Penrose–Hawking singularity theorems

The Penrose–Hawking singularity theorems are fundamental results in general relativity that provide conditions under which gravitational singularities can occur in the context of cosmology and black hole physics. Developed by Roger Penrose and Stephen Hawking in the 1960s and 1970s, these theorems demonstrate that under certain circumstances, the formation of singularities—regions of spacetime where the laws of physics break down and curvature becomes infinite—is inevitable.