José Senovilla (Basque U.): Singularity theorems in gravitation

I will review the rationale behind the singularity theorems and then proceed to an evaluation of their hypotheses and implications. Common misconceptions about the theorems and their conclusions will be clarified. Some of their rarely mentioned consequences will be analyzed, in particular, a discussion of spacetime extensions in relation to the theorems will be provided. Some recent advances as well as the nature of the singularity inside black holes will also be discussed.