Let's do this thought experiment. You have an insanely powerful rocket and it can accelerate to 0.999999c. Now you fly to a supermassive black hole and hover just above its event horizon, where the inner gravitational pull towards the singularity matches the outward thrust of your rocket.
Consider:
1. The black hole is non spinning, and doesn't distort space-time into swirling around it.
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The black hole is so massive that above the event horizon, you are not sphagettified.
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The rocket can shield the energy of extreme blueshifted photons that bombard you.
At this point over the event horizon, you would see like 1 million or even 1 billion years of the universe in 1 second of your life, right? Can you witness the end of the universe if you hung around for long enough?
And what if the black hole evaporates by Hawking Radiation before that? Will you immediately return to real time?
PS: This is quite different from falling into a black hole. In this thought experiment, we are not crossing the Event Horizon of the black hole in a split second, but we are physically hanging in there for a long time by Counter Force.
Edit: I'm not sure why this question has been marked as a duplicate, but this differs vastly from an observer falling into a black hole, and nowhere else has it been answered so perfectly and succinctly, as done by Mr. Bob. Many thanks to him.
Best Answer
A short answer to your question is yes. If you were to hover a short distance above the event horizon for short time, a very long time would pass for asymptotically flat observers.
Let's do some calculations! If you were to hover say distance $h\ll r_s$ above the event horizon, then the time dilation factor $\gamma$ that you would feel would be of the form
$$\gamma=\frac{1}{\sqrt{1-r_s/(r_s+h)}}\sim\sqrt{\frac{r_s}{h}}$$
And thus if you spend a small time $t$ above the event horizon, a time of $t\sqrt{r_s/h}$ would have passed for the rest of the universe. In particular, say you are $1$ meter above a stellar mass black hole (with three times the mass of the sun -- the minimal stellar black hole mass), the dilation factor is $\gamma\approx 100$. If you were to hover just one centimeter above, the dilation factor would be $\gamma\approx 1000$. If you want one million years to go by in one second, you would need to hover around 0.1 angstroms from the event horizon. On this range, the actual description of the event horizon most likely breaks down due to quantum mechanical effects.
Now let's consider a supermassive black hole of one million times the mass of the sun. Then to get one million years to pass in one second would require $h\approx 3\,\mu\text{m}$, which is much more realistic.
Now, your second question was about Hawking radiation. The short answer to your question is yes. A black hole will evaporate after a certain time (very large times for very large black holes). This timescale puts an effective limit to your travels to the future and thus means, since black holes don't seem to be able to live forever, you cannot continue this for an indefinite period.
Black holes are cool. Keep learning and and I hope this helped!