Curvature properties and Ricci solitons on Kiselev black hole spacetime

This work investigates the curvature features of the Kiselev black hole (KBH) spacetime, a solution of the Einstein field equations incorporating a non-zero cosmological constant. The investigation begins by identifying that the KBH spacetime is a [Formula: see text]-quasi-Einstein manifold, Einstein manifold of level [Formula: see text], Roter type, conformal 2-forms being recurrent, Ricci and projective 1-forms being recurrent, etc. Additionally, it is revealed that the nature of the KBH spacetime is pseudosymmetric, demonstrating various pseudosymmetries related to conharmonic, conformal and concircular curvature tensors (i.e. [Formula: see text] for [Formula: see text] with a smooth function [Formula: see text]) and Ricci pseudosymmetry due to projective curvature tensor (i.e. [Formula: see text]. Moreover, the study establishes that the tensors [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] have linear dependence on the difference [Formula: see text]. Also the significant relation “[Formula: see text]” is identified. The energy momentum tensor of the KBH spacetime is also demonstrated to be pseudosymmetric (i.e. [Formula: see text]), which is an intriguing discovery. The study also demonstrates that the KBH spacetime exhibits an almost [Formula: see text]-Ricci soliton as well as an almost [Formula: see text]-Ricci–Yamabe soliton. Finally, the paper provides a thorough comparative analysis between the point-like global monopole spacetime and KBH spacetime regarding separate types of symmetry and pseudosymmetry structures.