Symmetry and Pseudosymmetry properties with Ricci soliton of the Reissner-Nordström-de Sitter spacetime

Abstract

The primary objective of the article is to investigate the symmetry and pseudosymmetry properties of the Reissner-Nordström-de Sitter (briefly, RNdS) spacetime. The secondary aim of the paper is to explore the notion of Ricci solitons in RNdS spacetimes. The study is important due to the conceding of almost Ricci soliton and almost Ricci Yamabe soliton of the RNdS spacetime. The analysis shows that this spacetime satisfies multiple types of symmetric and pseudosymmetric conditions. It is interesting to note that RNdS spacetime reveled pseudosymmetry, conformal pseudosymmetry, Weyl projective pseudosymmetry, conharmonic pseudosymmetry, and concircular pseudosymmetry. Furthermore, in the RNdS spacetime, obtained by second order covariant derivatives $R\cdot R$ is linearly dependent on $Q(S,R)$ and $Q(g,C)$. It is demonstrated that the RNdS spacetime is 2-quasi Einstein and an Ein(2) space with recurrent conformal 2-forms. We derive the general form of the compatible tensors for this spacetime. The energy-momentum tensor of the RNdS spacetime is also shown to be pseudosymmetric and also the energy momentum tensor is pseudosymmetric due to conformal, conharmonic, concircular and projective curvature tensor. The energy momentum tensor is compatible with these curvature. We study a generalized notion of curvature inheritance and find that, with respect to the non-Killing vector fields $\partial/\partial r$ and $\partial/\partial θ$, the RNdS spacetime does not satisfy these inheritance conditions. However, the RNdS spacetime is shown to admit an almost Ricci soliton and an almost $η$-Ricci Yamabe soliton with respect to the non-Killing vector field $\partial/\partial r$ but with respect to the non-Killing vector field $\partial/\partial θ$ the spacetime does not admit such notions. Finally, we present a comparison between the RNdS and Vaidya-Bonner-de Sitter (VBdS) spacetimes.