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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.

Definitioner

singularity

Irregular boundary of spacetime in general relativity - region where spacetime simply comes to an end. Often, such boundaries are associated with spacetime curvature growing beyond all bounds and becoming infinitely large - so-called curvature singularities (notably Ricci singularities or Weyl singularities - but there are exceptions (for instance a conic singularities). According to general relativity, a singularity exists inside every black hole, and the starting point of any universe described by a big bang model is a singularity as well. The occurrence of singularities is a failure of general relativity - and a strong indication that the theory is incomplete. Instead, one could describe the earliest universe and the interior of black holes using a theory of quantum gravity. More information about singularities can be found in the spotlight texts Spacetime singularities and Of singularities and breadmaking.

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singularity theorems

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