A key tool used in the formulation and proof of the singularity theorems is the Raychaudhuri equation, which describes the divergence

On the list of doomsday scenarios that could wipe out the human race, super-smart killer robots rate pretty high in the public consciousness. a [ Insbesondere für diesen Beitrag erhielt Penrose 2020 den Nobelpreis (Hawking war bereits verstorben), da das Theorem die Existenz Schwarzer Löcher in der Allgemeinen Relativitätstheorie untermauert. In the early 1960s, the existence of black holes was a point of contention. In a May column in response to Transcendence, the sci-fi movie about the singularity starring Johnny Depp, Hawking criticized researchers for not doing more to protect humans from the risks of AI. These ideas were then used by Stephen Hawking to establish the existence of cosmological singularities such as the big bang and work by Penrose, Hawking and Robert Geroch established a number of singularity theorems which showed that gravitational singularities occurred in very many situations. Here is the null version: Other versions of the theorem involving the weak or strong energy condition also exist. ( Log Out /  Roger Penrose argued analogously in relativity. For example, in the collapse of a star to form a black hole, if the star is spinning and thus possesses some angular momentum, maybe the centrifugal force partly counteracts gravity and keeps a singularity from forming. “The physical extinction of the human race is one possibility,” he writes. Ultimately, no light emitted by the star escapes through the event horizon. However, it has since been shown that inflationary cosmologies are still past-incomplete[4], and thus require physics other than inflation to describe the past boundary of the inflating region of spacetime. This means that the boundary must either come from nowhere or the whole future ends at some finite extension. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization. While theoretical predictions pointed to their existence, the conception was not widely received. to be negative even if the Null Energy Condition holds.

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Stephen Hawking ushered in fundamental contributions in physics and cosmology and greatly revolutionized our understanding of black holes.

In the 1970s, using complex calculations, Stephen Hawking shattered the notion of black holes being entirely black by discovering the phenomenon of Hawking radiation. {\displaystyle \theta } Hawking SW and Ellis GFR. From Infogalactic: the planetary knowledge core, solutions of the Einstein field equations, "Inflationary spacetimes are not past-complete", http://relativity.livingreviews.org/open?pubNo=lrr-2004-9&page=articlesu7.html, Magnetospheric eternally collapsing object, https://infogalactic.com/w/index.php?title=Penrose–Hawking_singularity_theorems&oldid=192276, Articles needing additional references from December 2008, Articles with unsourced statements from December 2008, Articles lacking in-text citations from April 2009, Mathematical methods in general relativity, All articles needing additional references, Creative Commons Attribution-ShareAlike License, About Infogalactic: the planetary knowledge core, a situation where matter is forced to be compressed to a point (a space-like singularity), a situation where certain light rays come from a region with infinite curvature (time-like singularity). Oktober 2020 um 09:18 Uhr bearbeitet. 314(1519): 529–548. Dies ergibt sich direkt aus der Raychaudhuri-Gleichung und den Existenz- und Eindeutigkeitssätzen über gewöhnliche Differentialgleichungen. The Penrose theorem guarantees that some sort of geodesic incompleteness occurs inside any black hole whenever matter satisfies reasonable energy conditions. During inflation, the universe violates the dominant energy condition, and it was initially argued (e.g. In general relativity, a singularity is a place that objects or light rays can reach in a finite time where the curvature becomes infinite, or space-time stops being a manifold. {\displaystyle {E[{\vec {X}}]^{a}}_{a}=R_{mn}\,X^{m}\,X^{n}} It is still an open question whether time-like singularities ever occur in the interior of real charged or rotating black holes, or whether they are artifacts of high symmetry and turn into spacelike singularities when realistic perturbations are added.

In general relativity, a singularity is a place that objects or light rays can reach in a finite time where the curvature becomes infinite, or space-time stops being a manifold.

There are various possibilities for each ingredient, and each leads to different singularity theorems. These theorems, strictly speaking, prove that there is at least one non-spacelike geodesic that is only finitely extendible into the past but there are cases in which the conditions of these theorems obtain in such a way that all past-directed spacetime paths terminate at a singularity. In mathematics, there is a deep connection between the curvature of a manifold and its topology. When the null geodesics intersect, they are no longer on the boundary of the future, they are in the interior of the future. ] The concept had already resurfaced a number of times in the late 1770s and early 1800s before disappearing into oblivion. The particle pairs pop out of nothingness and materialize in empty space for a fraction of a second before annihilating together. The concept had already resurfaced a number of … For example, in the collapse of a star to form a black hole, if the star is spinning and thus possesses some angular momentum, maybe the centrifugal force partly counteracts gravity and keeps a singularity from forming. Hawking's singularity theorem is for the whole universe, and works backwards in time: in Hawking's original formulation, it guaranteed that the Big Bang has infinite density. This means that after a certain amount of extension, all potentially new points have been reached.          Sexual Content This means that for a geodesic to be a shortest length path, it must never intersect neighboring parallel geodesics. will be non-negative provided that the Einstein field equations hold and[6]. Or it could lead the artificial intelligence, or AI, to exterminate any creatures it views as competitors for control of the Earth—that would be us. ( Log Out /  Singularity, event horizon and Stephen Hawking’s theory explained. Create a free website or blog at WordPress.com. [8][9], Key results in general relativity on gravitational singularities, solutions of the Einstein field equations, Learn how and when to remove this template message, "Gravitational Lensing from a Spacetime Perspective", Magnetospheric eternally collapsing object, Fashion, Faith, and Fantasy in the New Physics of the Universe, Penrose interpretation of quantum mechanics, Black Holes and Baby Universes and Other Essays, https://en.wikipedia.org/w/index.php?title=Penrose–Hawking_singularity_theorems&oldid=983490505, Mathematical methods in general relativity, Short description is different from Wikidata, Articles needing additional references from December 2008, All articles needing additional references, Articles with unsourced statements from December 2008, Articles lacking in-text citations from April 2009, Creative Commons Attribution-ShareAlike License, a situation where matter is forced to be compressed to a point (a space-like singularity), a situation where certain light rays come from a region with infinite curvature (a time-like singularity). Die ersten beiden Bedingungen implizieren eine Fokussierung der kausalen Geodäten. Wenn 1–4 also zutreffen, muss die kausalgeodätische Vollständigkeit verletzt sein. While short, this time is, nonetheless, long enough for the particle pair to separate before annihilating. Stephen Hawking has long seen the latter as more likely, and he made his thoughts known again in a recent interview with the BBC. If all points in a connected manifold are at a finite geodesic distance from a small sphere, the manifold must be compact. Die verschiedenen Singularitätentheoreme unterscheiden sich in der Stärke der angewendeten Energiebedingung. WHEBN0000294408 Singularities can be found in all the black-hole spacetimes, the Schwarzschild metric, the Reissner–Nordström metric, the Kerr metric and the Kerr–Newman metric and in all cosmological solutions which don't have a scalar field energy or a cosmological constant. Stephen Hawking, the world-renowned Physicist is no longer among us. The world of the future would become ever more technologically advanced and complex, but we wouldn’t be around to see it. The earliest promoters of such an idea included the natural philosophers John Michell and Pierre-Simon Laplace. Hence general relativity cannot be used to show a singularity.

He described the spacetime geometry, known as Schwarzchild geometry, around a spherically symmetric compact centre, for instance a star, and showed that the structure of this geometry depends on the total mass of the object. as the derivative of the log of the determinant of the congruence volume. {\displaystyle \sigma _{ab}}