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Article
Publication date: 26 March 2021

H.M. Manjunatha, S.K. Narasimhamurthy and Zohreh Nekouee

The purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.

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Abstract

Purpose

The purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.

Design/methodology/approach

This paper is based on the features of λ-tensor and the technique of six-dimensional formalism introduced by Pirani and followed by W. Borgiel, Z. Ahsan et al. and H.M. Manjunatha et al. This technique helps to describe both the geometric properties and the nature of the gravitational field of the space-times in the Segre characteristic.

Findings

The Gaussian curvature quantities specify the curvature of Bertotti–Kasner space-time. They are expressed in terms of invariants of the curvature tensor. The Petrov canonical form and the Weyl invariants have also been obtained.

Originality/value

The findings are revealed to be both physically and geometrically interesting for the description of the gravitational field of the cylindrical universe of Bertotti–Kasner type as far as the literature is concerned. Given the technique of six-dimensional formalism, the authors have defined the Weyl conformal λW-tensor and discussed the canonical form of the Weyl tensor and the Petrov scalars. To the best of the literature survey, this idea is found to be modern. The results deliver new insight into the geometry of the nonstatic cylindrical vacuum solution of Einstein's field equations.

Details

Arab Journal of Mathematical Sciences, vol. 28 no. 1
Type: Research Article
ISSN: 1319-5166

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