Gravitational singularity
[1][2] A singularity in general relativity can be defined by the scalar invariant curvature becoming infinite[3] or, better, by a geodesic being incomplete.
[4] Gravitational singularities are mainly considered in the context of general relativity, where density would become infinite at the center of a black hole without corrections from quantum mechanics, and within astrophysics and cosmology as the earliest state of the universe during the Big Bang.
Physicists have not reached a consensus about what actually happens at the extreme densities predicted by singularities (including at the start of the Big Bang).
[5] General relativity predicts that any object collapsing beyond a certain point (for stars this is the Schwarzschild radius) would form a black hole, inside which a singularity (covered by an event horizon) would be formed.
Modern theory asserts that the initial state of the universe, at the beginning of the Big Bang, was a singularity.
[7][obsolete source] In this case, the universe did not collapse into a black hole, because currently-known calculations and density limits for gravitational collapse are usually based upon objects of relatively constant size, such as stars, and do not necessarily apply in the same way to rapidly expanding space such as the Big Bang.
Neither general relativity nor quantum mechanics can currently describe the earliest moments of the Big Bang,[8] but in general, quantum mechanics does not permit particles to inhabit a space smaller than their Compton wavelengths.
Equations for these physical theories predict that the ball of mass 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, re-normalization, and instability of a hydrogen atom predicted by the Larmor formula.
In classical field theories, including special relativity but not general relativity, one can say that a solution has a singularity at a particular point in spacetime where certain physical properties become ill-defined, with spacetime serving as a background field to locate the singularity.
Motivated by such philosophy of loop quantum gravity, recently it has been shown[12] that such conceptions can be realized through some elementary constructions based on the refinement of the first axiom of geometry, namely, the concept of a point [13] by considering Klein's prescription of accounting for the extension of a small spot that represents or demonstrates a point,[14] which was a programmatic call that he called as a fusion of arithmetic and geometry.
[15] Klein's program, according to Born, was actually a mathematical route to consider 'natural uncertainty in all observations' while describing 'a physical situation' by means of 'real numbers'.
An example of such a conical singularity is a cosmic string and a Schwarzschild black hole.
[17] 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.
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.
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.
For example, any observer inside the event horizon of a non-rotating black hole would fall into its center within a finite period of time.
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 time-like geodesics have no extensions into the past.
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.
Nor is it known whether singularities would still arise if the simplifying assumptions used to make the simulation were removed.
[19][20][21] Disappearing event horizons exist in the Kerr metric, which is a spinning black hole in a vacuum, if the angular momentum (
In this case, "event horizons disappear" means when the solutions are complex for
); i.e. the spin exceeds what is normally viewed as the upper limit of its physically possible values.
); i.e. the charge exceeds what is normally viewed as the upper limit of its physically possible values.
Also, actual astrophysical black holes are not expected to possess any appreciable charge.
values and the limits noted above; i.e., one just at the point of losing its event horizon, is termed extremal.
However, this concept demonstrates that black holes radiate energy, which conserves entropy and solves the incompatibility problems with the second law of thermodynamics.
The loss of energy also implies that black holes do not last forever, but rather evaporate or decay slowly.
This will occur at a cosmological redshift of more than one million, rather than the thousand or so since the background radiation formed.
