On geometric properties of topologically charged Ellis-Bronnikov-type wormhole spacetime

Abstract

In this paper, we have studied the geometric properties of topologically charged Ellis-Bronnikov-type  wormhole (briefly, TCEBW) spacetime. The TCEBW spacetime is a static and spherically symmetric solution of the Einstein field equations with a non-zero cosmological constant. We obtained several important geometric properties viz. pseudosymmetry due to conformal curvature as well as conharmonic curvature, Ricci generalized pseudosymmetry and Ricci generalized projectively pseudosymmetry. Also, it is shown that the TCEBW spacetime is  generalized Roter type, $2$-quasi-Einstein, Einstein spacetime of level $3$ and its conformal $2$-forms are recurrent. As a special case, the geometric properties of Morris-Thorne wormhole spacetime are analyzed. Also,  we have shown that the TCEBW spacetime admits an almost $\eta$-Ricci-Yamabe soliton and  an almost $\eta$-Ricci soliton.  Finally, a comparison between Morris-Thorne wormhole  and TCEBW spacetime regarding their geometric structures is exhibited.