Characterizations of a Spacetime of Quasi‐Constant Sectional Curvature and F(R)$\mathcal {F}(\mathcal {R})$‐Gravity

• Published in: Fortschritte der Physik 2023-07, Vol.71 (6-7), p.n/a
• Main Authors: De, Uday Chand, De, Krishnendu, Zengin, Fusun Ozen, Demirbag, Sezgin Altay
• Format: Article
• Language: English
• Subjects: Curvature; Perfect fluids; f(R)$f(\mathcal {R})$‐gravity; Relativity; Spacetime of quasi‐constant sectional curvature
• ISSN: 0015-8208; 1521-3978
• DOI: 10.1002/prop.202200201

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 F(R)$\mathcal {F}(\mathcal {R})$‐gravity. As a result, various energy conditions are studied and analyzed our obtained outcomes in terms of a F(R)$\mathcal {F}(\mathcal {R})$‐gravity model. 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 F(R)$\mathcal{F}(\mathcal{R})\ $‐gravity. As a result, various energy conditions are studied and analyzed our obtained outcomes in terms of a F(R)$\mathcal{F}(\mathcal{R})\ $‐gravity model.