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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".
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 ...
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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.
By Penrose singularity theorem of 1964 it is known that if there is trapped null surface (and some other conditions) then a singularity must form, in 1983 Schoen and Yau proved how much matter must be crammed into a given volume to create a closed trapped surface, [1] sometimes referred as the Schoen-Yau black hole existence theorem [2] and ...
Penrose's idea is inspired by quantum gravity because it uses both the physical constants and .It is an alternative to the Copenhagen interpretation which posits that superposition fails when an observation is made (but that it is non-objective in nature), and the many-worlds interpretation, which states that alternative outcomes of a superposition are equally "real," while their mutual ...
Sard's theorem; Signature defect; Singular point of a curve; Singular point of an algebraic variety; The Singularity (film) Splitting lemma (functions) Springer resolution; Stratified Morse theory; The Swallow's Tail