Symmetry and pseudosymmetry properties of a point-like global monopole spacetime

The main objective of this paper is to investigate the symmetry and pseudosymmetry properties of a point-like global monopole (PGM) spacetime, which is a static and spherically symmetric solution of the Einstein’s field equations. It is shown that PGM spacetime fulfills pseudosymmetry due to Weyl conformal (resp., concircular, conharmonic) curvature tensor. It also obeys Ricci generalized conformal pseudosymmetry due to projective curvature tensor and it is Ricci generalized projective pseudosymmetric. Moreover, it is proved that PGM spacetime is [Formula: see text]-quasi Einstein, generalized quasi-Einstein, Einstein manifold of level [Formula: see text] and its Weyl conformal curvature [Formula: see text]-forms are recurrent. The energy–momentum tensor of the PGM spacetime realizes several types of pseudosymmetry, for example, it is pseudosymmetric due to Weyl conformal, concircular and conharmonic curvature tensors. Again both the Ricci tensor and the energy momentum tensor of PGM spacetime are compatible with Riemann, Weyl conformal, projective, conharmonic and concircular curvature tensors. Furthermore, it is exhibited that PGM spacetime reveals motion, curvature collineation and Ricci collineation for the non-Killing vector field [Formula: see text] but it neither possesses curvature collineation nor Ricci collineation for the non-Killing vector field [Formula: see text]. Also, it is shown that PGM spacetime admits [Formula: see text]-almost Ricci soliton for the non-Killing vector field [Formula: see text] but not for the non-Killing vector field [Formula: see text]. The notion of curvature inheritance (resp., curvature collineation) for the (1,3)-type curvature tensor and for the (0, 4)-type curvature tensor is analyzed in PGM spacetime and it is noticed that such notions for [Formula: see text] and (0, 4) curvature tensor are not equivalent. Finally, a significant comparison of the geometric properties between PGM spacetime and interior black hole spacetime is provided.