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A singularity in solutions of the Einstein field equations is one of three things: Spacelike singularities: The singularity lies in the future or past of all events within a certain region. The Big Bang singularity and the typical singularity inside a non-rotating, uncharged Schwarzschild black hole are spacelike.
The Rare Earth hypothesis argues that planets with complex life, like Earth, are exceptionally rare.. In planetary astronomy and astrobiology, the Rare Earth hypothesis argues that the origin of life and the evolution of biological complexity, such as sexually reproducing, multicellular organisms on Earth, and subsequently human intelligence, required an improbable combination of astrophysical ...
The key to understanding the character of metric evolution on approaching singularity is exactly this process of Kasner epoch alternation with flipping of powers p l, p m, p n by the rule eq. 37. The successive alternations eq. 37 with flipping of the negative power p 1 between directions l and m (Kasner epochs) continues by depletion of the ...
A gravitational singularity, spacetime singularity, or simply singularity, is a theoretical condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically. As such, a singularity is by definition no longer part of the regular spacetime and cannot be determined by "where" or "when".
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
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 ...
Since the physical behavior of singularities is unknown, if singularities can be observed from the rest of spacetime, causality may break down, and physics may lose its predictive power. The issue cannot be avoided, since according to the Penrose–Hawking singularity theorems, singularities are inevitable in physically reasonable situations.
Catastrophe theory studies dynamical systems that describe the evolution [5] of a state variable over time : ˙ = = (,) In the above equation, is referred to as the potential function, and is often a vector or a scalar which parameterise the potential function.