Practical time travel: time dilation above the event horizon

Question

Imagine there is a huge black hole with very small gravity gradient so that one doesn't get killed by spaghettification after even nearing the event horizon.

Now imagine a very curious creature wanting to know how the universe would evolve. Even though it isn't sure it will be able to return, it decided to travel just close enough to the event horizon to survive, and stay there until for as long as it can make.

For how far would the creature see the future? Is this even possible? What should one expect?

This question was inspired by Miller's planet from the movie Interstellar.

Answer 1

If you have a look at my question Does someone falling into a black hole see the end of the universe? the answers demonstrate that an observer falling into a black hole doesn't see into the arbitrarily distant future.

This question assumed a freely falling observer, but even if you have a rocket motor to hand it doesn't make much difference. Once inside the event horizon you cannot remain stationary. No matter how powerful a rocket you have you inevitably travel towards the singularity and hit it in a surprisingly short time. This is the point Fabrice makes in his answer.

If you have a powerful enough rocket and enough fuel you can hover just outside the event horizon and this way you can achieve arbitrarily large time dilations. But you have two problems.

Firstly the acceleration you need to hover above the horizon is:

$$ a=\frac{GM}{r^2}\frac{1}{\sqrt{1-\frac{r_s}{r}}} $$

where $M$ is the mass of the black hole, $r_s$ is the event horizon radius and $r$ is your position. As $r\rightarrow r_s$ the acceleration goes to infinity. Unless you have some miraculous way of resisting arbitrarily large $g$ forces you'll have a limit to the time dilations you can achieve.

The other factor is that the light from the rest of the universe falling into the black hole is increased in energy by a factor of $1/\sqrt{1-r_s/r}$ and this also goes to infinity as $r\rightarrow r_s$. So get close enough to the event horizon and the blue shifted light from the rest of the universe will roast you.

Answer 2

time travel between horizon and sigularity = $\pi G M/c^3$. i.e. a 100th of second for M = 1000 solar mass.

Answer 3

John Rennie's answer ends with a good point. If you see lots of universe happening for each of your own seconds then you are getting fried.

It's like if you watched to watch a years worth of recorded TV in a single day. You could blast 365 TVs at you, each playing a different days recording, and you'd see it all in a day, but you have 365 times as much light hitting you every second. In this case it just plays each days at you faster, but the same light is hitting you so you are really heating up.

But that's inevitable. Seeing more stuff every second of your life means more light hitting you every second of your life. So let's assume your goal was to only sometimes see the future.

The limits would be fuel, how much fuel can you use to hover above the horizon. And shielding. Trying to shield from gamma rays is hard, and they can mess with your nucleons so you want to be shielded.

But if you want to see the future and are worried about shielding, why not let the black hole do the shielding for you. You could try finding two black holes rushing in opposite directions at high speed (relative to the cosmic microwave background radiation) and follow one until it get close to the other and switch to following that one, though you'll probably get cooked during the switch, so maybe finding a bunch going in a circle so each switch is less dramatic. And every time, try to use each black hole as a shield and basically do the twin paradox trick with the black holes as shields for each trip (though watch out for lensing).

Or build a hollow black hole. Arrange your $10^{10^{100}}M_\odot$ of matter into a rigid shell that is a bit bigger than the event horizon. You get a normal flat spacetime inside. And a black hole spacetime outside. And your time on the inside ticks at the same rate as on the shell which is the rate just outside the event horizon of that huge black hole spacetime.

So your shell is being bombarded with gamma rays. But the shell is your shielding. How much time dilation you get is based on how much shielding you can manage. You can make a small hole to let some light in, and if you want to see it, just rush away from it at high speed so it isn't dangerous gamma radiation and watch it. Repeat whenever you want a look.

But you can't get a very effect with regular materials. The tidal forces are small at the horizon for a huge black hole, but to keep it from contracting they need that rocket like force. The strain of the material needs to provide a pressure and stress to produce that rocket like sized magnitude of acceleration. Each material can only handle so much. Plus if you start to succeed the material will start having gamma radiation pile on and unless it can reflect it then it will increase in energy and the event horizon will move outwards.

So the limits are fuel and ability to withstand the radiation if you succeed. Or how strong a material you can make and how well it can handle fatigue from the radiation if you succeed.

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There is a sense where you always see the distant future when you cross an event horizon.

That sense is that since your own clocks ticks slow compared to distant observers, your time is associated with the distant observers' distant futures. The time right before you cross the horizon is their super far future times.

So you do see the super far future. You are part of it. It's like you are immortal in the sense that people outside never stop seeing you. You are just very red and very slow.

It's seeing the far future of things far away that doesn't happen without effort. As you cross you see things nearby from recently and thibgs from far away from long ago. As always. And there is never a way around that, the things from far away simply take longer to get to you. Whatever you are seeing as you cross, the things broadcast after that won't get to to you until later. As always.

When you cross, the things you do after you cross are never seen by the things that stay outside. But they will forever be still getting ever slower broadcasts from before you crossed. So your pre crossing continues to be part of their present, always seeing a little bit of the newer things each second.