## Spaghettification, Calorification, Carbonization

Ok, Sylvester McCoy’s era of Doctor Who reference aside, this post will be about a horrible process of death via black hole called spaghettification. That’s right, spaghettification is actually the official word for what happens to stuff that goes in a black hole.

This post has been inspired by this Let’s Play Mario Galaxy video by chuggaconroy, who by the way, makes great videogame walkthrough videos. In it, he tries to explain what spaghettification is, starting from 7:15:

Although his explanation of spaghettification sounds awesome, it is incorrect. Of course, he is not a physics expert, so he gets major parts of the process wrong. That’s okay, though. Not everyone can be a physicist. I am not one either, but I understand it enough. If someone out there knows better, feel free to correct me. If you feel like my explanation is too much, then you can just watch the fun explanation of dismemberment  by Neil de Grasse Tyson below.

Anyways, my post will tackle two issues he got wrong on: general relativity and the spaghettification itself.

In it, he mentions that time would be really slow and you would feel everything bad happening to you really slowly. But according to relativity, things like time seem normal to the person experiencing the gravity well. For the person observing the poor fellow, though, it looks as if time is slowing down for that guy. In fact, as the guy gets closer to the event horizon (the border of the black hole in which light can’t escape), time keeps slowing down until it seems like it will take an eternity for the guy’s particle to enter the black hole.

“But wait!” you might ask, “Isn’t that contradictory? Either you are in the black hole, saying your last prayers before the suit rips, causing decompression and condemning you to a miserable death in which afterward, all the particles of your body rip apart into a spiraling string of spaghetti noodle which is unceremoniously sucked by the black hole, or everything  I said previously do happen except the spaghetti noodle seems to be suspended eternally right above the black hole. Which is right?”

Well, it’s a trick! Of course if you are near a black hole, you get sucked in. The thing is, light itself is also being sucked in. Therefore, the closer you are to a black hole, the more delay there is in light reaching the outside observer until at a certain point, light to seem to take forever to reach you. Now you are asking how come everything that has ever been to a black hole, including the star that collapsed into it, are never seen suspended eternally? Well, gravitational fields actually cause redshifts, which means every light the object emits goes towards the red. Red is a lower energy type of light, so at some point, an object going into a black hole redshifts so much that red goes towards the infrared, which goes towards radio waves, and gets weaker and weaker. This, or course, would render the object invisible. Plus, more and more of the light is being held back, until the last light particle is released as the last of the spaghetti noodle is being eaten. See this article for a better explanation.

The second thing I want to tackle is the process of spaghettification. What happens during spaghettification? Well, the details are not pretty. Neil de Grasse Tyson does the unpleasantness very well:

Now, as he said, there are two processes when it comes to spaghettification. The first one is horizontal compresstion caused by the fact that gravity goes towards the center of the sphere.The following picture will explain this in terms you can understand:

(Note: size of things may be exaggerated for the purpose of visualization)

See? There are horizontal forces acting on the falling person’s body.

The process of stretching, though, is a bit more difficult to explain. You have to understand the concept of tide, and the fact that it is the smallness of the black hole that counts, since a supermassive black hole wouldn’t spaghettify you.

Firstly, what causes a tide? The fact that the force of gravity differs depending on the distance (I hope you know your high school physics). So, in the case of you standing on the Earth, your legs are falling faster than your head. The difference is so small as to be unnoticeable. But what happens when two huge objects, like say the Earth and the moon interact? It is more noticeable. The Earth causes tide on the moon, and the moon causes tide on the Earth. Note, in both cases, both objects are huge, so the gravity felt by the sides facing each other is felt more strongly than the sides that are facing away from each other:

In any case, it causes the Earth’s water, since it is slushy, unlike rocks, to bulge on both sides more noticeably. But why does the Earth bulge on both sides if gravity always goes towards the direction of the mass that is causing it? Because objects have something called the center of mass, which is like the average location of all the mass of the object. From the object’s perspective, though, it is as if all the mass is concentrated there, and so the object acts like everything around it revolves around that center point. So, according to that point’s perspective, it is not being accelerated. Instead, it looks as if on the right, it is being stretched to the right, and to the left, it is being stretched to the left. You will quickly see what I mean by the picture below:

Now, imagine the Earth suddenly turns to a black hole and everyone dies, except you, since you are the evil mastermind who caused it. What would happen to the moon? It wouldn’t go away. What would happen, say, if there was a floating platform the same distance away from the black hole as the surface of the Earth is from the center of the Earth?:

It would feel as if you are standing on Earth. You see, when the Earth turned into a black hole, its size may have changed, but the amount of stuff that it is made of, mass, did not change. So in this case, a large amount of stuff is concentrated in a really small space. Unlike the Earth, though, where if you dig down, the gravity would become weaker because all the stuff below is going above your head, a black hole from the Earth is really small, and for emphasis, I repeat: All of Earth’s mass is concentrated in that tiny volume. By using Schwarzchild radius equation*, I can find what the size of the black hole would be if Earth turned into it:

$r=\frac{2Gm}{c^2}$

Where G is gravitational constant (basically, it means how much the strenght of gravity increases as more stuff is added), m is the mass of the black hole, and c being the speed of light, I see that if Earth turns into a black hole, its diameter would be 1.77 cm. Now, that is really small. And the thing about gravity is that it increases by the distance squared. Which means that at an original distance, if you go twice as far away, you feel gravity 4 times weaker, 3 times away is 9 times weaker, etc. The graph below will explain clearly:

So, if you get really close to a black hole, the gravity’s strength will increase much faster. Worst of all, the strength of a tide increases by the distance cubed. It means that at one point, your head will fall a lot faster than your legs. Also, remember how I told you that from the perspective of the center of mass, it is as if both sides of yours are pulling apart? Pretty much your body will be ripped apart from where your center of mass is. Yeah… You’re doomed:

And finally, you will be ripped apart half by half, as Mr. Tyson mentioned above, until you are nothing but a soupy string of atoms spiralling in the black hole, heating up so much it causes a huge emission of x-rays. As they say in the movies: “Nothing could have survived that.” Unlike the movies, though, the protagonist doesn’t come out alive.

*I know, I know, you hate math and your eyes are melting by the powerful emission of its evil complexity. But c’mon, it is a freaking equation that predicts the size of a black hole!