What name is given to the singularity theorems Hawking proved with Roger Penrose?

The singularity theorems Stephen Hawking proved with Roger Penrose are called the Penrose–Hawking singularity theorems. They are a group of results in general relativity showing that, under certain physical and geometric conditions, spacetime must contain incomplete paths called geodesics.

Roger Penrose’s 1965 work showed that gravitational collapse can inevitably produce a singularity inside a black hole when matter obeys suitable energy conditions. Hawking extended related ideas to cosmology, demonstrating that comparable reasoning could imply a past singularity in expanding-universe models, including the classical Big Bang picture.

The theorems do not describe a singularity as a simple point of infinite density, nor do they explain what replaces general relativity there. More precisely, they establish geodesic incompleteness: some possible paths through spacetime cannot be continued indefinitely. The result was important because it showed that black-hole singularities and cosmic singularities are not merely peculiar features of idealized mathematical solutions.

The name is sometimes shortened informally to the Penrose–Hawking singularity theorem, but the plural form is more accurate because several related theorems and versions exist.