Аннотация
In this paper, we study the gravitational collapse of a spherical symmetric star constituted of matter interacting with vacuum energy density [Formula: see text] in the background of spacetime curvature. We consider the gravitational collapse for closed, flat, and hyperbolic spacetime geometry [Formula: see text]. We take the process of gravitational collapse for an anisotropic fluid interacting with a growing vacuum energy density by taking a complete physically general-relativistic approach in the background of spacetime curvature. Here, we achieved analytic solutions with some assumptions of physical significance. We executed and interpreted the solutions for several cases of the equation of state parameters, [Formula: see text]. In all physical cases, we investigate the formation of a black hole and the naked singularity.