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| {{Inline|date=July 2012}}
| | Hello, I'm Williemae, a 28 year old from Bottrop Welheimer Mark, Germany.<br>My hobbies include (but are not limited to) Sand castle building, Trainspotting and watching Two and a Half Men.<br><br>Feel free to surf to my blog: [http://www.glamurtv.com/live-geo-news/ geo news news update] |
| {{General relativity|cTopic=Phenomena}}
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| A '''gravitational singularity''' or '''spacetime singularity''' is a location where the quantities that are used to measure the [[gravitational]] field become [[infinity|infinite]] in a way that does not depend on the coordinate system. These quantities are the scalar invariant [[Curvature of Riemannian manifolds|curvature]]s of spacetime, which includes a measure of the density of matter.
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| For the purposes of proving the [[Penrose–Hawking singularity theorems]], a [[spacetime]] with a singularity is defined to be one that contains [[Geodesic (general relativity)|geodesics]] that cannot be extended in a [[Smooth function|smooth]] manner.<ref>{{cite web|last=Moulay|first=Emmanuel|title=The universe and photons|url=http://fqxi.org/data/forum-attachments/Photon.pdf|publisher=FQXi Foundational Questions Institute|accessdate=26 December 2012}}</ref> The end of such a geodesic is considered to be the singularity. This is a different definition, useful for proving theorems.
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| The two most important types of spacetime singularities are '''''curvature singularities''''' and '''''conical singularities'''''.<ref name=uggla>{{cite web|last=Uggla|first=Claes|title=Spacetime singularities|work=Einstein Online|publisher=Max Planck Institute for Gravitational Physics|accessdate=26 December 2012}}</ref> Singularities can also be divided according to whether they are covered by an [[event horizon]] or not ([[naked singularity|naked singularities]]).<ref>{{cite book|last=Patrick Di Justo, Kevin Grazier|first=Patrick and Kevin Grazier|title=The Science of Battlestar Galactica|year=2010|publisher=John Wiley & Sons|location=New York|isbn=978-0470399095|pages=181|url=http://books.google.com/books?id=iK1YbKrNRcoC&printsec=frontcover#v=onepage&q&f=false}}</ref> According to [[general relativity]], the initial state of the [[universe]], at the beginning of the [[Big Bang]], was a singularity. Both [[general relativity]] and [[quantum mechanics]] break down in describing the Big Bang,<ref>{{cite web|last=Hawking|first=Stephen|title=The Beginning of Time|url=http://www.hawking.org.uk/the-beginning-of-time.html|work=Stephen Hawking: The Official Website|publisher=Cambridge University|accessdate=26 December 2012}}</ref> but in general, quantum mechanics does not permit particles to inhabit a space smaller than their wavelengths.<ref>{{cite book|last=Zebrowski|first=Ernest|title=A History of the Circle: Mathematical Reasoning and the Physical Universe|year=2000|publisher=Rutgers University Press|location=Piscataway NJ|isbn=978-0813528984|pages=180|url=http://books.google.com/books?id=2twRfiUwkxYC&printsec=frontcover#v=onepage&q&f=false}}</ref> Another type of singularity predicted by general relativity is inside a [[black hole]]: any [[star]] collapsing beyond a certain point (the [[Schwarzschild radius]]) would form a black hole, inside which a singularity (covered by an event horizon) would be formed, as all the matter would flow into a certain point (or a circular line, if the black hole is rotating).<ref>{{cite web|last=Curiel|first=Eric and Peter Bokulich|title=Singularities and Black Holes|url=http://plato.stanford.edu/entries/spacetime-singularities/|work=Stanford Encyclopedia of Philosophy|publisher=Center for the Study of Language and Information, Stanford University|accessdate=26 December 2012}}</ref> This is again according to general relativity without [[quantum mechanics]], which forbids wavelike particles entering a space smaller than their wavelength. These hypothetical singularities are also known as curvature singularities.
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| ==Interpretation==
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| Many theories in physics have [[mathematical singularities]] of one kind or another. Equations for these physical theories predict that the ball of mass of some quantity becomes infinite or increases without limit. This is generally a sign for a missing piece in the theory, as in the [[ultraviolet catastrophe]], [[renormalization]], and instability of a hydrogen atom predicted by the [[Larmor formula]].
