Why can’t you use a rope to rescue a person from a black hole?
It is not about the force. It is the lightcone.
It is not about the force. It is the lightcone.
There’s no way out of a black hole. Once you fall in, you are as good as toast. You will be spaghetified, sucked in, and dead. Not even light can escape a black hole.
All gravitating bodies, planets, stars, and so on have an escape velocity. This is the velocity you need in order to escape that body’s gravity from its surface. If you are higher than the surface, your escape velocity will be lower. If you are below its surface, then escape velocity doesn’t make a lot of sense.
A black hole is small enough that its escape velocity is greater than light. In fact, as far as we know, black holes have no surface at all. They are just points called singularities. Instead, they have an imaginary surface around them we call the event horizon. This imaginary surface is where the escape velocity is equal to light speed, the fastest speed anything in the universe can travel. Any closer to the black hole and the escape velocity is more than that.
It make sense that, if nothing can go faster than light, and the escape velocity is greater than that, then naturally, you can’t escape.
There is one problem with that logic that always bothered me, until I learned more about the physics of gravity. Here on Earth, escape velocities apply to things that are are in free fall, not experiencing any other forces. What if you are experiencing a force?
Imagine a space elevator. It takes you up as slow or fast as it wants out into space. Eventually, if you want to stay in space, you’ll have to exceed the escape velocity but only the escape velocity up there in space, not the one down here on Earth. So why can’t you use the same approach to escape a black hole? Just use an elevator or a rope to get above the event horizon and rocket away.
It turns out that if gravity worked the way that Sir Isaac Newton thought it did, you could do that. Newton said that gravity was a force. Any force can always be countered by a greater force. So, on a Newtonian black hole, you can escape just by exceeding the black hole’s force of gravity. If your rope is strong enough and somebody pulls you up with enough strength, then you could escape.
But gravity doesn’t work the way Sir Isaac Newton thought. It works the way Albert Einstein thought. A black hole doesn’t just pull on things with a strong force. It actually bends space and time. And it is that bending, not the force itself, that makes it impossible to escape a black hole.
In Einstein’s physics, every object has a pair of imaginary cones called light cones. These are four dimensional objects, but physicists often draw them in 3 or 2 dimensions. An object’s past lightcone shows all the parts of space that object could have come from without exceeding the speed of light and all the parts of space where something else could have affected it. The object’s future lightcone is all the parts of space it could reach likewise and all the parts of space it could affect. The absolute rule in Einsteinian physics is that nothing can go outside its lightcones, and nothing can affect or be affected by anything outside them either.
In ordinary space and time, our lightcones are all pretty much the same. They point into the future and past in the same direction no matter what speed we are traveling. But, near strongly gravitating objects like planets, stars, and especially black holes, the light cones can bend, twist, and turn.
When you are far away from a black hole, your lightcone is pretty much like everybody else’s. It points into the future and past. But, as you approach the black hole’s event horizon, your lightcone starts to bend. It bends towards the black hole’s center, the singularity.
This bending is as if your future is no longer pointing in the same direction as everybody else’s future. Instead, it is pointing more towards the singularity. Your past is pointing more away from the singularity.
When you reach the event horizon, nothing special happens to you, but at this point your entire future, represented by your future lightcone, lies within the event horizon. At this point, you cannot leave it and you cannot affect anything outside of it. You are trapped.
All this is well and good, but what happens if I lower myself by a rope through the event horizon?
Let’s think about ropes for a minute. They are really fibers that are held together by molecules. The molecules connect to each other through molecular bonds. Those bonds are electromagnetic. So, when you, say, pull on a rope, what happens is you start a wave of molecules pulling on one another down the rope with electromagnetic forces. The wave travels down the rope to the other end and anything attached to that will be pulled with it. At least, that’s what happens ordinarily.
With a black hole, you would see a very different result. One of the effects of black holes is that, for somebody watching from far away, anything happening nearer to the event horizon would appear to be slower than normal. Time itself is slowed down. In fact, time keeps slowing down until, at the event horizon, it appears to stop completely. So, when you pull on the rope and set off that wave of molecules tugging on one another, the wave moves slower and slower. By the time the wave hits the event horizon, it has stopped completely. You will never see anybody inside the horizon receive your tug.
For the person inside the event horizon, on the other end, things are a little different. They do receive the tug, but it has a different effect than intended. Instead of pulling them out of the black hole, it only slows their descent into it. The amount of slowing it can do depends on the person’s future lightcone. It can delay the inevitable, but it can’t pull them so much that they start to exit their lightcone. Since that lightcone is entirely inside the event horizon, they will never move back towards the surface. To do so, would be like moving back in time for them.
The same is true of any attempt to escape a black hole from inside the event horizon. Even a rocket capable of approaching near to the speed of light will be insufficient.
It turns out that black holes don’t just suck things in with incredible force. Rather, they change the causal nature of reality. Light cones are how causality is transmitted from past to future. Anything inside the lightcone of another thing has a causal relationship, causes in the past light cone and effects in the future. For somebody falling into a black hole, all things in the entire past and future of the universe end up in their past lightcone before they reach the singularity. It is as if, for them, the entire universe is in their past. It is done, from the Big Bang to heat death. Only the singularity is in the future. What happens after that, nobody knows.