Rigid singularity theorems in Lorentzian Geometry

Abstract

The importance of the singularity theorems in Lorentzian Geometry, which give su cient conditions on a spacetime entailing the incompleteness of its null or timelike geodesics, is well known. But equally important is to ascertain the rigidity of their conclusions if certain speci c key assumptions in these theorems are removed or weakened, a problem related to the genericity of the singularities in physically motivated contexts. In this talk I shall review the general setting of rigid singularity theorems and will present some examples, including some quite recent ones.