A note on some perfect fluid Kantowski-Sachs and Bianchi type III space-times and their conformal vector fields in f(R) theory of gravity

TL;DR

This paper investigates conformal vector fields in specific cosmological space-times within f(R) gravity, revealing that only certain cases admit proper conformal fields while others have Killing fields, with dimensions of 4 or 6.

Contribution

It identifies conditions under which perfect fluid Kantowski-Sachs and Bianchi type III space-times admit conformal vector fields in f(R) gravity, highlighting cases with proper conformal fields.

Findings

Two cases admit proper conformal vector fields.

Six cases have conformal fields as Killing vectors.

Conformal vector fields have dimensions 4 or 6.

Abstract

The purpose of this paper is to find conformal vector fields of some perfect fluid Kantowski-Sachs and Bianchi type III space-times in the f(R) theory of gravity using direct integration technique. In this study there exists only eight cases. Studying each case in detail, we found that in two cases proper conformal vector fields exist while in the rest of six cases conformal vector fields become Killing vector fields. The dimension of conformal vector fields is either 4 or 6.