# Black hole, escape velocity, going up?

I do know nothing can escape a black hole, and I understand popsci explanation of geodesics of space-time around and inside the event horizon.

I however have some trouble with following thought experiment, given there are many references that crossing event horizon of SMBH should be totally unnoticeable for the subject falling through:

I am at gym - a regular one, on Earth. Escape velocity of Earth is around 11.2 km/s. Yet I can lift weights up say one meter even at slower speed, say one meter per second.

Next, consider me hovering one meter above event horizon. As far as I know, for non-rotating BH this is totally possible. Similar to earth, I could lift weight up one meter at speed less than escape velocity (which at this point is speed of light minus x).

Now, I’m hovering one meter below the event horizon. Would I not be able to lift the weight up one meter at speed less than escape velocity (which at this point is speed of light plus y; not sure if x and y are equal), or would I not be able to hover at this position?

Assuming answer is no to either or both, how this would appear to me as the subject?

• No, you can't hover inside the event horizon. As you move forward in time you must also get closer to the centre of the BH. And it's not easy to hover just outside the EH, either. The required acceleration is unbearable for stellar mass BHs. It does get smaller for SMBHs, but to get it down to $10m/s^2$ you'd need a BH of around 15 trillion solar masses, about 75 times more massive than the largest BH yet found. Commented Nov 20, 2018 at 18:34
• Thanks for the comment @PM2Ring. I might want to adjust the thought experiment part so that let’s assume my space ship has practically infinite energy supplies and efficiency, ie if it takes billion gigawatts to hover we can afford and do that as long as it is theoretically possible (ie no magic, time machines nor faster-than-light) Commented Nov 20, 2018 at 21:24
• astronomy.stackexchange.com/questions/24642/… Commented Nov 20, 2018 at 21:53
• Inside the EH, all wordlines take you to the centre, no hovering is possible, no matter how much energy you have. Just outside the EH, you can hover if you can stand the g force, but that's unlikely. Sgr A*, the SMBH at the centre of the Milky Way is "only" 4 million solar masses. The hypothetical BH I mentioned previously is about 4 million times as massive as that. So to hover just above Sgr A* you need to pull about 4 million g. Even if your spaceship can do that, you won't survive. You'll be a thin red smear on the deck of your ship long before the acceleration got that high. Commented Nov 21, 2018 at 3:51
• OP, this is a good question but realize, you do face some basic newtonian physics issues here! Commented Nov 25, 2018 at 14:58

Nothing can be stationary inside the event horizon and everything, even light must travel inwards. Therefore there is no way that your analogy can work and is why using the idea of escape velocity is a really bad idea in General Relativity.

i.e. You cannot be at a fixed $$r$$ coordinate to lift a weight. You must be falling inwards, as must any weight you lift, as indeed must a light beam you direct radially outward.

This is more of a pure physics question and I'm not sure it would do well there either, but I can touch on some basics.

I am at gym - a regular one, on Earth. Escape velocity of Earth is around 11.2 km/s. Yet I can lift weights up say one meter even at slower speed, say one meter per second.

You can lift a weight at the gym and hold it there, but only by doing constant work. If you let go, it'll fall to the floor and make a noise, and perhaps get your membership revoked.

You could, in a thought experiment anyway, climb a ladder up into Earth's orbit, past the satellites and keep going out past Earth's Hill Sphere, where the gravity of the Sun would take over and you could let go and part ways with the Earth. It makes no difference how fast you climb the ladder but that would require applying continued work. Applying work has nothing to do with escape velocity. Escape velocity is like throwing a ball up into the air, once you let go of the ball, it has an initial velocity, and the "what goes up must come down" law takes over.

What comes up must come down, assuming we ignore air resistance, is a good way to explain escape velocity. If you throw something faster than 11.2 km/s, it won't ever come down, it'll keep going up until it escapes the Earth.

Escape velocity doesn't apply to rockets which apply several minutes of thrust to escape Earth's gravity and enter orbit. (technically in orbit is still in Earth's gravity well, but it's escaping a significant part of Earth's gravity it in order to remain in orbit) - see xkcd

Escape velocity only applies to initial velocity and it ignores air resistance.

Next, consider me hovering one meter above event horizon. As far as I know, for non-rotating BH this is totally possible. Similar to earth, I could lift weight up one meter at speed less than escape velocity (which at this point is speed of light minus x).

You can lift a weight 1 meter in your gym because the Earth's surface is holding you up. An event horizon has no surface, so there's nothing for you to stand upon. Also, your gym-weight would weigh (I don't want to calculate how much), but near the surface of a black hole gravity is so high that a feather would weigh probably thousands maybe hundreds of thousands of tons in your scenario. Lifting with no surface below you and feathers weighing tons poses several problems with your scenario. I'm not sure any of that applies to your question in your thought experiment, I'm just pointing out some of the difficulties that arise.

@PM2Ring points out that if the black hole is large enough the weight and surface gravity does decrease, which sounds odd, but seems correct, but no black holes are that large, and there's still the no surface to stand on.

Now, I’m hovering one meter below the event horizon. Would I not be able to lift the weight up one meter at speed less than escape velocity (which at this point is speed of light plus y; not sure if x and y are equal), or would I not be able to hover at this position?

You can't hover below the surface of a black hole unless you have an energy source that defies the laws of physics.

Perhaps it's easier to think of in terms of space-time, which I'm not an expert with, but the definition of space-time inside a black hole is such that no amount of acceleration can move any thing further away from the singularity. No fuel, no manual force can move any part of anything in a direction away from the center of the black hole. Every direction points to the center. Space inside a black hole becomes like like time. You can slow time down but you can't reverse it. Lifting something upwards is no more possible than stepping backwards in time.

I don't know if that helps. Maybe someone can explain it better than me.

• Thank you for your answer. I know the gravitational pull could be huge, but still it should be (theoretically) possible to hover above event horizon- even though it’ll cost a lot of energy. I guess based your answer, the observer should be able to see some changes in physics right at the moment of moving across the event horizon, as they become not capable of lifting the weight anymore (as all directions just point to the singularity). Also not sure if atoms would stay intact (I know electrons do not orbit mechanically in spheres, but seems nothing wouldn’t be able to orbit anything inside BH) Commented Nov 20, 2018 at 21:29
• @tuomas hover above, yes. Your question initially said hover below - I know that because I copied it into my question. As far as seeing changes in physics, there's still some debate on precisely what happens at the event horizon but my understanding, as a hobbyist, not a scientist, is that you wouldn't see any changes in the laws of physics at the event horizon. I agree with you about atoms not staying intact. That's also a potential problem. It's not so much that the physics changes it's the space time becomes inescapable. Commented Nov 20, 2018 at 21:58
• @tuomas -- Assuming a very large non-rotating blackhole, you would not notice any change in physics in your immediate vicinity as you crossed the event horizon. What you would notice is that the universe outside the black hole, which would already look severely distorted when you were near the event horizon, would gradually shrink into a redshifted ball that seemed to recede from you at an increasing rate no matter how much energy you spent trying to catch up to it. It would only be much later that your atoms were torn apart. Commented Nov 21, 2018 at 17:18

One way to think about the interior of a black hole is that it is as if the singularity is coming up at you at faster than the speed of light. Even if you shine a beam of light straight up, the singularity will come up behind it and eat it. This may sound like I am talking nonsense, but consider a Kruskal-Szekeres diagram. In the diagram at the Wikipedia article, 45-degree lines indicate the speed of light, but the hyperbola representing the singularity has a lower slope.