On Sultana–Dyer spacetime: Curvatures and geometric structures

Abstract

Sultana–Dyer black hole, obtained by a time-dependent conformal transformation of Schwarzschild black hole, is an exact solution of general relativity in spherical symmetry. This paper provides the investigation of geometrical properties of the Sultana–Dyer spacetime by means of covariant derivative(s) of the geometric quantity “curvature”. It is shown that such a spacetime is [Formula: see text]-quasi-Einstein, Einstein spacetime of level [Formula: see text] and fulfills the generalized Roter type condition. The spacetime admits pseudosymmetric Weyl curvature as well as pseudosymmetric conharmonic curvature. Also, Weyl compatibility and Riemann compatibility of the Ricci tensor are shown. Finally, a comparison is drawn between Schwarzschild and Sultana–Dyer spacetimes with respect to their curvature restricted geometric properties.