Hyperbolic Time Chamber
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The Hyperbolic Time Chamber (also referred to as The Room of Spirit and Time), from the manga Dragon Ball/Dragon Ball Z and the anime Dragon Ball Z, is a fictional place located on Kami's Lookout. Inside the Chamber time seems to pass very slowly, and there is a higher gravity level than that of Earth.
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Description
The Hyperbolic Time Chamber has an entrance at its centre, along with a storage house with food supplies and sleeping quarters. There is no night or day in the Chamber, but the surroundings remain a constant bright white. Its white floor is of undefined area, and the Chamber's boundaries are thought to stretch to infinity in all directions. The Hyperbolic Time Chamber represents a separate Dimension from that of Earth.
The time dilation that occurs in the Hyperbolic Time Chamber is 1 day of real time = 1 year in Hyperbolic Time Chamber time. The gravity in the Hyperbolic Time Chamber starts at 1G at its centre and increases proportionally to the distance away from the center (i.e. as one moves further away from the Chamber's centre, the gravity one feels increases).
This essentially allows for someone entering the Hyperbolic Time Chamber to get one year worth of intense training in a single day.
The entrance is a portal between the Earth and the Hyperbolic Time Chamber, and is the only way to travel between the two dimensions without ripping holes in the dimensional walls.
The Hyperbolic Time Chamber can only be used a few times per year, depending on when it was last used and how long that use was. Time passes very quickly while in use, so in order to reach some equilibrium time would have to pass very slow at a later time (spend 1 day in the Chamber, then stay out for a year), but perhaps because of its hyperbolic properties, this equilibrium doesn't have to be satisfied perfectly equally, and so the Time Chamber can be used at least twice every year.
Dragon Ball Z
Imperfect Cell Saga
Vegeta and his son Trunks enter the chamber to train for their attempt to prevent Cell from attaining his complete form. Both train as ascended Super Saiyans, and Trunks surpasses his father in brute strength, but has issues with not getting in the way of his father's pride, so Trunks hides his power level. Trunks unknowingly makes a mistake by using his time in the Hyperbolic Time Chamber to increase his strength, while sacrificing his speed and dexterity. Both Vegeta and Trunks fail to prevent Cell's completion.
Perfect Cell Saga
Goku and his son Gohan enter the chamber in preparation for the Cell Games. While training with his father, Gohan becomes a Super Saiyan, becoming the youngest Super Saiyan of his time. They both emerge from the chamber with a heightened control over their Super Saiyan transformation. They developed an optimization technique to stay in the Super Saiyan state for long periods of time in order to eliminate the strain from transforming. This allowed them to save energy for fighting, and worked so well they could even sleep while in Super Saiyan form. This training greatly assisted in Gohan's upgrade to Super Saiyan 2 during the Cell Games.
Piccolo, entered the chamber for meditation and self training, followed by Vegeta and Trunks entering again, increasing their power levels substantially. The Hyperbolic Time Chamber was not used again until after the Cell Games.
Fusion Saga
Goten, Chibi Trunks(Trunks), and Piccolo enter the Hyperbolic Time Chamber to lure in the horrible Super Buu. Buu enters the Chamber, Trunks and Goten use the Fusion Dance technique to become Gotenks, in preparation for fighting Buu. They introduce their Ghost attack and upgrade themselves to Super Saiyan while fused. During the battle, the Hyperbolic Time Chamber entrance is destroyed, leaving "no way out". Buu can't stand the thought of being stuck in the Hyperbolic Time Chamber (mostly because of his fondness towards chocolate, and the lack of it in this dimension). So Buu in an intense rage, screams at the top of his lungs. The scream is so loud, that it rips a hole between the Hyperbolic Time Chamber and the Earth's dimension. Buu gets out but it's too late for Gotenks and Piccolo, as the portal closes behind him. Gotenks and Piccolo attempt to recreate Buu's mad howl, and succeed only after Gotenks transforms into Super Saiyan 3, and yells their way out.
The Hyperbolic Time Chamber is rendered non-functional without a door, and must be repaired for future use.