Gravitational collapse and spacetime singularities

The nature of gravitational collapse was the subject of debate and controversy for much of the last century. During the 1960’s and 1970’s our understanding of general relativity consolidated and culminated in our modern understanding of black holes and spacetime singularities. Since then, there has been significant advances in understanding the dynamics of gravitational collapse and the nature of singularities that arise from collapse. This series of 5 lectures were presented at the X Brazillian School on Cosmology and Gravitation. The first lecture presents a detailed discussion of Schwarzschild spacetime and Oppenheimer-Snyder collapse. The subsequent lectures cover perfect-fluid collapse, critical phenomena, the relevance of self-similarity, cosmic censorship and finally the nature of singularities inside charged/rotating black holes. The presentation is intended as a starting point for students wishing to pursue research in general area of gravitational collapse and singularities. It is not mathematically rigorous.