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The Hawking singularity theorem is based on the Penrose theorem and it is interpreted as a gravitational singularity in the Big Bang situation. Penrose shared half of the Nobel Prize in Physics in 2020 "for the discovery that black hole formation is a robust prediction of the general theory of relativity".
The theorem also does not allow to tell when the singularity takes place, or if it is a gravitational singularity or any other kind of boundary condition. [ 7 ] Some physical theories do not discard the possibility of a non-accelerated expansion before a certain moment in time.
Theoretical physicist John Archibald Wheeler of Princeton University recommended this book to anyone interested in the implications of general relativity for cosmology, the singularity theorems, and the physics of black holes, presented in an almost Euclidean fashion, though he acknowledged that this is not a textbook due to its lack of ...
He may have been largely responsible for applying the term singularity theory to the area including the input from algebraic geometry, as well as that flowing from the work of Whitney, Thom and other authors. He wrote in terms making clear his distaste for the too-publicised emphasis on a small part of the territory.
Failure of the cosmic censorship hypothesis leads to the failure of determinism, because it is yet impossible to predict the behavior of spacetime in the causal future of a singularity. Cosmic censorship is not merely a problem of formal interest; some form of it is assumed whenever black hole event horizons are mentioned.
In general relativity, the Raychaudhuri equation, or Landau–Raychaudhuri equation, [1] is a fundamental result describing the motion of nearby bits of matter.. The equation is important as a fundamental lemma for the Penrose–Hawking singularity theorems and for the study of exact solutions in general relativity, but has independent interest, since it offers a simple and general validation ...
The Riemann singularity theorem was extended by George Kempf in 1973, [1] building on work of David Mumford and Andreotti - Mayer, to a description of the singularities of points p = class(D) on W k for 1 ≤ k ≤ g − 1.
A short proof of the theorem is as follows: Take as given that function f is meromorphic on some punctured neighborhood V \ {z 0}, and that z 0 is an essential singularity. . Assume by way of contradiction that some value b exists that the function can never get close to; that is: assume that there is some complex value b and some ε > 0 such that ‖ f(z) − b ‖ ≥ ε for all z in V at ...