Scenario that popped into my head about an event horizon - please comment

This popped into my head the other day while I was daydreaming.

An astronaut is orbiting an black hole, say, 25 meters outside of the event horizon. He takes out a harpoon and throws it toward the black hole so that it goes a few centimeters inside the event horizon, the rope fairly taut and still held by the astronaut. If I understand correctly, the astronaut would not notice anything unusual, yes? But when the astronaut pulled on the rope to retrieve the harpoon, he’d find that instead of the harpoon coming to him, he’d be dragging himself by the rope toward the harpoon. But it would just be sitting there floating in space, from the astronaut’s perspective, right?

Your scenario doesn’t give enough detail to say. It looks like it ought to be enough information, but it’s not: For actual solutions to things like this, you unfortunately need all of the details: The exact orbit the astronaut is taking, the direction he aimed the harpoon, and so on. Possible solutions include that the rope breaks, the astronaut pulls the harpoon back before it crossed the horizon, the astronaut himself has unknowingly already crossed the horizon before he even started pulling the rope back, and so on.

Gotcha, ya! Let’s turn the question around then: is there a plausible set of circumstances where my scenario will take place as described? Setting aside the plausibility of humans being able to place themselves in orbit around a black hole in the first place. And having a harpoon with them when they do.

Your point about maybe the astronaut has also crossed the event horizon makes me think I should ask: how fuzzy or well defined are event horizons? Can one talk about being a nanometer inside/outside or are they that well defined?

First off you will be pulled apart by tides because your feet are so much closer to the event horizon than your head. Second, as a result of time relativistic time dilation you will never see the harpoon actually cross the horizon. And the tidal forces will act even more strongly, the nearer it gets to the EH and the rope will break. And oh yes, tidal forces will also squeeze you, and the rope, and the harpoon very thin as you get to the EH. Not a fun place to be.

Depends on the size of the black hole. For small ones, yes, the tidal forces will kill you but for a truly huge one they might not. How rapidly those forces change depend on the “size” of the black hole (really, the radius of the event horizon but that’s dependent on the mass of the black hole) and the larger the black hole the less rapidly those forces change over a distance.

Remember, orbital mechanics has some counter-intuitive features. One of which is that if you have acquired enough energy to be orbiting a black hole, it’s going to take a corresponding amount of energy to de-orbit enough to get your harpoon down to the event horizon. Your buddy Space Ahab isn’t going to be able to pull it off. A few Saturn V’s might. I suspect this would manifest as the tidal forces that Hari Seldon mentioned – if you attempt to point your harpoon down from your current position, it would first bend, then probably disintegrate.

Oh, and no matter what the situation, even if the astronaut was really just sitting in empty space, he’d find that he was pulling himself to the harpoon. That’s just Newton’s Third Law, which holds even in relativity. If he puts a 100 N force on the rope, then the rope is putting a 100 N force on him.

Correct me if I’m wrong, but there’s a fundamental misconception about event horizons. We tend to imagine that if you slip inside the event horizon you’re toast but if you stay outside it by just a few meters you’ll be fine. That’s not true.*

The question is: will you fall into the black hole, yes or no. If you get too close and you don’t have enough speed, then the answer is yes. If you are far enough away and/or you’re moving fast enough, then the answer is no. The event horizon is the spot beyond which the answer is always yes, even if you’re moving at “c” (the speed of light in a vacuum).

So, if you’re only 25 meters away from the event horizon, you’d have to be traveling really really close to c in order to avoid falling in. If you’ve just barely got enough speed to not fall in, then you’re in an orbit. Probably several thousand laps per second. And if you wanted to lower the harpoon just one meter, now it needs enough speed to avoid falling in at a distance of only 24 meters, which is FASTER. So I’m gonna say that the rope would snap before you could lower it any more.

  • This reminds me of how, on Star Trek, the computer will say “15 seconds to fatal radiation exposure” as if 14 seconds means you’re fine but 16 seconds means you’re DEAD.

Actually, if you’re that close to an event horizon, assuming the hole is of a sane size, and you’re not falling in, then you must be in an open orbit, not “doing laps”. The closest you can be to a (non-rotating) black hole and still be in a closed orbit is three times the Schwarzschild radius.

The OP said “orbiting” but what you’re saying is that it’s not possible, so you’d have to be zipping past the black hole really really really fast, hence you would need split-second timing – no, wait, make that split-microsecond timing – to launch the harpoon before you suddenly find yourself thousands of miles away.

