Curvature related geometrical properties of topologically charged EiBI-gravity spacetime

The objective of this article is to study topologically charged Eddington-inspired Born–Infeld (briefly, EiBI) gravity spacetime. It is proved that the topologically charged EiBI spacetime executes different types of pseudosymmetry, viz. Ricci generalized pseudosymmetry as $R\cdot R=Q(S,R)$, Ricci generalized projectively pseudosymmetry as $P\cdot R=\frac{2}{3}Q(S,R)$, pseudosymmetry due to conformal curvature as $C\cdot C=-\frac{(r^2{\alpha }^2+2ϵ{\alpha }^2-r^2)}{6r^4}Q(g,C)$ and pseudosymmetry due to conharmonic curvature as $K\cdot K=-\frac{({\alpha }^2-1)}{2r^2}Q(g,K)$. Also, we have exhibited the linear dependence of $Q(g,C)$ and $Q(S,C)$ on the difference $(C\cdot R-R\cdot C)$. Moreover, it is exhibited that the topologically charged EiBI spacetime is an Einstein manifold of level 3, 2-quasi Einstein, conformal 2-forms are recurrent, Ricci 1-forms are recurrent and generalized Roter type. As a special case, we have acquired the geometric structures of point-like global monopole (briefly, PGM) spacetime and topologically charged Ellis Bronnikov Wormhole (briefly, TCEBW) spacetime. Also, we have explored that the topologically charged EiBI spacetime possesses almost $\eta$-Ricci-Yamabe soliton, almost $\eta$-Ricci soliton, and for a certain condition it admits almost Ricci soliton. Further, it is also verified that such a spacetime reveals generalized curvature inheritance and for a particular condition it admits curvature inheritance. In addition, it is fascinating to mention that the energy momentum tensor of the topologically charged EiBI spacetime satisfies several pseudosymmetric type conditions and also the tensors $Q(g,R)$, $Q(T,R)$ and $Q(S,R)$ are linearly dependent. Finally, the curvature-restricted geometric structures of topologically charged EiBI spacetime and Morris–Thorne Wormhole (briefly, MTW) spacetime are compared concerning the different types of symmetry and pseudosymmetry properties.