A geometrical view on space-time singularities

At the beginning of the development of General Relativity, from specific solutions of the Einstein field equations arose the existence of singular points inside the defined space-time, then called singularities. The existence of these objects seemed to be due to the presence of particular symmetries inside a solution. It can be shown that it is possible to prove that singularities are not the result of some peculiar solution. Such a proof is not trivial and requires the use of geometrical considerations. In this thesis, I shall introduce a series of results and definitions, allowing us to state and prove a series of theorems that predict the existence of singularities by showing that a particular space-time possesses some kind of incompleteness. These theorems are called the singularity theorems. In addition to that, I shall also include a series of considerations about the conditions that such theorems require, as well as a brief discussion about their consequences in physics.