: In this paper, the P -curvature tensor is introduced and investigated, which generalizes projective, conharmonic, M -projective and the set of W i curvature tensors introduced by Pokhariyal and Mishra.
References
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On shear free normal flows of a perfect fluid
TL;DR: In this article, the authors consider the case where the flow lines of a perfect fluid form a time-like shear-free normal congruence and show that all the degenerate fields admit at least a one-parameter group of local isometries with space-like trajectories.
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Concircular Curvature Tensor and Fluid Spacetimes
Zafar Ahsan,Shah Alam Siddiqui +1 more
TL;DR: In this paper, the relativistic significance of concircular curvature tensors has been explored and the existence of Killing and conformal Killing vectors has been established for spacetimes satisfying Einstein field equations.
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Space-times with covariant-constant energy-momentum tensor
M. C. Chaki,Sarbari Ray +1 more
TL;DR: In this paper, it was shown that a general relativistic space-time with covariant-constant energy-momentum tensors is Ricci symmetric, and two particular types of such general space-times were considered and determined.
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Relativistic segnificance of curvature tensors
TL;DR: In this paper, new curvature tensors have been defined on the lines of Weyl's projective tensor and it has been shown that the order in which the vectors in question are arranged before being acted upon by the tensor in question plays an important role in shaping the various physical and geometrical properties of a tensor.
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On Riemannian manifolds admitting $W_2$-curvature tensor
TL;DR: In this article, the authors studied the properties of flat spacetimes under some conditions regarding the W2-curvature tensor and showed that the energy momentum tensor satisfying the Einstein's equations with a cosmological constant is a quadratic conformal Killing tensor.