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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".
General relativity predicts that any object collapsing beyond a certain point (for stars this is the Schwarzschild radius) would form a black hole, inside which a singularity (covered by an event horizon) would be formed. [2] The Penrose–Hawking singularity theorems define a singularity to have geodesics that cannot be extended in a smooth ...
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 a model with large extra dimensions (10 or 11), the values of Planck constants can be radically different, and the formulas for Hawking radiation have to be modified as well. In particular, the lifetime of a micro black hole with a radius below the scale of the extra dimensions is given by equation 9 in Cheung (2002) [ 28 ] and equations 25 ...
In general relativity, it was noted that, under fairly generic conditions, gravitational collapse will inevitably result in a so-called singularity. A singularity is a point where the solutions to the equations become infinite, indicating that the theory has been probed at inappropriate ranges.
Hawking conceded the bet in 1997, due to the discovery of the special situations just mentioned, which he characterized as "technicalities". Hawking later reformulated the bet to exclude those technicalities. The revised bet is still open (although Hawking died in 2018), the prize being "clothing to cover the winner's nakedness". [6]
The Penrose process (also called Penrose mechanism) is theorised by Sir Roger Penrose as a means whereby energy can be extracted from a rotating black hole. [1] [2] [3] The process takes advantage of the ergosphere – a region of spacetime around the black hole dragged by its rotation faster than the speed of light, meaning that from the point of view of an outside observer any matter inside ...
Because of Gödel's theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel's theorem applies to them." [48] Stephen Hawking was originally a believer in the Theory of Everything, but after considering Gödel's Theorem, he concluded that one was not ...