Gravitational singularity

General relativity
${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}$
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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”. Gravitational singularities exist at a junction between general relativity and quantum mechanics; therefore, the properties of the singularity cannot be described without an established theory of quantum gravity. Trying to find a complete and precise definition of singularities in the theory of general relativity, the current best theory of gravity, remains a difficult problem.^[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]

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.^[2] The density would become infinite at the singularity. General relativity also predicts that the initial state of the universe, at the beginning of the Big Bang, was a singularity of infinite density and temperature.^{[5][obsolete source]} However, classical gravitational theories are not expected to be accurate under these conditions, and a quantum description is likely needed.^[6] For example, quantum mechanics does not permit particles to inhabit a space smaller than their Compton wavelengths.^[7]