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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.
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.
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.
Initial singularity, a hypothesized singularity of infinite density before quantum fluctuations caused the Big Bang and subsequent inflation that created the Universe Penrose–Hawking singularity theorems , in general relativity theory, theorems about how gravitation produces singularities such as in black holes
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.
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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: