Gravitational singularity
From Freepedia
| General relativity |
| Related topics |
A gravitational singularity occurs when an astrophysical model, typically based on general relativity, predicts some type of pathological behavior of space-time, such as a point of infinite space-time curvature. The term is closely related to the mathematical notion of "singularity": a gravitational singularity occurs when the equations produce a mathematical singularity.
The notion of singularities as points where space-time curvature "blows up" 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 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, 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 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 paradoxically infinite. However, the basic Big Bang model does not include 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 scientific representation of matter becoming so compressed that can have an infinate mass with no physical volume. This type of singularity only occurs when a neutron star is so massive that is completely bent inwards opoun itself untill its gravitational force
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 principle. However, in 1991 Shapiro and 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 is 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 2005, no theory of quantum gravity has been experimentally confirmed.
References
- Wald, R. M.: General Relativity, University Of Chicago Press (1984)
- Shapiro, S. L., and Teukolsky, S. A.: Formation of Naked Singularities: The Violation of Cosmic Censorship, Phys. Rev. Lett. 66, 994-997 (1991)
