Penrose-Hawking theorem





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The Penrose-Hawking singularity theorems characterize spacetimes in the theory of Einstein-gravity (general relativity) which have “singularities”, points where the Riemann curvature is undefined (or would be undefined if these points were included in the spacetime manifold) such as appears notably in black hole spacetimes.

Hellman suggest this theorem as an example of noncomputable physics. See Frank for a response.

A related problem is that of the maximal Cauchy development for the Einstein equations. In this case, at least Zorn's lemma can be avoided.


  • Stephen Hawking?, Roger Penrose, The Nature of Space and Time Princeton: Princeton University Press. ISBN 0-691-03791-4. (1996)

  • Wikipedia, Penrose-Hawking singularity theorem

  • Geoffrey Hellman, Mathematical constructivism in spacetime, British Journal for the Philosophy of Science 49 (3):425-450 (1998) PDF

  • Matthew Frank, Axioms and aesthetics in constructive mathematics and differential geometry. PhD-thesis, Chicago, 2004.

  • Jan Sbierski, On the Existence of a Maximal Cauchy Development for the Einstein Equations - a Dezornification PDF

For further developments see

Last revised on July 24, 2018 at 01:17:14. See the history of this page for a list of all contributions to it.