gravitational singularity

The term gravitational singularity (often shortened to singularity) is used for the presumed point in the center of a black hole where density and gravity are infinite. In mathematics (such as mathematical models), the term, singularity refers to situations where some quantity mathematically goes to infinity, and the assumptions you ordinarily make based upon slopes of functions, etc., do not hold. A gravitational singularity is a class of such mathematical singularities within general relativity. Models of non-rotating black holes (Schwarzschild black holes) have such a point at the center, but in rotating black holes (Kerr black holes), the corresponding singularity is a ring around the center (a ring singularity). (At some high density, nothing prevents gravity from drawing the mass to a mathematical point, implying a density rising to infinity.) Generally, such a gravitational singularity must be surrounded by an event horizon, but some models of very small black holes consist of a naked singularity, i.e., one without the surrounding event horizon. There are theorized impediments to the existence of small black holes which may make these impossible: in particular, how the laws of GR interplay with quantum mechanics is not clear.

Singularity is actually a mathematical term that applies to features of some functions, e.g., points where the function's value is infinity, and above-described gravitational singularity is such a mathematical singularity in GR's functions that describe gravity. Mathematical singularities also occur in other physical (including astrophysical) models, sometimes due to a model's simplifications. There are cases where transforming a model (of a physical phenomenon) to a different set of parameters allows equivalent mathematics to avoid the singularities.