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

Ghulam Shabbir

Faculty of Engineering Sciences, GIK Institute of Engineering Sciences and Technology, Topi, Swabi, KPK, Pakistan

E-mail Address: shabbir@giki.edu.pk

Corresponding author.

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Fiaz Hussain

Department of Mathematics, The Islamia University of Bahawalpur, Pakistan

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A. H. Kara

School of Mathematics and DST-NRF Center of Excellence in Mathematical and Statistical Sciences, University of the Witwatersrand, Johannesburg, Wits 2050, South Africa

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, and

Muhammad Ramzan

Department of Mathematics, The Islamia University of Bahawalpur, Pakistan

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https://doi.org/10.1142/S0217732319500792Cited by:26 (Source: Crossref)

Abstract

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

Keywords:

PACS: 04.20.-q, 04.20.Jb, 04.50.Kd

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