Recent developments on Gravitational Collapse Final States

The final fate of massive collapsing matter clouds has been a fundamental topic in black hole physics and gravitation theory for past many years.We discuss the current developments here. While the general theory of relativity predicts a necessary occurrence of space-time singularity in such a scenario, the formation of event and apparent horizons in collapse is very much a subject of current investigations. It is in fact the formation and behavior of the apparent horizon that decides whether the singularity is enveloped in a black hole, or it may be a visible for far away observers in the space-time. We point out that the apparent horizon and trapped surfaces formation is determined in terms of initial data for collapse and the allowed evolutions by Einstein equations. The black hole and naked singularities in gravitational collapse involve key open issues such as genericity and stability aspects related to these outcomes, and other problems in terms of their applications in relativistic
astrophysics. We discuss some of these issues and recent developments in this talk.