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Encyclopedia > Gravitational singularity

A gravitational singularity (sometimes spacetime singularity) is, approximately, a place where quantities which are used to measure the gravitational field become infinite. Such quantities include the curvature of spacetime or the density of matter. More accurately, a spacetime with a singularity contains geodesics which cannot be completed in a smooth manner. The limit of such a geodesic is the singularity. This article covers the physics of gravitation. ... The infinity symbol ∞ in several typefaces. ... In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension at least 3 is too complicated to be described by a single number at a given point. ... In physics, density is mass m per unit volume V. For the common case of a homogeneous substance, it is expressed as: where, in SI units: ρ (rho) is the density of the substance, measured in kg·m-3 m is the mass of the substance, measured in kg V is... This article or section does not cite any references or sources. ... In physics, spacetime is a mathematical model that combines space and time into a single construct called the space-time continuum. ... In physics, and specifically general relativity, geodesics are the world lines of a particle free from all external force. ... Smooth could mean many things, including: Smooth function, a function that is infinitely differentiable, used in calculus and topology. ...


The two most important types of spacetime singularities are curvature singularities and conical singularities. Singularities can also be divided according to whether they are covered by an event horizon or not (naked singularities). According to general relativity the initial state of the universe, at the beginning of the Big Bang, was a singularity, or single point. Another type of singularity predicted by general relativity is inside a black hole: any star collapsing beyond a certain point 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). These singularities are curvature singularities. For the science fiction film, see Event Horizon (film). ... blah blah blah, some people believe God made the universe and that is all there is. ... General relativity (GR) [also called the general theory of relativity (GTR) and general relativity theory (GRT)] is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... The Universe is defined as the summation of all particles and energy that exist and the space-time in which all events occur. ... According to the Big Bang model, the universe emerged from an extremely dense and hot state. ... Simulated view of a black hole in front of the Milky Way A black hole is an object with a gravitational field so powerful that a region of space becomes cut off from the rest of the universe – no matter or radiation (including light) that has entered the region can... STAR is an acronym for: Organizations Society for Telescopy, Astronomy, and Radio, a non-profit New Jersey astronomy club. ...

Contents

Interpretation

Many theories in physics have mathematical singularities of one kind or another. Equations for these physical theories predict that the rate of change 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 and in renormalization. In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability. ... In mathematics, the derivative of a function is one of the two central concepts of calculus. ... The ultraviolet catastrophe, also called the Rayleigh-Jeans catastrophe, was a prediction of early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation with infinite power. ... Figure 1. ...


In supersymmetry, a singularity in the moduli space happens usually when there are additional massless degrees of freedom in that certain point. Similarly, it is thought that singularities in spacetime often mean that there are additional 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 closed strings, while the degrees of freedom are "stuck" to the singularity and related either to open strings or to the twisted sector of an orbifold. This article or section is in need of attention from an expert on the subject. ... In algebraic geometry, a moduli space is a parameter space for families of algebraic objects (such as algebraic varieties, morphisms, vector bundles). ... Unsolved problems in physics: What causes anything to have mass? The U.S. National Prototype Kilogram, which currently serves as the primary standard for measuring mass in the U.S. Mass is the property of a physical object that quantifies the amount of matter and energy it is equivalent to. ... The phrase degrees of freedom is used in three different branches of science: in physics and physical chemistry, in mechanical and aerospace engineering, and in statistics. ... The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ... Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point... A string is the fundamental object of study in a branch of theoretical physics called string theory. ... A string is the fundamental object of study in a branch of theoretical physics called string theory. ... In topology and group theory, an orbifold (for orbit-manifold) is a generalization of a manifold. ...


