Collapse Dynamics of a Star of Dark Matter and Dark Energy

In this work, 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 anisotropic fluid is chosen as the candidate for dark energy. It is investigated how dark energy modifies the collapsing process and 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 $\mathrm{\Sigma }$ and $V^{\pm }$, where $\mathrm{\Sigma }$ represents the boundary of the star and $V^{-}(V^{+})$ denotes the interior (exterior) of the star. The junction conditions for matching $V^{\pm }$ over $\mathrm{\Sigma }$ are specified. Role of Dark energy in the formation of apparent horizon is studied and central singularity is analyzed.