Overview
The most common kind of Forward Temporal Drive (FTD) is a piece of technology involving the use of a captured black hole to travel forwards through the time dimension without passing daringly close to an uncaptured black hole or moving at absurd speeds. A black hole is kept in a case creating a bubble of massive gravitational forces. Exotic matter has many functions here: it holds the black hole in place acting as a containment field, balances the gravitational forces in the bubble, controls the effects so that a timeship isn't kept in permanent timelapse, and manipulates the edge of the bubble to allow objects to enter without being torn apart.
One of the most common ways to measure the speed of timelapse is the factor. It is exponential, so factor 5 is 16x faster than factor 1, or real time in 0g and at a standstill.
The maximum speed of a FTD is determined by the mass of the black hole within the casing, which is in turn limited by the size of the casing. A black hole that is too massive may allow timeships to enter timelapse at several dozen factors, however it will be extremely hard to contain and the bubble will be very hard to keep balanced. Extreme acceleration in space could result in the black hole defying the containment field, moving through the case and consuming the timeship.
Uses
FTDs are typically used in timelapse tourism to allow the observation of extremely slow events rapidly, to fast forward to a desired time, or in exploration of time. One example of timelapse tourism is a timebase near Foremholl, observing the slow glimmer of Foremholl at factor ~12. Many claim the glimmer is therapeutic and almost hypnotic from the timebase, but not so much in real time. Other timebases exist around popular locations, such as newly born nebulae, gas giants and large black holes.
Possible Illnesses
'Hypnotism' around such therapeutic objects while also within a timeship has led to some suspicion that lots of exposure to the exotic matter and/or gravitational effects can lead to mental illnesses - but this has largely been dismissed as a harmless side effect. Studies are sometimes carried out on those who use timeships, but never get much traction in the scientific community. Some even speculate that the effects felt by users are a strain of BHIP, being rightfully taken with a shaker of salt.
Besides the mental side of things, some are more prone to episodes of conditions, such as Humans, which experience bleeding around weak areas of the skin more frequently in timebases, such as nosebleeds and scabs falling apart. Another example is the Zythyns who experience a weakening of the tentacles. This has been taken much more seriously, and people are not allowed near timeships if they experience certain conditions.
Backwards Time Acceleration
As well as using gravity to pull objects forward through the time current, tachyons can be used to drag an object backwards, slowing it down through time. This is known as a Backwards Temporal Drive (BTD). Such tech isn't as widely used as a FTD can be used in space travel where timelapsing comes in handy, however it has its applications in making construction endlessly quicker and accelerating research on species in artificial habitats. Just like a FTD, factors are used to measure the speed of an object through time, but in this case, factors divide instead of multiply. A chamber fitted with a BTD running at factor 16 would allow you to observe a baseline human's lifetime in just under a day, while a day would last a lifetime for the human inside. Such a factor would require a lot of energy however. Entire space stations have been constructed in days using giant BTD chambers.
Terminology
The Bubble is the edge of a containment field
Timelapse is when a timeship or timebase releases its temporal drive.
A ship that uses a Temporal Drive for temporary hops through time is known as a timeship. This term is also sometimes used as an umbrella term for anything with a Temporal Drive.
A station or base that uses a Temporal Drive for permanent traversal through time, and temporary stops to allow for refuelling and objects to enter, is known as a timebase.