Or, I suppose you could launch the harpoon a few minutes before you arrive at the black hole, when you’re still millions of miles away. In that split microsecond when you’re passing the black hole, I predict that the rope would break.

Of course, all this is assuming that your ship is made of unobtainium and neither it, nor the contents of the ship, would be torn apart by the tidal forces. That shouldn’t be hard, just build the ship out of massless strings and frictionless pulleys and make sure all the astronauts are spherical cows.

Zipping past is a kind of orbit. And the really precise timing isn’t a problem: If we can assume that we have the technology to reach a black hole, then we can assume that we have the technology for the exact timing.

Didn’t we do this topic just a week or so ago? The gist of the OP was something like: Ignoring all factors that I think are ignorable, just to keep it simple, can I lower an object on a rope part way past the event horizon and then pull it back, and what happens? The overwhelming response, by many of the same responders as in this thread, was along the lines: You just can’t simplify it like that and ignore all the stuff you are trying to ignore.

Here it is!

Damn! Sorry about that. Thank you all for taking the time to address my specific take on it, though.

I don’t dispute that this is technically true, but it’s certainly not what was meant by the OP. “orbiting an black hole, say, 25 meters outside of the event horizon” implies that the distance from the event horizon is constant, hence it’s a circular orbit. And you’re telling me that a circular orbit just doesn’t work at those distances.

This was a good thread. From now on whenever I orbit a black hole I’ll make sure to have a harpoon with me.

It’s not quite coming to me, but there’s gotta be a line about someone’s life consumed with harpooning the Great Black Whole.

Eh, I viewed the essential part of the OP to be “passing very close to the horizon without quite falling in”, not “staying near the horizon for an extended period of time”. So a flyby would still be within the spirit of the question.

I think if you do this, physics dictates that you end up in the backside of a library pushing books and tapping on a watch in a vain attempt to signal your daughter to stop your past self from screwing around with event horizons in the first place.
At least that’s what I got out of it. Don’t remember the harpoon though, are you sure it’s not a wise ass robot that looks like a giant cereal box?

Let’s imagine this scenario: the astronaut remains outside the black hole and the rope is slack until the astronaut winches the harpoon back in.

If the harpoon is falling into the black hole, after a certain finite amount of time has passed, no matter how quickly* the astronaut winches the harpoon back in, from the astronaut’s point of view the rope will never go taut and actually start to pull the harpoon back. Though from the astronaut’s point of view the harpoon never actually crosses the event horizon, after the above amount of time has passed there is nothing the astronaut can do to bring the harpoon back to them**

*Of course as long as the rope is being winched back in at a speed less than or equal to c.

**If the harpoon has its own power or an observer closer to the black hole does something the harpoon could still be brought back to the astronaut before it crossed the event horizon, so the astronaut certainly would not say it had crossed the event horizon at this point.

Here’s a Penrose diagram I drew to illustrate my last post:

http://i.imgur.com/w2VnFYL.png

The blue curve is the wordline of the astronaut, the red curve is the worldline of the harpoon.

The yellow lines represents an influence propagating at the speed of light from the astronaut to the harpoon and propagating back from the harpoon to the astronaut, also the speed of light. Notice that when the influence reaches the harpoon as it crosses the event horizon, it does not go back to the astronaut until the infinite future.

The grey curve represents a constant Schwarzschild time coordinate.

Just got a chance to go back and read through all these responses in detail. Some follow up:

Hari and Broomstick raised the point that the tidal forces are going to be a real problem to surviving where I’ve imagined the astronaut. I didn’t realize that even though you were outside the EH, that you would still be torn apart, so thank you for pointing that out. I swear that in popular science (as opposed to Popular Science) discussions about event horizons they say things like “you wouldn’t notice anything amiss as you cross the event horizon”. Here’s an example from this site:

Well, yes it would, because apparently you’d probably be torn to oblivion by tidal forces, well before you reached that point, probably.

Finagle pointed out that to move from a higher orbit to a lower orbit in general would actually require significant energy. So help me understand this: if one is, say, orbiting the Earth at the ISS radius, and throws a baseball down toward the Earth, what happens to the ball? Let’s say for the sake of argument the astronaut throws the ball perfectly in alignment with the centre of the Earth at, oh, 60 km/hr. I’ll change it to Earth from the black hole so we don’t have to worry about tidal forces.

sbunny8 and Chronos – thank you for correcting my misconception about being actually able to orbit the black hole at the radius I indicated. And I now know what a Schwarzschild radius is!

Asympotically fat Thank you for the Penrose diagram. First of all, it taught me what a Penrose diagram is. Second of all, it really helped me understand the situation.