In the fictional world of Doctor Who, the Eye of Harmony is the nucleus of an artificial black hole created by the Time Lords to provide energy for their home world of Gallifrey and their time travel technology.
The Eye was originally mentioned in the Fourth Doctor serial The Deadly Assassin (1976), where it was revealed as the source of power that sustained Gallifrey. According to the ancient records, the legendary Time Lord Rassilon captured and placed the Eye – the nucleus of a black hole – beneath the Time Lord's citadel on Gallifrey (the Panopticon). Rassilon placed the black hole's nucleus in an eternally dynamic equation against the mass of Gallifrey and so that as long as the Eye existed in this "balanced state", the power of the Time Lords would "neither flux nor wither". However, it remained there for so long that it passed into legend. Until the Fourth Doctor and the renegade Time Lord known as The Master rediscovered it in The Deadly Assassin, the Time Lords had forgotten its location, some even believing it to be mythical or no longer in existence.
As seen in The Deadly Assassin, the Eye was linked to two other Gallifreyan artifacts, the Sash of Rassilon and the Great Key of Rassilon. The Sash was essential for the wearer to control and manipulate the Eye safely without being sucked into its gravity well and the Great Key was an ebonite rod that could be used to drain energy from the Eye. The Great Key was later renamed the Rod of Rassilon in The Invasion of Time (1978) to distinguish it from the other Great Key, a component of the De-mat gun.
In The Deadly Assassin and the 1996 Doctor Who television movie, The Master tried to use the Eye to steal himself a new set of regenerations from the Doctor.
Prior to this, in the 1973 story The Three Doctors, another figure from Time Lord history was introduced. Omega was a solar engineer who, in trying to provide an energy source for the Time Lords' time travel experiments, harnessed the power of a supernova. However, this apparently killed Omega and created a black hole. Unknown to anybody for millennia, Omega was not dead, but merely trapped beyond the event horizon of the black hole in an anti-matter universe.
The first connection between Omega and Rassilon was made by Alan Moore in his 1980 Doctor Who Monthly comic strip story Star Death (DWM #47). Star Death showed the proto-Time Lords trying to collapse the star Qqaba into a black hole and harness its "energy stream". Omega and Rassilon were both members of this project, and when sabotage sent Omega hurtling into the newly created black hole, he was presumed lost. Rassilon then took control of the project, and the power of the black hole. It was not made explicit, however, that this black hole was the same one that provided the Eye of Harmony. (Qqaba would also be mentioned in the 1998 novel The Infinity Doctors by Lance Parkin.)
This connection appeared next in the 1988 serial Remembrance of the Daleks, where Omega's stellar manipulation device was dubbed the Hand of Omega and became the object of a struggle between two competing factions of Daleks. Although the televised story made no mention of Rassilon, the 1991 novelisation of the serial (though again of unclear canonicity) by the story's writer Ben Aaronovitch, drawing on elements of the so-called "Cartmel Masterplan", made the connection between the two Time Lords explicit. The story of Omega's supernova becoming the black hole that provided Rassilon with the Eye of Harmony became part of the fan-accepted mythology and was incorporated into the Virgin New Adventures novels.
The 1996 television movie revealed a new function for the Eye. No longer just a power source for Gallifrey, in the movie an artifact referred to as the Eye of Harmony was part of the TARDIS and, for the first time, was stated to be the TARDIS's primary power source, located in the centre of the TARDIS' cloister room. It was also shown that leaving the TARDIS's Eye open for too long would result in a spacetime distortion as the space around the Eye was exposed to the gravitational effects of the singularity; the Earth is nearly destroyed in the process. The Eye of Harmony can be opened using human eyes, meaning the Master, despite possessing a human body, cannot open it as he has retained snake-like eyes. The Master is sucked into the Eye of Harmony and apparently killed when he fights the Doctor.
However, having the Eye of Harmony on board the TARDIS contradicted the idea that the Eye itself was on Gallifrey. To reconcile this, fan speculation held that this was not the real Eye, but merely a name applied to a remote link to the actual Eye that powered the craft (possibly in the same way the Time Lords transmitted energy from Gallifrey to the TARDIS in The Three Doctors), or alternatively, the Eye had been somehow transferred to the TARDIS. The former conjecture became established fanon, and was taken up in the spin-off media and was eventually confirmed by the official BBC website.
The Past Doctor Adventures novel The Quantum Archangel by Craig Hinton offered another explanation by claiming that all TARDISes built after a certain point, including the Type 40 the Doctor uses, have a mathematically modelled duplicate of the Eye with all its attendant features, thus helping the TARDISes cope with the previously-discovered power problems inherent if they travel too far away from the original Eye.
The television movie also reveals a link between the Eye of Harmony on board the TARDIS and the Doctor's own eyes. The Master uses the Eye to see what the Doctor is seeing at the same moment. The symbiosis between a Time Lord and his TARDIS has been hinted at before, such as in the Sixth Doctor story "The Two Doctors" in which The Sontarans try to isolate the Doctor's symbiotic nuclei in an attempt to construct their own time machine.
In the episodes "Boom Town" and "Utopia", the TARDIS needed to 'refuel' by absorbing energy from a 'scar' left by a closed space/time rift in Cardiff, implying that it is not powered entirely by the Eye at this time. The former episode also revealed that the TARDIS console concealed the 'Heart of the TARDIS', a mysterious glowing energy source that the Doctor associated (in "The Parting of the Ways") with the energies of the time vortex.
The Tenth Doctor makes an oblique reference to the Eye's creation in the episode "The Satan Pit" when he says: "My people practically invented black holes. Well... in fact they did." The Master also mentions in "The Sound of Drums" that the rockets on Earth have "black hole manipulators", which suggests that the Time Lords have knowledge of the physics of black holes.
In the episode "Hide", the Doctor is able to utilise a "subset of the Eye of Harmony" to access a pocket universe by running various cables from the TARDIS.
In the episode "Journey to the Centre of the TARDIS", the Eye of Harmony is seen in the TARDIS (whose inner dimensions are said to be infinite). The Doctor describes it as an "exploding star in the act of becoming a black hole [...] suspended in a permanent state of decay." It is revealed that one can only survive in the room housing the Eye of Harmony "for a minute or two", and that further exposure would liquefy the cells in the body and burn skin.
This 1976 explanation of Time Lord power followed closely from a period of extensive scientific exploration and validation relating to black holes in the scientific world, lasting from approximately 1964–1974, during which key discoveries related to the power, energy, and possible time-related properties of black holes was undertaken. (See: Timeline of black hole physics)