Geometrical Properties of a Point-like Global Monopole Spacetime

Abstract

The aim of this paper is to study the geometric properties of the point-like global monopole (briefly, PGM) spacetime, which is a static and spherically symmetric solution of the Einstein's field equations. It has shown that PGM spacetime admits various types of pseudosymmetry structures, such as pseudosymmetry due to Weyl conformal curvature tensor, pseudosymmetry due to concircular curvature tensor, pseudosymmetry due to conharmonic curvature tensor, Ricci generalized conformal pseudo-symmetric due to projective curvature tensor, Ricci generalized projective pseudo-symmetric. Moreover, it has proved that PGM spacetime is $2$-quasi Einstein, generalized quasi-Einstein, Einstein manifold of degree $2$, and its Weyl conformal curvature $2$-forms are recurrent. The energy-momentum tensor of the PGM spacetime realizes several types of pseudosymmetry, and its Ricci tensor is compatible with Riemann curvature, Weyl conformal curvature, projective curvature, and conharmonic curvature and concircular curvature. Further, it has shown that PGM spacetime admits motion, curvature collineation, and Ricci collineation. Also, the notion of curvature inheritance (resp., curvature collineation) for the (1,3)-type curvature tensor is not equivalent to the notion of curvature inheritance (resp., curvature collineation) for the (0,4)-type curvature tensor as it has shown that such distinctive properties were possessed by PGM spacetime. Hence the notions of curvature inheritance defined by Duggal \cite{Duggal1992} and Shaikh and Datta \cite{ShaikhDatta2022} are not equivalent.