singularity theorems

Theorems, proven by Roger Penrose and Stephen Hawking, that state under which circumstances singularities are inevitable in general relativity. As the theorems assume the laws of general relativity and certain general properties of matter, but nothing else, they are valid quite generally. In particular, these theorems prove that, in the frame-work of general relativity, every black hole must contain a singularity, and every expanding universe like ours must have begun in a big bang singularity.