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This paper is devoted to the study of curvature properties of Hayward black hole (briefly, HBH) spacetime, which is a solution of Einstein field equations (briefly, EFE) having non-vanishing cosmological constant. We have proved that the HBH spacetime is an Einstein manifold of level 2, 2-quasi Einstein, generalized quasi-Einstein and Roter type manifold. Also, it is shown that the nature of the HBH spacetime is pseudosymmetric and it obeys several types of pseudosymmetries, such as, pseudosymmetry due to concircular, conformal and conharmonic curvature (i.e., F ⋅ F = L Q (g , F) for F = W , C , K with a smooth scalar function L), and it also possesses the relation R ⋅ R − L Q (g , C) = Q (S , R). It is engrossing to mention that the nature of energy momentum tensor of the HBH spacetime is pseudosymmetric. On the basis of curvature related properties, we have made a comparison among Reissner–Nordström spacetime, interior black hole spacetime and HBH spacetime. It is noteworthy to mention that the gravitational force of the point-like global monopole spacetime is much stronger than that of HBH spacetime. Also, it is shown that the HBH spacetime admits an almost η -Ricci soliton as well as an almost η -Ricci-Yamabe soliton. Finally, an elegant comparative study is delineated between the HBH spacetime and the point-like global monopole spacetime with respect to different kinds of symmetry, such as, motion, curvature collineation, curvature inheritance etc. • This paper aims to the study of curvature properties of Hayward black hole spacetime. • We have proved that the spacetime is an Ein(2), 2-quasi Einstein and Roter type. • Also shown that the nature of the spacetime obeys several types of pseudosymmetries. • We have compared Reissner–Nordström, interior black hole and HBH spacetime. • Also, the HBH spacetime admits an almost η -Ricci and almost η -Ricci-Yamabe solitons. [ABSTRACT FROM AUTHOR]

• Two new exact and analytic solutions of the Einstein–Maxwell field equations describing compact anisotropic charged stars satisfying the Karmarkar condition in the background of Bardeen black hole geometry are studied. • The validity of the solutions is verified by performing several physical tests. • The solutions satisfy all the physical requirements necessary for well-behaved models. • The models represent neutron star in Vela X-1. In this paper, we present two new exact and analytic solutions of the Einstein–Maxwell field equations describing compact anisotropic charged stars satisfying the Karmarkar condition in the background of Bardeen black hole geometry. The solutions are composed of two parts: The inner region of the star is described by class I Karmarkar space-time, while exterior of the star is characterized by both the Bardeen and the Reissner–Nordstrom space-times. Physical analysis of the matter and thermodynamical variables show that the models are well-behaved. For our parametric set of values, we conclude that the Bardeen black hole metric can be used as an alternate to the exterior Reissner–Nordstrom metric. [ABSTRACT FROM AUTHOR]