Spherical and Aspherical Gravitational Collapse: Locally and Globally Naked Singularities

We discuss the gravitational collapse of spherically symmetric as well as aspherical dust clouds modeled by the Lemaitre-Tolman-Bondi (LTB) metric and the Szekeres metric, respectively. In both these cases, we specifically incorporate non-marginally bound cases. To begin with, we revisit the Datt-Oppenheimer-Snyder collapse. It is modelled by the Freidmann-Lemaitre-Robertson-Walker (FLRW) metric which is a special case of the LTB metric. We then derive the evolution of the apparent horizon, the event horizon, and the formation of a spacetime singularity at the end of the collapse in all cases. Finally, we depict conditions under which such singularities can be locally as well as globally naked.