Narrow Results

The objective of the present paper is to study weakly Ricci symmetric spacetimes. Among others, we prove that a weakly Ricci symmetric spacetime obeying Einstein’s field equation without cosmological constant represents stiff matter. Moreover, it is shown that the local cosmological structure of a weakly Ricci symmetric perfect fluid spacetime can be identified as Petrov type $I$, $D$ or $O$. Next, we prove that a dust and dark fluid weakly Ricci symmetric spacetime satisfying Einstein’s field equation without cosmological constant is vacuum. Finally, we show the non-existence of radiation era in such a spacetime.

The object of the present paper is to study almost pseudo-$Q$-symmetric manifolds $A{(\mathrm{\text{PQS}})}_n$. Some geometric properties have been studied which recover some known results of pseudo $Q$-symmetric manifolds. We obtain a necessary and sufficient condition for the ${𝒬}$-curvature tensor to be recurrent in $A{(\mathrm{\text{PQS}})}_n$. Also, we provide several interesting results. Among others, we prove that a Ricci symmetric $A{(\mathrm{\text{PQS}})}_n$ is an Einstein manifold under certain condition. Moreover we deal with ${𝒬}$-flat perfect fluid, dust fluid and radiation era perfect fluid spacetimes respectively. As a consequence, we obtain some important results. Finally, we consider $A{(\mathrm{\text{PQS}})}_4$-spacetimes.

The aim of this paper is to study certain types of metrics such as conformal $\eta$-Ricci soliton and Yamabe soliton in general relativistic spacetime. Here, we have shown the nature of the soliton when the spacetime with semisymmetric energy–momentum tensor admits conformal $\eta$-Ricci soliton, whose potential vector field is torse-forming. We have studied certain curvature conditions on the spacetime that admits conformal $\eta$-Ricci soliton. Also, we have enriched the importance of the Laplace equation on the spacetime admitting conformal $\eta$-Ricci soliton. Next, we have given some applications of physical connection of dust fluid, dark fluid and radiation era on general relativistic spacetime admitting conformal $\eta$-Ricci soliton and Yamabe soliton.

In this research paper, we determine the nature of conformal $\eta$-Ricci–Bourguignon soliton on a general relativistic spacetime with torse forming potential vector field. Besides this, we evaluate a specific situation of the soliton when the spacetime admitting semi-symmetric energy–momentum tensor with respect to conformal $\eta$-Ricci–Bourguignon soliton, whose potential vector field is torse-forming. Next, we explore some characteristics of curvature on a spacetime that admits conformal $\eta$-Ricci–Bourguignon soliton. In addition, we turn up some physical perception of dust fluid, dark fluid and radiation era in a general relativistic spacetime in terms of conformal $\eta$-Ricci–Bourguignon soliton. Finally, we examine necessary and sufficient conditions for a 1-form $\eta$, which is the $g$-dual of the vector field $\xi$ on general relativistic spacetime to be a solution of the Schrödinger–Ricci equation.