Curvature properties of Melvin magnetic metric

TL;DR

This paper explores the curvature properties of the Melvin magnetic spacetime metric, revealing its pseudosymmetry, Roter type classification, and various geometric conditions, contributing to the understanding of its geometric structure.

Contribution

It provides a detailed analysis of the Melvin magnetic metric's curvature properties, including conditions for Roter type, pseudosymmetry, and compatibility with various geometric tensors.

Findings

Melvin magnetic metric is generalized Roter type and $Ein(3)$.

The metric satisfies a pseudosymmetric Weyl conformal tensor condition.

It is 2-quasi-Einstein with recurrent Weyl conformal 2-forms.

Abstract

This paper aims to investigate the curvature restricted geometric properties admitted by Melvin magnetic spacetime metric, a warped product metric with $1$-dimensional fibre. For this, we have considered a Melvin type static, cylindrically symmetric spacetime metric in Weyl form and it is found that such metric, in general, is generalized Roter type, $Ein(3)$ and has pseudosymmetric Weyl conformal tensor satisfying the pseudosymmetric type condition $R\cdot R-Q(S,R)=\mathcal L' Q(g,C)$. The condition for which it satisfies the Roter type condition has been obtained. It is interesting to note that Melvin magnetic metric is pseudosymmetric and pseudosymmetric due to conformal tensor. Moreover such metric is $2$-quasi-Einstien, its Ricci tensor is Reimann compatible and Weyl conformal $2$-forms are recurrent. The Maxwell tensor is also pseudosymmetric type.