Collapse Dynamics of a Star of Dark Matter and Dark Energy

We study the collapse dynamics of an inhomogeneous spherically symmetric star made of dark matter (DM) and dark energy (DE). The dark matter is taken in the form of a dust cloud while an anisotropic fluid is chosen as the candidate for dark energy. It is investigated how dark energy modifies the collapsing process, and it is examined whether dark energy has any effect on the Cosmic Censorship Conjecture. The collapsing star is assumed to be of finite radius, and the space-time is divided into three distinct regions Sigma and V-+/-, where Sigma represents the boundary of the star and V-(V+) denotes the interior (exterior) of the star. The junction conditions for matching V-+/- over Sigma are specified. The role of Dark energy in the formation of an apparent horizon is studied, and the central singularity is analyzed.