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A gravitational singularity occurs when an astrophysical model, typically based on general relativity, predicts a point of infinite curvature. The term is closely related to the mathematical meaning of "singularity": a gravitational singularity occurs when the equations produce a mathematical singularity.

The Big Bang cosmological model of the universe contains a gravitational singularity at the start of time (t=0). At the "Big Bang Singularity," the model predicts that the density of the universe and the curvature of space-time are infinite.

Basically, a singularity is a point and from that point one gets infinities which tends to make any understanding or measurement at that specific point impossible. The one exception to this concerns a Kerr solution in which the singularity forms a ring.

Hawking's solution around this as far as cosmology goes was to impose the idea of an instanton in time. With such a model there is no T=0 point from the perspective of time. Many physicists believe that gravitational singularities are "unphysical", meaning that general relativity ultimately ceases to be an accurate description of gravity somewhere in the vicinity of what would otherwise be a singularity. This is where what is termed quantum gravity comes into play. However, Hawking's proposal is just one of many put forth at present.