A common use for time dilation in science fiction is for a ship moving at speeds close to the speeds of light and for those on the ship the journey takes less time than for those observing at another location, so those on the ship have aged less in relation to the others.
The space within the ergosphere the area just outside of the event horizon is said to be an area where space is dragged due to the rotating black hole and time dilation exists. It is believed that known materials could withstand the gravitational forces in this area and as long as the black hole isnt feeding there should be no high energy rays and particles to damage something.
There is a proposed method of using the ergosphere to create energy using the Penrose process but it is the time dilation uses I am interested in for this question.
If a very advanced civilization was able to manipulate black holes for their own purposes, including the Penrose process and similar ideas to use the black holes rotation to create more energy, they could experiment with the time dilation, maybe put computers in there to run experiments under those conditions or possibly find other uses for that space.
Using the space to age slower has been done in science fiction before and I cant really think what experiment or manufacturing process or something else would benefit from being done in a space that essentially experiences less time, If they experienced more time than the outside observers then it would be great for tasks that take a long time but it isn't so i am struggling to find other uses for the time dilation.
Are there any other uses than the ones I mentioned for the time dilation space in the ergosphere that an advanced civilization would benefit from?