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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.
System relatedness: the effects of a singularity are characteristic of the system. Uniqueness: The nature of a singularity does not arise from the scale of the cause, so much as of its qualitative nature. Irreversibility: Events at a singularity commonly are irreversible; one cannot un-crack a glass with the same force that cracked it.
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 ...
In his work, and in collaboration with Penrose, Hawking extended the singularity theorem concepts first explored in his doctoral thesis. This included not only the existence of singularities but also the theory that the universe might have started as a singularity. Their joint essay was the runner-up in the 1968 Gravity Research Foundation ...
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
The Vivanti–Pringsheim theorem is a mathematical statement in complex analysis, that determines a specific singularity for a function described by certain type of power series. The theorem was originally formulated by Giulio Vivanti in 1893 and proved in the following year by Alfred Pringsheim. More precisely the theorem states the following:
Robert P. Geroch (Geroch group, singularity theorems, GHP formalism), Kurt Gödel (Gödel dust solution, closed timelike curves), Robert H. Gowdy (Gowdy solutions), Marcel Grossmann (taught Einstein the necessary mathematical tools for general relativity), Allvar Gullstrand (Gullstrand–Painlevé coordinates)