Pseudo generalized Ricci-recurrent spacetimes and modified gravity

TL;DR

This paper introduces and analyzes pseudo generalized Ricci-recurrent spacetimes, exploring their properties, examples, and implications in modified gravity theories, including energy conditions and specific spacetime classifications.

Contribution

It defines a new class of Ricci-recurrent spacetimes, provides examples, and investigates their behavior in modified gravity frameworks with energy condition analysis.

Findings

Pseudo generalized Ricci-recurrent spacetimes exist and are characterized.

Certain conformally flat Ricci-recurrent spacetimes are pseudo quasi-Einstein.

These spacetimes can represent perfect fluids in modified gravity theories.

Abstract

In this paper we introduce and characterize a pseudo generalized Ricci-recurrent spacetimes and produce an example to verify the existence of such a spacetime. Then we demonstrate that a conformally flat generalized Ricci-recurrent spacetime with certain condition is a pseudo quasi-Einstein spacetime. Besides, it is proved that a pseudo generalized Ricci-recurrent generalized Robertson-Walker spacetime represents a perfect fluid spacetime. Lastly, we study the impact of this spacetime under $f(\mathcal{R},T^2)$ and $f\left(\mathcal{R}^{\ast}\right)$ gravity scenario and deduce several energy conditions.