I don't understand why the ship didn't suffer spaghettification when entering the black hole. What was the explanation for this?
The hole in the movie was of such a geometry that objects approaching the event horizon were not subject to spaghettification. Spaghettification happens when there are enormous GRADIENTS in force, per se, not merely enormous forces...what I mean by this is if my whole being is instantly subjected to an enormous pull from the singularity, there's no problem, because I'll just instantly be moved.
The spaghettification problem occurs when there's an enormous pull on my feet, but a less enormous pull on my head. How these forces occur depends on the geometry of the mass. A sphere should spaghettify, if my understanding is correct...what exactly a non-spaghettifying geometry for a black hole would be is prolly a question for the Physics board, and is certainly beyond my grasp of the physics.
There was a line in the movie saying something along the lines that the tidal forces were mild and could be survived.
UPDATE: and here, in fact, is a question about non-spaghettifying black hole geometry, and it is, indeed, beyond my grasp :).
Spaghettification is caused by tidal forces, due to the gravitational pull on one side of an object being stronger than the other side (like a stronger pull on your feet than your head if you're falling in feet-first), and the strength of tidal forces at the event horizon decreases with increasing mass. The black hole Gargantua in Interstellar is meant to be a supermassive black hole with mass about 100 million times that of the Sun, similar to the supermassive black holes seen at the center of various galaxies including our own--see this article for example. As mentioned here, a supermassive black hole wouldn't have deadly tidal forces at the event horizon, only much closer to the singularity. Likewise, see the comment from astrophysicist Neil DeGrasse Tyson here:
If you don’t want to be ripped apart by the tidal forces of a black hole, you’d need to move in and around a supermassive black hole, because the larger a black hole is, the shallower the tidal forces. So, a supermassive black hole would have very shallow tidal forces and likely would not rip you apart if you came near it or descended past the event horizon. It’s the stellar mass black holes that would rip you apart if you got too close.
And this comment from a piece by Stephen Hawking:
If you fall towards a black hole feet first, gravity will pull harder on your feet than your head, because they are nearer the black hole. The result is, you will be stretched out longwise, and squashed in sideways.. If the black hole has a mass of a few times our sun, you would be torn apart, and made into spaghetti, before you reached the horizon. However, if you fell into a much larger black hole, with a mass of a million times the sun, you would reach the horizon without difficulty. So, if you want to explore the inside of a black hole, choose a big one.
Problem 4 on this NASA page actually calculates the tidal acceleration for a supermassive black hole 100 million times the mass of the Sun, and finds that at the event horizon it would be only 0.00020 cm/sec^2 across a distance of 2 meters (the height of a tallish man), which is so weak as to be unnoticeable.
It should also be noted that spinning black holes have an entirely different structure from non-spinning black holes. In particular, they have two horizons -- one future horizon, like the ones you're familiar with, and one past horizon -- a surface where you must have come from. Once you've passed through the past horizon, you're then in a normal sort of geometry. I wouldn't be surprised if you could work out a set of parameters where the trip inside is survivable.
For an easy analogy to understand the principle, think about the bending radius of the Earth and the gravity at its surface. Someone standing at the surface of the Earth will likely see it as flat and will have to take a deep look at the visible horizon to determine that it is indead a sphere. (The clouds touching the horizon is an indication that the Earth is not flat. If it was flat, the separation between the clouds and the earth would remain visible.). However, if the Earth were much smaller, say like a ball, you could easily see that it is not flat. Likewise, if it was much bigger, something like Jupiter, it would appears even more flat.
You can see something similar with big mountains. On Earth, you can see the slope when you are standing on most mountains, even if it's big. However, if you were standing on the mount Olympus on Mars, you wouldn't even see it that you are standing on a mountain because it's so big.
Now, take a look at the gravity. At the surface of the Earth, it's approximately 9.8ms^2. Now, if you go on the surface of Jupiter, the gravity would be much bigger than that; so that to get a gravity similar to the one on the Earth's surface, you would have to stand in a much higher position. For the bending radius, we already now that it is already smaller at the surface of Jupiter because of its bigger size. Therefore, the bending radius on a position on Jupiter where the gravity is the same as on Earth would be even much more smaller.
The spaggettification and the slowing of time of a black hole follow the same principles. In the movie, the black hole is a super-massive black hole; with a mass of 100 million times that of the Sun; which you can compare to the mass of only a few suns for an ordinary (small) black hole.
The slowing of time is like gravity, the more massive the black hole is, the farther you must stand to get the exact same amount of slowing down as you would get for smaller one. However, for the spaghettification, this is a gradient and it's therefore comparable in property to the bending radius of an object. At the position where the slowing down in time for a super-massive black hole will be the same as for a small one, you will be so far from it that the gradient of gravity around you will be very low; so low in fact that it will be insufficient to create any spaghettification effect. The well known spaghettification effect so often cited when described what would happen if you were to approach a black hole is only valid for small black holes. For super-massive black holes, this effect doesn't exists. (There is a gradient of gravity around super-massive black holes, but like when you are standing on a very big mountain, it will be way to small to have any measurable effect on a humain body.)
To add to the other answers...
Speghettification would not have happened at the event horizon of the supermassive black hole because the tidal forces are weak there.
However, speghetiification would still have happened as the observer approached the singularity.
Also tidal forces depend upon both the gravity gradient and the size of the object in that gradient. Smaller objects (like a human body) experience much smaller forces than large objects like planets or moons.
This really explains a lot. It tells of tidal force of the massive black hole is so little until you get closer to the singularity. https://www.quora.com/Interstellar-2014-movie/Why-does-the-concept-of-Spaghettification-not-apply-to-things-entering-the-black-hole-in-Interstellar