(covers information from several alternate timelines)
A singularity, or quantum singularity, is an extremely dense region of the spacetime continuum which produces extremely powerful gravitational forces. Singularities can be produced both naturally, as in black holes, or artificially.
In 2371, Lieutenant Jadzia Dax's body acted as a singularity during the planet Meridian's dimensional shifting. Dax's presence during the shift destabilized the planet's quantum matrix, threatening complete destruction of Meridian. As Dax was acting like an anchor, the crew of the USS Defiant was forced to beam her up in order for the shift to be completed. (DS9: "Meridian")
Quantum singularities can also be utilized as interdimensional rifts. In 2374, the Borg created a series of quantum singularities via the generation of resonant graviton beams, in an attempt to invade fluidic space. Seven of Nine was later able to modify USS Voyager's navigational deflector to perform the same function, and took the ship through the rift. (VOY: "Scorpion", "Scorpion, Part II")
Another novel use of a quantum singularity was in 2378, when the crew of Voyager was able to bounce a tachyon beam off of one and successfully establish communication with Starfleet, on the other side of the galaxy. This communication was limited by the fact that the singularity was only in alignment for eleven minutes every day. (VOY: "Author, Author")
Types of singularities
A microscopic singularity (or microsingularity) is a naturally occurring phenomenon that can be described as a tiny black hole.
In 2151, the Enterprise NX-01 rendezvoused with a Tesnian ship at an asteroid field, at which time a microsingularity collided with the Tesnian ship and caused it to crash. Three microsingularities also struck Enterprise, dissipating on impact when they encountered its polarized hull plating. Shortly after, Shuttlepod 1 was also struck by a microsingularity, which passed directly through its hull and threatened on-board life support. (ENT: "Shuttlepod One")
In 2371, a microscopic singularity passed through the Sol system and exploded, producing a surge of temporal energy which shifted the chroniton particles lodged in the Defiant's ablative armor matrix into a high level of temporal polarization. This caused a transporter beam passing through the polarized particles carrying Captain Benjamin Sisko, Lieutenant Dax, and Doctor Julian Bashir, to be redirected through time to San Francisco, the year 2024. It also created a subspace bubble around the Defiant, isolating it from changes to the timeline inadvertently effected by the three officers. Using the remaining polarized chronitons, Chief O'Brien and Major Kira were able to recreate the accident and rescue their stranded crewmates, after restoring the timeline. (DS9: "Past Tense, Part I", "Past Tense, Part II")
In 2374, Voyager discovered a ten thousand year-old communications relay network being used by the Hirogen in the Delta Quadrant. Analysis indicated that each of the relay stations utilized a harvested microsingularity as a power source. While engaged in battle with an Hirogen vessel, the Voyager crew used an antithoron burst to destabilize the containment field around one of the singularities and increase its gravitational pull. The plan worked, but the containment field failed, destroying the relay station and causing the singularity to grow into a black hole. While Voyager was able to escape, the Hirogen ship was destroyed. (VOY: "Message in a Bottle", "Hunters")
Artificial quantum singularity
An artificial quantum singularity (also known as a confined, or forced quantum singularity) was a method utilized by the Romulans for generating energy, instead of the more traditional matter-antimatter reaction used in Federation starships. In order to remain undetected while cloaked, nullifier cores were used to precisely balance the radiative emissions of the ship's engines. (TNG: "Face of the Enemy")
In 2369, a race of aliens from another time continuum mistook a Romulan Warbird's artificial quantum singularity for a natural black hole. Placing their embryonic young in the singularity's gravity well for the purpose of incubation, they soon realized that their young had become trapped. Later, when the USS Enterprise initiated a power transfer beam in an attempt to help the damaged Warbird, the beam's interaction with the compromised singularity created a temporal aperture, disrupting spacetime around both ships, creating a series of temporal fragments. (TNG: "Timescape")
In 2371, the temporal energy being radiated from the artificial quantum singularity of a cloaked Warbird orbiting station Deep Space 9 interacted with the delta-series radioisotopes which Chief O'Brien had absorbed due to the explosion of a plasma conduit. This had the effect of causing O'Brien to shift forward in time by approximately five hours every time the singularity emitted temporal radiation at a specific wavelength. Later, O'Brien and Doctor Bashir were able to control O'Brien's time shifts by flooding his body with more of the isotopes and calibrating the decay rate to match the temporal frequency of the singularity. (DS9: "Visionary")
Type-four quantum singularity
A type-four quantum singularity is a highly-localized disturbance in the spacetime continuum, characterized by a gravimetric flux density of over two thousand percent.
In 2371, Voyager encountered and became trapped within the event horizon of a type-four quantum singularity in the Delta Quadrant. Due to massive temporal distortions being emitted from the singularity, the crew of Voyager encountered time-delayed reflections of their own ship, initially making them believe that they had encountered another vessel being pulled into the singularity. Eventually, they were able to find their way out by exiting through a breach in the event horizon which they had created when they initially entered. (VOY: "Parallax")
The term singularity is derived from mathematics, and for gravitational singularities refers to points of infinite or near-infinite density or space curvature.