Time loop

A time loop, also known as an ouroboros loop (AUDIO: The Tears of Isis) chronic hysteresis, (TV: Meglos) and called tempetrification by the people of Manussa, (PROSE: The Terrible Manussa) was a loop in time in which the occupants experienced the same events in endless repetition.

Science
An accurate time loop took little energy to perpetuate. An incomplete time loop (where each repetition was not the same as the last or the loops were not the same length) was unstable. Energy requirements increased with each iteration. (PROSE: The Pirate Loop)

While there was no known technological method of escaping a time loop, the Fourth Doctor and Romana broke a time loop by deliberately recreating the events of the loop out of phase with the loop itself. (TV: Meglos) The Third Doctor was able to escape the time loop he created around Axos by boosting the signal. This might indicate that the person creating a time loop could still leave it. (TV: The Claws of Axos) As he later related, however, due to the Time Lords tampering with his TARDIS and knowledge of time travel, the loop he created was not an accurate time field/threshold, (AUDIO: The Feast of Axos) so this may have allowed his exit.

Characteristics
The Third Doctor attempted to explain the concept to the Brigadier and Jo Grant as a "loop in time," the same events in space occurring over the same place in time. Time loops had the appearance of the infinity symbol, (TV: The Claws of Axos) a figure of eight looping through four dimensions.

The threshold of a time loop, possibly called the "time barrier," could be crossed into. Echoes of the past and future could be experienced, such as messages repeating themselves. This was evidence that various futures were possible; a message from the future did not guarantee those events would happen as time was in flux. A time loop would eventually decay naturally over six billion years. (AUDIO: The Feast of Axos)

Chaotic time loops could have the appearance of a spiral or spider web. (AUDIO: Spider's Shadow)

Occurrences
Several planets were placed into time loops by the Time Lords, including the War Lords' planet, (TV: The War Games, PROSE: Timewyrm: Exodus) the Vardan homeworld, (TV: The Invasion of Time) and Planet 5. (TV: Image of the Fendahl, PROSE: The Taking of Planet 5) Leela thought the time loop into which Planet 5 was placed was "very clever", but the Fourth Doctor replied that it was "criminal". (TV: Image of the Fendahl) They intended to time loop the Hoothi worlds, but the Hoothi had vanished. (PROSE: Love and War)

Axos was placed into a time loop (TV: The Claws of Axos) but some part of it was freed by Chiyoko to ensure her own existence. (COMIC: The Child of Time) The rest of it was released by an expedition attempting to harness it as a power source, but the Sixth Doctor later restored the time loop, trapping Axos in the moment of its own destruction. (AUDIO: The Feast of Axos)

While the completed Key to Time would have stopped time altogether, five pieces and a makeshift sixth made of chronodyne was enough to generate a temporary time loop. The Fourth Doctor put the Marshal of Atrios's Command Capsule in a time loop to stop him from destroying Zeos, but his incomplete control of the Key initially put the entire universe in a loop apart from the TARDIS console. (TV: The Armageddon Factor)

Meglos used a time loop to trap the Fourth Doctor and Romana in the TARDIS and prevent them reaching Tigella, but the loop was incomplete, allowing them to break free of it after they realised what had happened by repeating the opening moments of the loop on their own. (TV: Meglos)

Koel Paddox unintentionally trapped himself in a time loop when he attempted to duplicate the Arboretans' ability to live their lives over again, transferring his mind into his past self at the moment of birth but unable to change any actions committed by his past self. (PROSE: Festival of Death)

Events on the planet Puxatornee were essentially caught in a time loop, as the Seventh Doctor and Melanie Bush were forced to create two different alternate timelines when they arrived on this world, with residents of each timeline unwittingly creating the other by attempting to avert or cause the assassination of President Bailey thirty years ago. (AUDIO: Flip-Flop)

The Daleks were trapped in a time loop inside the Time Vortex. (AUDIO: The Time of the Daleks)

Jack Harkness was trapped in a two-week time loop with his fellow renegade Time Agent John Hart for five years. (TV: Kiss Kiss, Bang Bang)

Lucie Miller materialised the TARDIS inside a time loop when she and the Eighth Doctor chased the rogue time-traveller Nick Zimmerman after he deliberately placed himself within one to prevent his wife Rachel from dying. (AUDIO: No More Lies)

The Eighth Doctor and Charley Pollard got trapped inside a time loop and space loop in an Edwardian house. (AUDIO: The Chimes of Midnight)

When the Brilliant was attacked by space pirates, the engine was engaged and accidentally caused an incomplete time loop. Though things were brought back after destruction, it was inconsistent and mistakes were made. The Tenth Doctor finally fixed the time loop, causing less damage. (PROSE: The Pirate Loop)

In 1937, a demon trapped Casey and Marie Ward in a time loop on their wedding night, to dance to "The Band Played On", until they went insane. (PROSE: The Very Real Mystery of Wester Drumlins)

The Trickster placed Sarah Jane Smith, Peter Dalton, the Tenth Doctor, and Sarah's friends in a time loop in the hotel where Sarah and Peter's wedding was taking place, with Peter and Sarah trapped in one second and the Doctor and Sarah's friends in another. (TV: The Wedding of Sarah Jane Smith)

A crashed time ship trying to find a pilot for itself created several time loops in the local area during its failed attempts to repair itself. (TV: The Lodger)

The Doctor's TARDIS put River Song in a time loop to stop its explosion killing her, simultaneously putting itself in a time loop at the moment of its own destruction so that it could serve as a substitute sun for Earth, until she was rescued by the Eleventh Doctor. (TV: The Big Bang)

In 2050, due to the Oroborus consuming time, time distortions such as time loops occurred across London. (TV: Oroborus)

The life cycle of the Cinder was a form of time loop; the creature was defeated by the First Doctor and Vicki Pallister in 1814. Its surviving form was accidentally taken back to the 12th century B.C. by Vicki. That form would eventually grow into the creature defeated in 1814. (AUDIO: Frostfire)

The Eighth Doctor set up a time loop inside Edward Fyne's body to temporarily slow down the progress of his tyger-fever. (PROSE: The Eye of the Tyger)

The Fifth and the Eighth Doctor used their TARDISes to trap the Dalek Prime in a time loop. (AUDIO: The Four Doctors)

The whole of the Divergent Universe was in a time-loop, throughout its whole existence, preventing time-travel inside the universe as it was impossible to focus on specific temporal coordinates as every moment had happened several times before; Rassilon had been through this loop 85 times by the time the Eighth Doctor caught up to him, despite the Doctor entering the Divergent Universe less than an hour after Zagreus threw Rassilon into the universe. (AUDIO: The Next Life)

George Smythe placed himself and his family in a time loop to prevent his wife from leaving him. Barbara Wright convinced him to end the loop and let his wife go. (PROSE: Every Day)

The headquarters for the Remonstration Bureau was put in a time loop to protect it from attack. (PROSE: The Book of the War)

The Doctor's TARDIS created a time loop in ELF Storage to resurrect the Thirteenth Doctor after she was exterminated by a Executioner Dalek. The TARDIS was unable to sustain the loop, resulting in it starting slightly later each iteration, but the repeats enable the Doctor and her allies to devise a way to destroy the Executioner Daleks. (TV: Eve of the Daleks)

Loop temporal