abstract:In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability. See Singularity theory for general discussion of the geometric theory, which only covers some aspects.
Whether the singularityis an actual point of infinite density or just a mathematicalinadequacy of GR is unclear, as the equations of GR break down inside black holes.