Violation of cosmic censorship in the gravitational collapse of a dust cloud in five dimensions

We analyze the null geodesic equations in five-dimensional spherically symmetric spacetime with collapsing inhomogeneous dust cloud. By using a new method, we prove the existence and non-existence of solutions to null geodesic equations emanating from the central singularity for smooth initial distribution of dust. Moreover, we also show that the null geodesics can extend to null infinity in a certain case, which implies violation of the cosmic censorship conjecture