Introduction to the Singularity Theorems

The singularity theorems developed by Roger Penrose and Stephen Hawking are profound and fundamental results in General Relativity. They proved that spacetime singularities would form under general physical conditions relevant to gravitational collapse and expanding universes, without the assumption of high degrees of symmetry that had been present in previous studies of singular spacetimes. Penrose and Hawking developed methods to study global properties of spacetime and relate focal points of geodesic congruences to geodesic incompleteness under appropriate initial or boundary conditions. This talk aims to give a brief introduction to these methods and how they are related to singular behaviour of spacetimes.