Zero Room

A Zero Room, or a Zero Cabinet, was, as described by the First Doctor, a room that was cut off from the rest of the universe, being removed from time and space.

Zero Rooms were used by the Time Lords in times of difficult regeneration or to rapidly heal. There was, for instance, a renowned polygonal Zero Room under the Junior Senate Block on Gallifrey. Such rooms could also be found aboard their TARDISes. (TV: Castrovalva)

They were cut off from the random electrical and radiological influences of the rest of the universe. They were ideal for neurological healing. (AUDIO: The Invasion of E-Space)

They had a tranquil atmosphere. As the Fifth Doctor demonstrated to his companions, some physical laws did not hold as strongly in a Zero Room as in the rest of the universe. For instance, he could levitate in his TARDIS's Zero Room at will. The Zero Room also enhanced his telepathic abilities so he could speak to his companions while resting. (TV: Castrovalva)

The Doctor's TARDIS
When the First Doctor wanted to rest and contemplate, he used the Zero Room. (PROSE: The Rag & Bone Man's Story)

Romana II put the Fourth Doctor in the Zero Room after his synapses were damaged. (AUDIO: The Invasion of E-Space)

The Zero Room was used by the Fifth Doctor following the regeneration of his fourth incarnation. In order to generate enough power to break free of Event One, part of the structure of the TARDIS needed to be ejected. Unfortunately, the Zero Room was one of the areas destroyed. Using the remaining walls of the room, Nyssa was able to construct the Zero Cabinet. It had the same properties as the room, which allowed the Doctor to continue recuperating while he was within it. Nyssa and Tegan found the cabinet light enough to carry, in part because the Doctor used levitation to negate his own weight. However, if the Doctor did not concentrate on keeping himself levitated, the cabinet became too heavy to carry, due to his weight, and would plummet to the ground. (TV: Castrovalva) He would later use it to occasionally rest after an adventure. (PROSE: Dr. Fifth)

Later, the Zero Room was reconstructed in the TARDIS. (AUDIO: Zaltys, Renaissance of the Daleks)

The Sixth Doctor used the Zero Room to return Peri to full health when she began to age rapidly due to inter-dimensional travel. (AUDIO: The Macros) He later used used it to stabilise Charlotte Pollard when she was sick. (AUDIO: Patient Zero) He also used it to lessen the effects of time going backwards, when trying to detach a parasitic being from the TARDIS. (COMIC: Funhouse)

The Seventh Doctor kept a reconstructed Zero Room. (PROSE: Deceit)

Soon after the TARDIS became infected by an organic material from Tír na n-Óg, the Seventh Doctor began adapting the Zero Room into another console room, disconnected from the universe, so he could escape the effects. (PROSE: Cat's Cradle: Witch Mark, Deceit) This control room/Zero Room was lost when the Doctor ejected it from the TARDIS in an attempt to destroy Pool. (PROSE: Deceit)

In the post-War universe, the Eighth Doctor rested in the Zero Room for the months before his wedding with Scarlette while his sickness worsened. His companions and the Henrietta Street House residents visited him there. The only decoration was a portrait of the Doctor's grandfather hanging on the wall facing the bed. (PROSE: The Adventuress of Henrietta Street)

During the early period of the Last Great Time War, the Eighth Doctor told the War Ollistra that his TARDIS lacked a Zero Room. (AUDIO: Day of the Vashta Nerada)

The War Doctor allowed Karlax to use the Zero Room after he regenerated. (PROSE: Engines of War)

By the time of the Tenth Doctor's use of the TARDIS, the Zero Room was in desperate need of a cleaning. When the Doctor made a tour of the ship alongside Rose-the-Cat, he noted that the Zero Room was infected with disconnected floating pieces of rubbish. (COMIC: A Rose by Any Other Name)

The Twelfth Doctor jettisoned the Zero Room, allowing the Celestial Toymaker to use it as his new Toyroom. He remarked afterwards to Clara Oswald that he would need a new Zero Room. (COMIC: Relative Dimensions)

The Monk's TARDIS
After fleeing from the Last Great Time War, hid in England, where he posed as King Henry VIII. He kept the real Henry VIII hidden in his TARDIS' Zero Room. (AUDIO: Divorced, Beheaded, Regenerated)

Other
A Zero Cabinet was among the refuse that washed up on the Tick-Tock World. In the original timeline, it had been claimed by Nocta who used it to ride out the various purges carried out by the Xesto, unwilling to share it with any others who were stranded on the planet. After Nocta's death, Susan Foreman claimed the Cabinet and lived a hellish existence on the planet. When the planet's properties resulted in Susan being able to navigate the time tracks though willpower alone, she reached out to her past self and attempted to bar her from entering the Cabinet. At the advice of the First Doctor, the two Susans instead touched each other, the Blinovitch Limitation Effect catapulting the TARDIS crew back to the initial crash and allowing them to avert it. (AUDIO: Tick-Tock World)

Behind the scenes
A scene with Rory Williams trapped in the Zero Room was cut from The Doctor's Wife.

In real life there's "low stimulus" rooms that are painted in subdued colors and have minimal furniture, to help de-stress people. So it's similar to a Zero Room, minus floating.