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| In [[supersymmetry]], a singularity in the [[moduli space]] happens usually when there are additional [[mass]]less degrees of freedom in that certain point. Similarly, it is thought that singularities in spacetime often mean that there are additional [[Degrees of freedom (physics and chemistry)|degrees of freedom]] that exist only within the vicinity of the singularity. The same fields related to the whole spacetime also exist; for example, the [[electromagnetic field]]. In known examples of [[string theory]], the latter degrees of freedom are related to [[String (physics)#Types of strings|closed string]]s, while the degrees of freedom are "stuck" to the singularity and related either to [[String (physics)#Types of strings|open string]]s or to the twisted sector of an [[orbifold]].
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| Some theories, such as the theory of [[loop quantum gravity]] suggest that singularities may not exist. The idea is that due to [[quantum gravity]] effects, there is a minimum distance beyond which the force of gravity no longer continues to increase as the distance between the masses becomes shorter.
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| The [[Einstein–Cartan theory|Einstein-Cartan]]-Sciama-Kibble theory of gravity naturally averts the gravitational singularity at the Big Bang.<ref>{{cite journal |author=Poplawski, N. J. |authorlink=Nikodem Popławski |year=2012 |title=Nonsingular, big-bounce cosmology from spinor-torsion coupling |journal=[[Physical Review D]] |volume=85 |pages=107502 |doi=10.1103/PhysRevD.85.107502|arxiv = 1111.4595 |bibcode = 2012PhRvD..85j7502P }}</ref> This theory extends general relativity to matter with intrinsic angular momentum ([[spin (physics)|spin]]) by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the [[torsion tensor]], as a variable in varying the action. The minimal coupling between torsion and [[Dirac spinor]]s generates a spin–spin interaction in [[fermion]]ic matter, which becomes dominant at extremely high densities and prevents the scale factor of the Universe from reaching zero. The Big Bang is replaced by a cusp-like [[Big Bounce]] at which the matter has an enormous but finite density and before which the Universe was contracting.
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| ==Types==
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| ===Curvature===
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| Solutions to the equations of [[general relativity]] or another theory of [[gravity]] (such as [[supergravity]]) often result in encountering points where the [[Metric (mathematics)|metric]] blows up to infinity. However, many of these points are completely [[Smooth function|regular]], and the infinities are merely a result of using an inappropriate [[coordinate system]] at this point. In order to test whether there is a singularity at a certain point, one must check whether at this point [[Diffeomorphism invariance|diffeomorphism invariant]] quantities (i.e. [[scalar (physics)|scalar]]s) become infinite. Such quantities are the same in every coordinate system, so these infinities will not "go away" by a change of coordinates.
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| An example is the [[Schwarzschild metric|Schwarzschild]] solution that describes a non-rotating, [[Electric charge|uncharged]] black hole. In coordinate systems convenient for working in regions far away from the black hole, a part of the metric becomes infinite at the [[event horizon]]. However, [[spacetime]] at the event horizon is [[Smooth function|regular]]. The regularity becomes evident when changing to another coordinate system (such as the [[Kruskal coordinates]]), where the metric is perfectly [[Smooth function|smooth]]. On the other hand, in the center of the [[black hole]], where the metric becomes infinite as well, the solutions suggest singularity exists. The existence of the singularity can be verified by noting that the [[Kretschmann scalar]], being the square of the [[Riemann tensor]] i.e. <math>R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}</math>, which is diffeomorphism invariant, is infinite.
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| While in a non-rotating black hole the singularity occurs at a single point in the model coordinates, called a "point singularity". In a rotating black hole, also known as a [[Kerr black hole]], the singularity occurs on a ring (a circular line), known as a "[[ring singularity]]". Such a singularity may also theoretically become a [[wormhole]].<ref>If a rotating singularity is given a uniform electrical charge, a repellent force results, causing a [[ring singularity]] to form. The effect may be a stable [[wormhole]], a non-point-like puncture in spacetime that may be connected to a second ring singularity on the other end. Although such wormholes are often suggested as routes for faster-than-light travel, such suggestions ignore the problem of escaping the black hole at the other end, or even of surviving the immense [[tidal force]]s in the tightly curved interior of the wormhole.</ref>
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| More generally, a spacetime is considered singular if it is [[Geodesic (general relativity)#Geodesic incompleteness and singularities|geodesically incomplete]], meaning that there are freely-falling particles whose motion cannot be determined beyond a finite time, being after the point of reaching the singularity. For example, any observer inside the [[event horizon]] of a non-rotating black hole would fall into its center within a finite period of time. The classical version of the [[Big Bang]] [[physical cosmology|cosmological]] model of the [[universe]] contains a causal singularity at the start of [[time]] (''t''=0), where all time-like geodesics have no extensions into the past. Extrapolating backward to this hypothetical time 0 results in a universe with all spatial dimensions of size zero, infinite density, infinite temperature, and infinite space-time curvature.
