Almost pseudo-Ricci symmetric spacetime solutions in $F(R)$-gravity

TL;DR

This paper investigates 4D almost pseudo Ricci symmetric perfect fluid spacetimes within $F(R)$-gravity, establishing conditions linking Robertson-Walker spacetimes and exploring energy conditions in specific models.

Contribution

It characterizes $(APRS)_4$ spacetimes in $F(R)$-gravity and connects them with Robertson-Walker spacetimes under certain conditions, also analyzing energy conditions in toy models.

Findings

Robertson-Walker spacetime is $(APRS)_4$ under specific conditions.

Various energy conditions are examined in $F(R)$-gravity models.

Conditions for $(APRS)_4$ spacetimes are established.

Abstract

The objective of the present paper is to study 4-dimensional almost pseudo Ricci symmetric perfect fluid spacetimes $(APRS)_4$. We show that a Robertson-Walker spacetime is $(APRS)_4$ and vice versa under certain condition imposed on its scale factor. Some popular toy models of $F(R)$-gravity are also studied under the current setting and various energy conditions are investigated.