The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metric. It is shown that generalized pp-wave spacetime is Ricci generalized pseudosymmetric, 2-quasi-Einstein and generalized quasi-Einstein in the sense of Chaki. As a special case it is shown that pp-wave spacetime is semisymmetric, semisymmetric due to conformal and projective curvature tensors, R-space by Venzi and satisfies the pseudosymmetric type condition P · P = − 1 3 Q(S, P ). Again we investigate the sufficient condition for which a generalized pp-wave spacetime turns into pp-wave spacetime, pure radiation spacetime, locally symmetric and recurrent.Finally, it is shown that the energy-momentum tensor of pp-wave spacetime is parallel if and only if it is cyclic parallel. And the energy momentum tensor is Codazzi type if it is cyclic parallel but the converse is not true as shown by an example. Finally we make a comparison between the curvature properties of the Robinson-Trautman metric and generalized pp-wave metric.

: In the differential geometry of certain F -structures, the role of W -curvature tensor is very well known. A detailed study of this tensor has been made on the spacetime of general relativity. The spacetimes satisfying Einstein field equations with vanishing W -tensor have been considered and the existence of Killing and conformal Killing vector fields has been established. Perfect fluid spacetimes with vanishing W -tensor have also been considered. The divergence of W -tensor is studied in detail and it is seen, among other results, that a perfect fluid spacetime with conserved W -tensor represents either an Einstein space or a Friedmann-RobertsonWalker cosmological model.

A process for using curvature invariants is applied as a new means to evaluate the traversability of Lorentzian wormholes and to display the wormhole spacetime manifold. This approach was formulated by Henry, Overduin and Wilcomb for Black Holes in Reference [1]. Curvature invariants are independent of coordinate basis, so the process is free of coordinate mapping distortions and the same regardless of your chosen coordinates. The four independent Carminati and McLenaghan (CM) invariants are calculated and the non-zero curvature invariant functions are plotted. Three example traversable wormhole metrics (i) spherically symmetric Morris and Thorne, (ii) thin-shell Schwarzschild wormholes, and (iii) the exponential metric are investigated and are demonstrated to be traversable.

In the present paper, LP -Kenmotsu manifolds admitting η -Ricci solitons have been studied. Moreover, some results for η -Ricci solitons in LP-Kenmotsu manifolds in the spacetime of general relativity have also been proved. Through a nontrivial example, we have given a proof for the existence of η-Ricci solitons in a 5-dimensional LP-Kenmotsu manifold.

A spacetime denotes a pure radiation field if its energy momentum tensor represents a situation in which all the energy is transported in one direction with the speed of light. In 1989, Wils and later in 1997 Ludwig and Edgar studied the physical properties of pure radiation metrics, which are conformally related to a vacuum spacetime. In the present paper we investigate the curvature properties of special type of pure radiation metrics presented by Ludwig and Edgar. It is shown that such a pure radiation spacetime is semisymmetric, Ricci simple, R-space by Venzi and its Ricci tensor is Riemann compatible. It is also proved that its conformal curvature 2-forms and Ricci 1-forms are recurrent. We also present a pure radiation type metric and evaluate its curvature properties along with the form of its energy momentum tensor. It is interesting to note that such pure radiation type metric is Ein(3) and 3-quasi-Einstein. We also find out the sufficient conditions for which this metric represents a generalized pp-wave, pure radiation and perfect fluid. Finally we made a comparison between the curvature properties of Ludwig and Edgar's pure radiation metric and pp-wave metrics.