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Imagine some science fiction scenario where two people are floating through space holding hands orbiting a black hole. If one person falls close enough to the black hole that they're within the event horizon, but the other person has a velocity such that they're orbiting just outside the event horizon, will they both be sucked in?

Is the answer than they act as a single body, and they'll be sucked in when their combined mass equivalent passes over the event horizon?

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In order to orbit, you have to be outside the photon sphere, which is 3/2 the Schwarzschild radius. It's theoretically possible for the person on the outside to continue holding hands and not fall in, even though the person on the inside will hit the singularity in a finite time. This is because, from the perspective of someone outside the black hole, it takes an infinite amount of time to fall in. It's just that due to time dilation, only a finite amount of time passes.

Edit:

It will probably be easier to think of it with hyperbolic motion instead of a black hole, since it works with general relativity. You're on a spaceship with constant acceleration. Someone behind you would have to accelerate faster to keep up with you. Suppose your friend falls off the ship, and you grab his hand. Unfortunately, he falls beyond the event horizon. The light that leaves him as he's about to cross it will slowly reach you, but you'll never see him cross it. You'll see him redshift and slow down exponentially. Your hand will also slow down exponentially, so only a finite amount of blood will reach it and come back.

From his point of view, he will quickly pass your event horizon, taking your hand with him. At this point, even if he were to reach the speed of light, he'd stay a finite distance behind you. Except that since you're accelerating, due to lorentz contraction that distance is actually increasing. He will be pulled away from you, and even if he lets go of you, your hand will eventually be pulled from your body.

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  • $\begingroup$ If that's the case, what will happen to them as this is going on? Will the person falling into the black hole stretch inwards, but appear physically normal to the person on the outside? $\endgroup$ – ZECTBynmo Mar 12 '15 at 5:49
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"Tidal force" is the change of force acting on a body as one part of it is closer to a source of gravity than another. When 2 people are holding hands, if one is closer to the black hole they will feel a stronger pull which will cause them to pull harder on the arm of the other. As they get closer to the black hole this force will get even stronger, eventually leading to "spaghettification" when the tidal forces are so strong that across one's body the change in force is enough to stretch it dramatically. It is likely that before the bodies are subject to spaghettification they will lose their grip on each other.

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  • $\begingroup$ In a front of event horizon of a supermassive black hole you will not feel such a dramatic tidal forces. These forces appear essential when gravity force gradient is big, that could be inside of relatively small gravity fields, for example inside of "regular" black holes that appear in place of collapsed star, not inside of quasars $\endgroup$ – Dmitry Ilukhin Mar 13 '15 at 13:54
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Event horizon is a place where any force effect could not spread out of particle anywhere but inside of a hole. Particles of your "hand" inside of it could not cause any effect to you outside, same if you move away from them with speed of light. In front of small black holes this could make spaghetti out of you, but if you dive inside of hole like Gargantua, these effects will be soft enough to you to feel good and stay unharmed, but you could never contact your friends outside in any way

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