Search

The main aim of this article is to investigate a spacetime of quasi-constant sectional curvature. At first, the existence of such a spacetime is established by several examples. We have shown that a spacetime of quasi-constant sectional curvature agrees with the present state of the universe and it represents a Robertson Walker spacetime. Moreover, if the spacetime is Ricci semi-symmetric or Ricci symmetric, then either the spacetime represents a spacetime of constant sectional curvature, or the spacetime represents phantom era. Also, we prove that a Ricci symmetric spacetime of quasi-constant sectional curvature represents a static spacetime and the spacetime under consideration is of Petrov type I, D or O. Finally, we concentrate on a quasi-constant sectional curvature spacetime solution in $\mathcal{F}(\mathcal{R})$-gravity. As a result, various energy conditions are studied and analysed our obtained outcomes in terms of a $\mathcal{F}(\mathcal{R})$-gravity model., Comment: arXiv admin note: text overlap with arXiv:2402.15354

The goal of this research paper is to investigate curvature inheritance symmetry in conformally flat spacetime. Curvature inheritance symmetry in conformally flat spacetime is shown to be a conformal motion. We have proven that a conformally flat spacetime reduces to Einstein spacetime if admits curvature inheritance symmetry. A few results on conformally flat spacetimes that obey Einstein's field equation with or without a cosmological constant, if admits the curvature inheritance symmetry. The energy-momentum tensor is to be covariantly constant in a 4-dimensional relativistic perfect fluid spacetime which is also conformally flat spacetime, admits curvature inheritance, and obeys Einstein's field equations in the presence of a cosmological constant. Moreover, it is also obtained that such spacetimes with perfect fluid satisfy the the vacuum-like equation of state consecutively it is dark matter. Finally, in the third part of the article, the case compatible with all Theorems from Theorem \ref{Th2.1} to Theorem \ref{Th2.5n} is shown. On the other hand, it has also been emphasized that it is an example of de Sitter spacetime. It has been demonstrated that this spacetime also has a conformal killing vector.