Search

The W 2 -curvature tensor is an important geometric invariant with relativistic significance, introduced in the early 1970s by Pokhariyal and Mishra, which can be identified in class 4 in the classification of skew-symmetric operators. In this work, we investigate 4-dimensional space-times admitting W 2 -curvature tensor in f (R , G) modified theory of gravity. It is proved that the W 2 -curvature flat perfect fluid space-times obeying f (R , G) gravity represent inflation. Also, it is shown that the isotropic pressure and the energy density of such space-times are constant. It is to be noted that in such space-times the considered energy conditions are consistently satisfied if the scalar curvature is positive. Next, we study perfect fluid space-times admitting divergence free W 2 -curvature tensor in f (R , G) gravity. Amongst other results, we prove that if the energy-momentum tensor of such space-times is bi-recurrent, then either the space-times represent inflation or their isotropic pressure and energy density are constants. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the study of pseudo Z -symmetric spacetimes (in short, (P Z S) 4) admitting harmonic conformal curvature tensor in F (R) -gravity. First, we prove that a (P Z S) 4 spacetime admitting harmonic conformal curvature tensor is conformally flat and this spacetime is a RW spacetime. For these manifolds, we determine the scale factor a (t) in a spatially flat RW spacetime and we obtain the scalar curvature of this spacetime. We find the properties of (P Z S) 4 spacetimes with harmonic conformal curvature tensor. After that, the isotropic pressure and the energy density are found for such a manifold in F (R) -gravity. At the end, choosing F (R) = R , we prove that the density parameter is 1 and this spacetime has the properties of type I (Big Rip). [ABSTRACT FROM AUTHOR]

The objective of the present research article is to examine the behavior of spacetime with content of matter having magnetism say relativistic magneto-fluid spacetime. We discuss some geometrical properties of relativistic magneto-fluid spacetime. Next, we assume the relativistic magneto-fluid spacetime with Codazzi type and Ricci cyclic type matter tensor and study various results. In addition, we turn up some curvature characteristics of relativistic magneto-fluid spacetime. Finally, we provide some physical perception of relativistic magneto-fluid spacetime. [ABSTRACT FROM AUTHOR]

Our aim is to characterize the Lorentzian manifolds endowed with a type of semi-symmetric non-metric connection. It is proven that a Lorentzian manifold with a type of semi-symmetric non-metric connection is a GRW space-time. To minimize the gap between the RW space-time and the GRW space-time, we establish a bridge between them. It is shown that a weakly Ricci symmetric GRW space-time is a stiff matter fluid. We also classify the space-times by using the Petrov's classification. Finally, we construct an example of a 4-dimensional Lorentzian manifold admitting a semi-symmetric non-metric connection whose associated vector field is a unit timelike concircular vector field. [ABSTRACT FROM AUTHOR]

The purpose of this article is to study implications of a Ricci soliton warped product manifold to its base and fiber manifolds. First, it is proved that if a warped product manifold is Ricci soliton then its factors are Ricci soliton. Then we study Ricci soliton on warped product manifolds admitting either a conformal vector field or a concurrent vector field. Finally, we study Ricci soliton on some warped product space-times. [ABSTRACT FROM AUTHOR]

The object of the present paper is to introduce and investigate the P -curvature tensor that generalizes projective, conharmonic, M -projective and the set of W i curvature tensors introduced by Pokhariyal and Mishra. It is proven that pseudo-Riemannian manifolds admitting a traceless P -curvature tensor are Einstein and those admitting flat P -curvature tensor has a constant curvature. Classification theorems for pseudo-Riemannian manifolds admitting a divergence-free P -curvature tensor are given in each subspace of Gray's decomposition of the covariant derivative of the Ricci tensor. Space–times having a flat P -curvature tensor or a divergence free P -curvature tensor are scrutinized. Finally, perfect fluid space–times admitting various features of the P -curvature tensor are considered. [ABSTRACT FROM AUTHOR]

We characterize the three-dimensional Riemannian manifolds equipped with a semi-symmetric metric ρ -connection under the assumption that the Riemannian metric is a Yamabe soliton. It is shown that a three-dimensional Riemannian manifold endowed with a semi-symmetric ρ -connection, whose metric is Yamabe soliton, is a manifold of constant sectional curvature − 1 and the Yamabe soliton is expanding with soliton constant − 6. Finally, we give an example of a three-dimensional Riemannian manifold and validate our findings. [ABSTRACT FROM AUTHOR]

The object of the present paper is to characterize spacetimes with different types of energy–momentum tensor. At first we consider spacetimes with pseudo symmetric energy–momentum tensor T. We obtain a necessary and sufficient condition for a spacetime with pseudo symmetric energy–momentum tensor to be a pseudo Ricci symmetric spacetime. Next we consider the spacetimes with Codazzi type of energy–momentum tensor and several interesting results are pointed out. Moreover, some results related to perfect fluid spacetimes with different forms of energy–momentum tensors have been obtained. We study spacetimes with quadratic Killing energy–momentum tensor T and show that a GRW spacetime with quadratic Killing energy–momentum tensor is an Einstein space. Finally, we have considered general relativistic spacetimes with semisymmetric energy–momentum tensor and obtained some important results. [ABSTRACT FROM AUTHOR]