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Symmetry and pseudosymmetry properties of Vaidya-Bonner-de Sitter spacetime

Absos Ali Shaikh, Shyamal kumar Hui, Mousumi Sarkar, V. Amarendra Babu

Abstract

The primary focus of the current study is to explore the geometrical properties of the Vaidya-Bonner-de Sitter (briefly, VBdS) spacetime, which is a generalization of Vaidya-Bonner spacetime, Vaidya spacetime and Schwarzschild spacetime. In this study we have shown that the VBdS spacetime describes various types of pseudosymmetric structures, including pseudosymmetry due to conformal curvature, conharmonic curvature and other curvatures. Additionally, it is shown that such a spacetime is 2-quasi-Einstein, Einstein manifold of level 3, generalized Roter type, and that conformal 2-forms are recurrent. The geometric features of the Vaidya-Bonner spacetime, Vaidya spacetime, and Schwarzschild spacetime are obtained as a particular instance of the main determination. It is further established that the VBdS spacetime admits almost Ricci soliton and almost η-Yamabe soliton with respect to non-Killing vector fields. Also, it is proved that such a spacetime possesses generalized conharmonic curvature inheritance. It is interesting to note that in the VBdS spacetime the tensors Q(T,R), Q(S,R) and Q(g,R) are linearly dependent. Finally, this spacetime is compared with the Vaidya-Bonner spacetime with respect to their admitting geometric structures, viz., various kinds of symmetry and pseudosymmetry properties.

Symmetry and pseudosymmetry properties of Vaidya-Bonner-de Sitter spacetime

Abstract

The primary focus of the current study is to explore the geometrical properties of the Vaidya-Bonner-de Sitter (briefly, VBdS) spacetime, which is a generalization of Vaidya-Bonner spacetime, Vaidya spacetime and Schwarzschild spacetime. In this study we have shown that the VBdS spacetime describes various types of pseudosymmetric structures, including pseudosymmetry due to conformal curvature, conharmonic curvature and other curvatures. Additionally, it is shown that such a spacetime is 2-quasi-Einstein, Einstein manifold of level 3, generalized Roter type, and that conformal 2-forms are recurrent. The geometric features of the Vaidya-Bonner spacetime, Vaidya spacetime, and Schwarzschild spacetime are obtained as a particular instance of the main determination. It is further established that the VBdS spacetime admits almost Ricci soliton and almost η-Yamabe soliton with respect to non-Killing vector fields. Also, it is proved that such a spacetime possesses generalized conharmonic curvature inheritance. It is interesting to note that in the VBdS spacetime the tensors Q(T,R), Q(S,R) and Q(g,R) are linearly dependent. Finally, this spacetime is compared with the Vaidya-Bonner spacetime with respect to their admitting geometric structures, viz., various kinds of symmetry and pseudosymmetry properties.
Paper Structure (7 sections, 14 theorems, 61 equations)

This paper contains 7 sections, 14 theorems, 61 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Vaidya-Bonner-de Sitter spacetime admitting symmetry and pseudosymmetry structures
  4. Symmetry and Ricci soliton admitted on VBdS spacetime
  5. Energy momentum tensor of VBdS spacetime
  6. VBdS spacetime Vs. Vaidya-Bonner spacetime
  7. Acknowledgment

Key Result

Proposition 3.1

The VBdS spacetime is neither an Einstein manifold nor a quasi-Einstein manifold, but rather $(i)$ it is $2$-quasi-Einstein as rank $(S-\varphi g)=2$ for $\varphi=\frac{r^4 \lambda+q^2}{r^4}$. $(ii)$ In the VBdS spacetime the common form of a tensor compatible with $R$ is where $\mathcal{H}_{ij}$ are arbitrary scalars.

Theorems & Definitions (27)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • Definition 2.7
  • Definition 2.8
  • Definition 2.9
  • Definition 2.10
  • ...and 17 more