Gravitational singularity

A gravitational singularity or space-time singularity is a location in space-time where the gravitational field of a celestial body becomes infinite in a way that does not depend on the coordinate system. The quantities used to measure gravitational field strength are the scalar invariant curvatures of space-time, which includes a measure of the density of matter. Since such quantities become infinite within the singularity, the laws of normal space-time could not exist.

A type of singularity predicted by general relativity is inside a black hole: any star collapsing beyond a certain point (the Schwarzschild radius) would form a black hole, inside which a singularity (covered by an event horizon) would be formed. The Penrose–Hawking singularity theorems define a singularity to have geodesics that cannot be extended in a smooth manner. The termination of such a geodesic is considered to be the singularity.

According to modern general relativity, the initial state of the universe, at the beginning of the Big Bang, was a singularity. Both general relativity and quantum mechanics break down in describing the earliest moments of the Big Bang, but in general, quantum mechanics does not permit particles to inhabit a space smaller than their wavelengths.

Many theories in physics have mathematical singularities of one kind or another. 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.

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