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The monodromy theory of differential equations, in the complex domain, around singularities, does however come into relation with the geometric theory. Roughly speaking, monodromy studies the way a covering map can degenerate, while singularity theory studies the way a manifold can degenerate; and these fields are linked.
Singularity (system theory), in dynamical and social systems, a context in which a small change can cause a large effect Gravitational singularity, in general relativity, a point in which gravity is so intense that spacetime itself becomes ill-defined
[95] [96] Because AI is a major factor in singularity risk, a number of organizations pursue a technical theory of aligning AI goal-systems with human values, including the Future of Humanity Institute (until 2024), the Machine Intelligence Research Institute, [93] the Center for Human-Compatible Artificial Intelligence, and the Future of Life ...
The Penrose–Hawking singularity theorems define a singularity to have geodesics that cannot be extended in a smooth manner. [6] The termination of such a geodesic is considered to be the singularity. Modern theory asserts that the initial state of the universe, at the beginning of the Big Bang, was a singularity.
In recent times, chaos theory has attracted a great deal of work, but deterministic chaos is just a special case of a singularity in which a small cause produces a large observable effect as a result of nonlinear dynamic behavior. In contrast the singularities raised by Maxwell, such as a loose rock at a singular point on a slope, show a linear ...
The singularity at the center of a Schwarzschild black hole is an example of a strong singularity. Space-like singularities are a feature of non-rotating uncharged black holes as described by the Schwarzschild metric , while time-like singularities are those that occur in charged or rotating black hole exact solutions.
In general relativity, a naked singularity is a hypothetical gravitational singularity without an event horizon.. When there exists at least one causal geodesic that, in the future, extends to an observer either at infinity or to an observer comoving with the collapsing cloud, and in the past terminates at the gravitational singularity, then that singularity is referred to as a naked ...
A coordinate singularity occurs when an apparent singularity or discontinuity occurs in one coordinate frame, which can be removed by choosing a different frame. An example of this is the apparent singularity at the 90 degree latitude in spherical coordinates. An object moving due north (for example, along the line 0 degrees longitude) on the ...