Spherically symmetric gravitational collapse in the background of Chaplygin gas

In this paper, we consider the spherically symmetric shear-free gravitational collapse in the background of Chaplygin gas as dark energy. In the interior of a star, the dark energy components are assumed to be generalized and modified Chaplygin gas. The equation of state for the generalized and modified Chaplygin gas is [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are model parameters. The exterior of the star is considered to be a Schwarzschild de Sitter/anti-de Sitter metric, and discuss the junction conditions. We discuss the dynamics of singularity formation by calculating the collapsing rate of the system. We discuss the singularity formation in both forms of the Chaplygin gas case and observe that this model possesses the central singularity; also, it is found that such collapsing fluids favor the formation of black holes.