On pseudo W_2-symmetric manifolds with applications to f(R) gravity

Syied, Abdallah; Abu-Donia, Hassan M.; Shenawy, Sameh

doi:10.21608/bfszu.2023.177194.1211

On pseudo W_2-symmetric manifolds with applications to f(R) gravity

Document Type : Original Article

Authors

¹ Mathematics department, faculty of science, Zagazig university

² Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt

³ Basic Science Department, Modern Academy for Engineering and Technology, Maadi, Egypt,

10.21608/bfszu.2023.177194.1211

Abstract

In this article, we define new kind of manifolds, namely pseudo W_2-symmetric manifolds. We first focus on studying the geometric properties of pseudo W_2-symmetric manifold. Pseudo W_2-symmetric spacetimes and Pseudo W_2-symmetric perfect fluid space-times in f(R) theory of gravity are invesitgated. We get in this case the form of the isotropic pressure p. Also, the form of energy density σ is obtained. As final point of study, some energy conditions are studied. The above mentioned studies and many others give us a great motivation to study the geometric properties of pseudo W_2-symmetric manifold and consider Pseudo W_2-symmetric spacetimes and Pseudo W_2-symmetric perfect fluid space-times in f(R) theory of gravity.
We organized this article as follows. I section 1, geometric properties of this manifold are considered. In section 2, general properties of pseudo W_2-symmetric manifold are considered. Next, pseudo W_2-symmetric spacetime and pseudo W_2-symmetric perfect fluid spacetime in f(R) gravity are investigated.

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