Gravitational singularity – Wikipedia, the free encyclopedia

A gravitational singularity or spacetime singularity is a location where the force of gravity has become effectively infinite, and the quantities that are used to measure the gravitational field of a singularity become infinite in a way that does not depend on the coordinate system from the standpoint of any observer of the singularity. These quantities are the scalar invariant curvatures of spacetime, which includes a measure of the density of matter. The laws of normal spacetime could not exist within a singularity and it is currently postulated that matter cannot cross the event horizon of a singularity due to the effects of time dialation.[1][2][3] Singularities are theorized to exist at the center of Black Holes, within Cosmic Strings, and as leftover remants from the early formation of the Universe following the Big Bang. Although gravitational singularities were proposed by Einstein in his General Relativity Theory, their existence has not been confirmed. [4][5][6][7]

For the purposes of proving the PenroseHawking singularity theorems, a spacetime with a singularity is defined to be one that contains geodesics that cannot be extended in a smooth manner.[8] The end of such a geodesic is considered to be the singularity. This is a different definition, useful for proving theorems.[9][10]

The two most important types of spacetime singularities are curvature singularities and conical singularities.[11] Singularities can also be divided according to whether or not they are covered by an event horizon (naked singularities are not covered).[12] According to modern general relativity, the initial state of the universe, at the beginning of the Big Bang, was a singularity.[13] Both general relativity and quantum mechanics break down in describing the Big Bang,[14] but in general, quantum mechanics does not permit particles to inhabit a space smaller than their wavelengths (See: Wave-particle_duality).[15]

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).[16] 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.

In theoretical modeling with supersymmetry theory, a singularity in the moduli space (a geometric space using coordinates to model objects, observers, or locations) happens usually when there are additional massless degrees of freedom (dimensions) at a certain point. Similarly, in String Theory and in M Theory, it is thought that singularities in spacetime often mean that there are additional degrees of freedom (physical dimensions beyond the four dimensions described by General Relativity) that exist only within the vicinity of the singularity. The same fields related to the whole spacetime are postulated to also exist according to this theory; 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 (A theoretical construct of abstract mathematics). This is however, only a theory.[17][18]

A theory supported by Stephen Hawkings called the Black hole information paradox postulates that matter cannot cross the event horizon of a singularity or black hole and remains as stored information just beyond the event horizon and is slowly released as Hawking radiation or held at the event horizon permanently due to the effects of time dialation. "The information is not stored in the interior of the black hole as one might expect, but in its boundary - the event horizon," he told a conference at the KTH Royal Institute of Technology in Stockholm, Sweden. (meaning that as matter enters the event horizon of a black hole the deeper it travels inside the black hole, the slower time flows for that matter relative to an observer outside the black hole watching the matter travel through the event horizon. Time essentially slows until it virtually stops as the matter reaches the event horizon of the singularity and can never make it to the center and is held there forever).[19]

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 completely regular, and the infinities are merely a result of using an inappropriate coordinate system at this point (meaning that Einsteins partial differential equations that describe spacetime curvature and gravity produce infinite values if you provide bad data). In order to test whether there is a singularity at a certain point, one must check whether at this point diffeomorphism invariant quantities (coordinates in a coordinate system describing an observer in such a way that the relationships of the physical law being tested do not vary based on the coordinates of the observer being at different locations) which are scalars become infinite (a scalar is a pure number representing a value, like length). Such quantities are the same in every coordinate system, so these infinities will not "go away" by a change of coordinates. (when proper coordinate systems are used to describe an observers location, no matter what system is employed, a singularity will always produce these infinites using Einstein's partial differential equations to describe space time curvature).

An example is the Schwarzschild solution that 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 a 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. , 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), known as a "ring singularity". Such a singularity may also theoretically become a wormhole.[20]

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. An example of such a conical singularity is a cosmic string. Cosmic strings are theoretical, and their existence has not yet been confirmed. [21]

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.[22][23][24]

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.[25][26]

The Einstein-Cartan-Sciama-Kibble theory of gravity naturally averts the gravitational singularity at the Big Bang. This theory extends general relativity to matter with intrinsic angular momentum (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 spinors generates a spinspin interaction in fermionic 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 (what is theorized is that matter exerts a counterforce based upon the spin (angular momentum) which is present in all fermionic matter that will resist the effects of gravity beyond a certain point of compression and a singularity can never fully form). [27]

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Gravitational singularity - Wikipedia, the free encyclopedia