Pseudo generalized Ricci-recurrent spacetimes with certain applications to modified gravity

TL;DR

This paper introduces and characterizes pseudo generalized Ricci-recurrent spacetimes, explores their properties in cosmological models, and examines their implications within $f( ext{R})$ gravity, including energy conditions.

Contribution

It defines a new class of Ricci-recurrent spacetimes, provides examples, and analyzes their role in modified gravity and cosmology.

Findings

Pseudo generalized Ricci-recurrent spacetimes exist and can model perfect fluids.

Such spacetimes can represent dark energy epochs or static universes.

Energy conditions are derived for these spacetimes in $f( ext{R})$ gravity.

Abstract

In this article we introduce and characterize a pseudo generalized Ricci-recurrent spacetimes. At first, we produce an example to justify the existence of such a spacetime. Then, it is provided that a pseudo generalized Ricci-recurrent generalized Robertson-Walker spacetime represents a perfect fluid spacetime and a pseudo generalized Ricci-recurrent perfect fluid spacetime represents either a dark energy epoch of the Universe or, the velocity vector field is parallel, conservative, acceleration-free, vorticity-free, and shear-free and becomes a static spacetime. Lastly, we study the impact of this spacetime under $f(\mathcal{R})$ gravity scenario and deduce several energy conditions.