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). 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.