Curvature properties of Bardeen black hole spacetime

TL;DR

This paper analyzes the curvature properties of the Bardeen black hole spacetime, revealing its pseudosymmetry, recurrent structures, and Einstein manifold characteristics, and compares it with Reissner-Nordström spacetime.

Contribution

It provides a detailed geometric analysis of the Bardeen black hole spacetime, highlighting its pseudosymmetry and recurrent structures, which are novel insights into its geometric nature.

Findings

Bardeen spacetime is pseudosymmetric and has various pseudosymmetries.

It is a weakly generalized recurrent manifold and satisfies a special recurrent-like structure.

The spacetime is an Einstein manifold of level 2 and Roter type.

Abstract

The Bardeen solution corresponding to Einstein field equations with a cosmological constant is a regular black hole. The main goal of this manuscript is to investigate the geometric structures in terms of curvature conditions admitted by this spacetime. It is found that this spacetime is pseudosymmetric and possess several kinds of pseudosymmetries. Also, it is a manifold of pseudosymmetry Weyl curvature and the difference tensor C.R-R.C linearly depends on the tensors Q(g;C) and Q(S;C). It is interesting to note that such a spacetime is weakly generalized recurrent manifold and satisfies special recurrent like structure. Further, it is an Einstein manifold of level 2 and Roter type. The energy momentum tensor of this spacetime is pseudosymmetric and finally a worthy comparison between the geometric properties of Bardeen spacetime and Reissner-Nordstr\"om spacetime is given.