Types of singularities

Curvature singularities

Solutions to the equations of general relativity or another theory of gravity (such as supergravity), often result in encountering points where the metric blows up to infinity. However, many of these points are in fact completely regular. Moreover, the infinities are merely a result of using an inappropriate coordinate system at this point. Thus, in order to test whether there is a singularity at a certain point, one must check whether at this point diffeomorphism invariant quantities (i.e. scalars) become infinite. Such quantities are the same in every coordinate system, so these infinities will not "go away" by a change of coordinates. General relativity (GR) [also called the general theory of relativity (GTR) and general relativity theory (GRT)] is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... Gravity is a force of attraction that acts between bodies that have mass. ... In theoretical physics, supergravity (supergravity theory) refers to a field theory which combines the two theories of supersymmetry and general relativity. ... In mathematics a metric or distance function is a function which defines a distance between elements of a set. ... In mathematical analysis, a differentiability class is a classification of functions according to the properties of their derivatives. ... In mathematics as applied to geometry, physics or engineering, a coordinate system is a system for assigning a tuple of numbers to each point in an n-dimensional space. ... In theoretical physics, general covariance (also known as diffeomorphism invariance) is the invariance of physical laws (for example, the equations of general relativity) under arbitrary coordinate transformations. ... A scalar may be: Look up scalar in Wiktionary, the free dictionary. ...


An example is the Schwarzschild solution which describes a non-rotating, 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 regular. The regularity becomes evident when changing to another coordinate system (such as the Kruskal coordinates), where the metric is perfectly 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 square of the Riemann tensor, RμνρσRμνρσ, which is diffeomorphism invariant, is infinite. 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), defined as a "ring singularity." Such a singularity may also theoretically become a wormhole (see notes**). It has been suggested that Deriving the Schwarzschild solution be merged into this article or section. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... For the science fiction film, see Event Horizon (film). ... In physics, spacetime is a mathematical model that combines space and time into a single construct called the space-time continuum. ... In mathematical analysis, a differentiability class is a classification of functions according to the properties of their derivatives. ... In general relativity, Kruskal-Szekeres coordinates are a coordinate system for a Schwarzschild geometry. ... In mathematical analysis, a differentiability class is a classification of functions according to the properties of their derivatives. ... Simulated view of a black hole in front of the Milky Way A black hole is an object with a gravitational field so powerful that a region of space becomes cut off from the rest of the universe – no matter or radiation (including light) that has entered the region can... In differential geometry, the Riemann curvature tensor is the most standard way to express curvature of Riemannian manifolds, or more generally, any manifold with an affine connection, torsionless or with torsion. ... A rotating black hole (Kerr black hole or Kerr-Newman black hole) is a black hole that possesses angular momentum. ... In general relativity the gravitational singularity at the centre of a rotating black hole (a Kerr black hole) is supposed to form a circle rather than a point. ... Analogy to a wormhole in a curved 2D space (see Embedding Diagram) Artists impression of a wormhole as seen by an observer crossing the event horizon of a Schwarzschild wormhole, which is similar to a Schwarzschild black hole but with the singularity replaced by an unstable path to a...


More generally, a spacetime is considered singular if it is geodesically incomplete, meaning that there are freely-falling particles whose motion cannot be determined at a finite time at the point of reaching the singularity. For example, any observer below the event horizon of a nonrotating black hole would fall into its center within a finite period of time. The simplest Big Bang cosmological model of the universe contains a causal singularity at the start of time (t=0), where all timelike geodesics have no extensions into the past. Extrapolating backward to this hypothetical time 0 results in a universe of size 0 in all spatial dimensions, infinite density, infinite temperature, and infinite space-time curvature. In physics, and specifically general relativity, geodesics are the world lines of a particle free from all external force. ... For the science fiction film, see Event Horizon (film). ... According to the Big Bang model, the universe emerged from an extremely dense and hot state. ... Physical cosmology, as a branch of astrophysics, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. ... The Universe is defined as the summation of all particles and energy that exist and the space-time in which all events occur. ... A pocket watch, a device used to tell time Look up time in Wiktionary, the free dictionary. ...