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| ===Conical===
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| A conical singularity occurs when there is a point where the limit of every [[Diffeomorphism invariance|diffeomorphism invariant]] quantity is finite, in which case [[spacetime]] is not smooth at the point of the limit itself. Thus, spacetime looks like a [[Cone (geometry)|cone]] around this point, where the singularity is located at the tip of the cone. The metric can be finite everywhere if a suitable [[coordinate system]] is used.
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| An example of such a conical singularity is a [[cosmic string]].
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| ===Naked===
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| {{main|Naked singularity}}
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| Until the early 1990s, it was widely believed that [[general relativity]] hides every singularity behind an event horizon, making naked singularities impossible. This is referred to as the [[cosmic censorship hypothesis]]. However, in 1991, physicists Stuart Shapiro and [[Saul Teukolsky]] performed computer simulations of a rotating plane of dust that indicated that general relativity might allow for "naked" singularities. What these objects would actually look like in such a model is unknown. Nor is it known whether singularities would still arise if the simplifying assumptions used to make the simulation were removed.
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| ==Entropy==
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| {{see|Black hole|Hawking radiation|Entropy}}
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| Before [[Stephen Hawking]] came up with the concept of Hawking radiation, the question of black holes having entropy was avoided. However, this concept demonstrates that black holes can radiate energy, which conserves entropy and solves the incompatibility problems with the second law of thermodynamics. Entropy, however, implies heat and therefore temperature. The loss of energy also suggests that black holes do not last forever, but rather "evaporate" slowly. Small black holes tend to be hotter whereas larger ones tend to be colder. All known black hole candidates are so large that their temperature is far below that of the cosmic background radiation, so they are all gaining energy. They will not begin to lose energy until a cosmological redshift of more than one million is reached, rather than the thousand or so since the background radiation formed.
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| ==See also==
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| * [[Penrose-Hawking singularity theorems]]
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| * 0-dimensional singularity: [[magnetic monopole]]
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| * 1-dimensional singularity: [[cosmic string]]
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| * 2-dimensional singularity: [[Domain wall (string theory)|domain wall]]
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| * [[Fuzzball (string theory)]]
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| ==Notes==
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| {{reflist|2}}
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| ==References==
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| {{refbegin}}
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| * {{cite journal | last = Shapiro | first = Stuart L. | authorlink = | coauthors = [[Saul Teukolsky|Teukolsky, Saul A.]] | title = Formation of naked singularities: The violation of cosmic censorship | date = 1991 | journal = [[Physical Review Letters]] | volume = 66 | issue = 8 | pages = 994–997 | doi = 10.1103/PhysRevLett.66.994 | pmid = 10043968 | bibcode=1991PhRvL..66..994S}}
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| * {{cite book | author = [[Robert Wald|Robert M. Wald]] | title = [[General Relativity (book)|General Relativity]] | publisher = [[University of Chicago Press]] | year = 1984 | isbn = 0-226-87033-2 }}
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| * {{cite book | author = [[Charles W. Misner]] | coauthors = [[Kip Thorne]] & [[John Archibald Wheeler]] | title = [[Gravitation (book)|Gravitation]] | publisher = [[W. H. Freeman]] | year = 1973 | isbn = 0-7167-0344-0 }} §31.2 The nonsingularity of the gravitational radius, and following sections; §34 Global Techniques, Horizons, and Singularity Theorems
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| {{refend}}
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| * Roger Penrose(1996)"[http://www.ias.ac.in/jarch/jaa/17/213-231.pdf Chandrasekhar, Black Holes, and Singularities]"
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| * Roger Penrose(1999)"[http://www.ias.ac.in/jarch/jaa/20/233-248.pdf The Question of Cosmic Censorship]"
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| * Τ. P. Singh"[http://www.ias.ac.in/jarch/jaa/20/221-232.pdf Gravitational Collapse, Black Holes and Naked Singularities]"
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| ==Further reading==
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| * ''[[The Elegant Universe]]'' by [[Brian Greene]]. This book provides a layman's introduction to string theory, although some of the views expressed are already becoming outdated. His use of common terms and his providing of examples throughout the text help the layperson understand the basics of string theory.
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| {{Relativity}}
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| [[Category:Concepts in physics]]
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| [[Category:General relativity]]
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| [[Category:Lorentzian manifolds]]
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| [[Category:Physical paradoxes]]
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Hello, I'm Williemae, a 28 year old from Bottrop Welheimer Mark, Germany.
My hobbies include (but are not limited to) Sand castle building, Trainspotting and watching Two and a Half Men.
Feel free to surf to my blog: geo news news update