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A '''singularity''' (sometimes '''spacetime singularity''') is, approximately, a place where quantities which are used to measure the [[gravitational]] field become [[infinity|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.

A '''singularity''' (sometimes '''spacetime singularity''') is, approximately, a place where quantities which are used to measure the [[gravitational]] field become [[infinity|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.

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. [[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.

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. [[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.

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 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 ''Kretschmann scalar'' or square of the [[Riemann tensor]], which is diffeomorphism invariant - is infinite.

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 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 ''Kretschmann scalar'' or square of the ''Riemann tensor'', 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, the singularity occurs on a ring (a circular line), defined as a "[[ring singularity]]". Such a singularity may also theoretically become a [[wormhole]]. 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.

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, the singularity occurs on a ring (a circular line), defined as a "[[ring singularity]]". Such a singularity may also theoretically become a [[wormhole]]. 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.

===Naked===

===Naked===

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 Stuart Shapiro and Saul 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.

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 Stuart Shapiro and Saul 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.

==Notes==

==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.

* 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.

==Notes and references==

==Notes and references==

* Formation of naked singularities: The violation of cosmic censorship  [http://link.aps.org/abstract/PRL/v66/p994]  

* Formation of naked singularities: The violation of cosmic censorship  [https://link.aps.org/abstract/PRL/v66/p994]  

* General Relativity ISBN 0-226-87033-2 }}

* General Relativity ISBN 0-226-87033-2

* Gravitation, ISBN 0-7167-0344-0 }} §31.2 The nonsingularity of the gravitational radius, and following sections; §34 Global Techniques, Horizons, and Singularity Theorems

* Gravitation, ISBN 0-7167-0344-0 §31.2 The nonsingularity of the gravitational radius, and following sections; §34 Global Techniques, Horizons, and Singularity Theorems

==Further reading==

==Further reading==

* ''[[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.

* ''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.

[[Category: Physics]]

[[Category: Physics]]