A gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system. These quantities are the scalar invariant curvatures of spacetime, some of which are a measure of the density of matter.
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. The end of such a geodesic is considered to be the singularity. This is a different definition, useful for proving theorems.
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. 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 also known as curvature singularities.
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 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,singularity serial,singularity key,singularity codes, 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.
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 become shorter.
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.
An example is the Schwarzschild solution that describes a nonrotating, 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 Kretschmann scalar or square of the Riemann tensor, singularity gameplay,singularity review,R????R????, which is diffeomorphism invariant, is infinite. While in a nonrotating 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.[1]
More generally, a spacetime is considered singular if it is geodesically incomplete, meaning that there are freelyfalling 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. code singularity,singularity serial key.The classical version of the 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 spacetime curvature.
