Characterization of generalized quasi-Einstein manifolds and modified gravity

TL;DR

This paper investigates generalized quasi-Einstein manifolds, classifies certain spacetimes, explores their physical implications, and examines their role within F(R)-gravity, including energy condition analyses.

Contribution

It provides a classification of GQE spacetimes with parallel time-like vectors and explores their physical and gravitational implications within F(R)-gravity.

Findings

GQE spacetimes are classified as Robertson-Walker and quasi-constant curvature types.

F(R)-gravity admits GQE spacetimes with parallel unit time-like vectors.

Energy conditions are analyzed for these spacetimes.

Abstract

In this work, a detailed examination of a specific case of a generalized quasi-Einstein manifold (GQE)n is provided. It begins by exploring generalized quasi-Einstein spacetimes under certain conditions. The analysis then focuses on cases that admit a parallel time-like vector field. Among the findings, it is demonstrated that such spacetimes can be categorized as generalized Robertson-Walker spacetimes, Robertson-Walker spacetimes, and quasi-constant curvature spacetimes. Additionally, the physical implications of these results are discussed. It is also investigated (GQE)4 spacetimes, which accept F(R)-gravity and feature a parallel unit time-like vector field. Finally, various energy conditions are analyzed based on the results related to F(R)-gravity.