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Gravitational singularity
*** Shopping-Tip: Gravitational singularity
{{General relativity}} {{expert}}
A '''gravitational singularity''' occurs when an
astrophysics astrophysical model, typically based on
general relativity, predicts some type of
physical paradox pathological behavior of
space-time, such as a point of
infinity infinite space-time
curvature. In this point, everything will be infinitely deflected by an infinite gravitational well.
The edge of a gravitational singularity is called the event horizon. In a
black hole for example, until this point, light(or a theoretical body) can still escape the singularity. Pending that it
*Moves at the speed of light
*Travels in a direction directly perpendicular to the surface of the event horizon.
After this point, nothing can escape.
The term is closely related to the
mathematics mathematical notion of "
Mathematical singularity singularity": a gravitational singularity occurs when the equations produce a
mathematical singularity.
Discussion
The notion of singularities as points where space-time curvature reaches infinity is the one that is most intuitive. However, singularities can exist even if the curvature of space-time is finite everywhere. Not all geometries whose
metric tensor blows up at some point must be actual geometric singularities; some of them are merely coordinate singularities and may be removed by a redefinition of coordinates.
More generally, a space-time is considered singular if:
* It is
geodesic (general relativity) geodesically incomplete, meaning that there are freely-falling observers whose existence is finite in at least one direction of time (as measured by their local clocks). For example, any observer below the
event horizon of a nonrotating
black hole would fall into its center within a finite period of time, at which moment laws of physics would break down and it would become impossible to predict the observer's further evolution. Thus, we say that there is a gravitational singularity in the center of the black hole.
* Space-time also has to be
inextendible space-time inextendible, i.e. not to be a proper subset of some bigger space-time. It is fairly easy to construct space-times that possess incomplete
geodesics from regular
Minkowski space by removing points, yet we want to avoid calling such constructs 'singularities'. See
Rindler coordinates for a fairly involved example where an apparent singularity arises by cutting a wedge out of Minkowski space, followed by a coordinate transformation.
If these two conditions are met, it is said that singularities are located at the "points" where "incomplete" observers start and/or end their existence.
The
Big Bang cosmology cosmological model of the
universe contains a gravitational singularity at the start of
time (''t''=0). At the "Big Bang Singularity," the model predicts that the density of the universe and the curvature of space-time are
physical paradox paradoxically infinite. However, the basic Big Bang model does not include
quantum mechanics quantum effects, so its predictions are valid only shortly after the projected singularity.
A singularity also exists within a
black hole, where general relativity predicts a region of infinite curvature. In a non-rotating black hole, the singularity occurs at a single point in the model coordinates, and is called a "point singularity". In a rotating black hole, the singularity occurs on a ring, and is called a "
ring singularity". Rotating black holes are sometimes referred to as
Kerr black holes. A singularity in a black hole is the theoretical representation of
matter becoming so compressed that it can have unlimited
density with no physical
volume. This type of singularity only occurs when a
neutron star is so
massive that it is completely bent inwards upon itself due to its own gravitational forces.
Until the early
1990s, it was widely believed that general relativity hides every singularity behind an
event horizon, making
naked singularity naked singularities impossible. This is referred to as the
cosmic censorship hypothesis. However, in
1991 Stuart Shapiro Shapiro and
Saul Teukolsky Teukolsky performed computer simulations of a rotating plane of dust which indicated that general relativity allows for naked singularities. What these objects would actually look like is unknown. Nor is it known if singularities would still arise if the simplifying assumptions used to make the simulation tractable were removed.
The singularity is an object that challenges so many ideas in
physics (such as the idea of mass without volume) that it is described as unphysical (i.e. it cannot really exist under present assumptions about physical science). This does not mean that it does not exist, but it does mean that it would take a new view and a few new theories about
physics to change the current state belief. It is generally assumed that a theory of
quantum gravity - a theory that unifies
general relativity with
quantum mechanics - will provide a better description of what actually occurs where
general relativity predicts a singularity. However,
as of 2006, no theory of
quantum gravity has been experimentally confirmed.
References
* Shapiro, S. L., and Teukolsky, S. A.: ''Formation of Naked Singularities: The Violation of Cosmic Censorship'', Phys. Rev. Lett. '''66''', 994-997 (1991)
* Wald, Robert M.: ''General Relativity'', ch. 9, University of Chicago Press (1984)
Category:Lorentzian manifolds
Category:paradoxes
da:Gravitationel singularitet
de:Singularität (Astronomie)
es:Singularidad
fr:Singularité
he:×¡×™× ×’×•×œ×¨×™×•×ª כבידתית
hu:Gravitációs szingularitás
nl:Singulariteit
ja:特異点
pt:Singularidade gravitacional
sl:Gravitacijska singularnost
fi:Singulariteetti
th:ภาวะเà¸à¸?à¸?านเชิงความโน้มถ่วง
zh:引力奇点
*** Shopping-Tip: Gravitational singularity
