black hole spacetimes | vanishing angular momentum | positive angular momentum |
---|---|---|
vanishing charge | Schwarzschild spacetime | Kerr spacetime |
positive charge | Reissner-Nordstrom spacetime | Kerr-Newman spacetime |
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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.
The original article:
Review:
Klaas Landsman, Singularities, black holes, and cosmic censorship: A tribute to Roger Penrose (arXiv:2101.02687)
José M. M. Senovilla, A critical appraisal of the singularity theorems (arXiv:2108.07296)
See also:
For further developments see
In view of constructive mathematics:
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
Last revised on August 18, 2021 at 10:53:42. See the history of this page for a list of all contributions to it.