Conical singularities

A conical singularity occurs when there is a point where the limit of every 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 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. In theoretical physics, general covariance (also known as diffeomorphism invariance) is the invariance of physical laws (for example, the equations of general relativity) under arbitrary coordinate transformations. ... In physics, spacetime is a mathematical model that combines space and time into a single construct called the space-time continuum. ... A cone is a basic geometrical shape: see cone (solid). ... In mathematics as applied to geometry, physics or engineering, a coordinate system is a system for assigning a tuple of numbers to each point in an n-dimensional space. ...


Naked singularities

Main article: Naked singularity

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 Shapiro and Teukolsky performed computer simulations of a rotating plane of dust which 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. blah blah blah, some people believe God made the universe and that is all there is. ... For the band, see 1990s (band). ... General relativity (GR) [also called the general theory of relativity (GTR) and general relativity theory (GRT)] is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... This article or section is in need of attention from an expert on the subject. ... 1991 (MCMXCI) was a common year starting on Tuesday of the Gregorian calendar. ... Saul Teukolsky is one of the pioneers of numerical relativity - the subject that deals with computing facts of general relativity using supercomputers. ...


Notes

  • See the discussion of entropy and Hawking radiation under black hole. 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 holes 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 a million is reached, rather than the thousand or so since the background radiation formed.
  • 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 which 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 forces in the tightly curved interior of the wormhole.

Simulated view of a black hole in front of the Milky Way A black hole is an object with a gravitational field so powerful that a region of space becomes cut off from the rest of the universe – no matter or radiation (including light) that has entered the region can... In physics, Hawking radiation (also known as Bekenstein-Hawking radiation) is a thermal radiation thought to be emitted by black holes due to quantum effects. ... In general relativity the gravitational singularity at the centre of a rotating black hole (a Kerr black hole) is supposed to form a circle rather than a point. ... Analogy to a wormhole in a curved 2D space (see Embedding Diagram) Artists impression of a wormhole as seen by an observer crossing the event horizon of a Schwarzschild wormhole, which is similar to a Schwarzschild black hole but with the singularity replaced by an unstable path to a...

Popular culture

In the Stargate SG-1 episode 200, in a parody scene, it is mentioned that a singularity is about to explode. One of the characters even points out that this is impossible. This is used to great effect as a nod to scientific errors made in science fiction. Stargate SG-1 (often abbreviated as SG-1) is a science fiction television series, part of the Stargate franchise. ... 200 is an episode from Season 10 of the science fiction television series Stargate SG-1. ...


In the movie Event Horizon, the creator of the ship (played by Sam Neill) talks of how the ship can travel faster than light, partly due to its ability to produce a singularity. For the science fiction film, see Event Horizon (film). ...


Further reading

1. The Elegant Universe by Brian Greene. This book provides a layperson's introduction to string theory, although some of the views expressed are already becoming outdated. The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory is a book by Brian Greene which introduces string theory and provides a comprehensive though non-technical assessment of the theory and some of its shortcomings. ... Brian Greene Brian Greene (born February 9, 1963), is a physicist and one of the best-known string theorists. ...


References

Saul Teukolsky is one of the pioneers of numerical relativity - the subject that deals with computing facts of general relativity using supercomputers. ... 1991 (MCMXCI) was a common year starting on Tuesday of the Gregorian calendar. ... A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ... 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the CE era. ... January 18 is the 18th day of the year in the Gregorian calendar. ... Robert Wald (b. ... In physics and especially relativity, General Relativity is a popular textbook on Einsteins theory of general relativity written by Robert Wald. ... Charles W. Misner is one of the authors of Gravitation. He has also invented Misner space, a topology and relativity-related mathematical structure. ... Kip S. Thorne Professor Kip Stephen Thorne, Ph. ... John Archibald Wheeler (born July 9, 1911) is an eminent American theoretical physicist. ... A book on gravitation (often considered the Bible by researchers for its prominence) by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler. ...

See also


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