spacetimedude said:
Okay. So in this case, the only force that matters is the tidal force (difference of gravitational force on your feet and head)? What I thought was that although the gravitational field is uniform, the acceleration (like when the rocket first launches from the ground) is really high that the person would get squished. Or is the acceleration really not that high? I was thinking this way because inside the horizon, the gravity is strong enough to keep the light from escaping, while on the outside, the light can still escape. Isn't there a huge difference in gravitational field, thus accelerating a lot when you pass the horizon?
Perhaps I can help. Let's look at astronauts in orbit. Let's say one orients his feet towards the Earth and his head away from it. His head will be attracted less strongly than his feet will. This of course is obvious if we look at the math for gravity, as it falls off with distance. So the 5-6 feet between his feet and his head mean that gravity gets weaker by a very small amount at his head than his feet. This difference in strength is called a gradient. The strength of gravity is so low for the Earth that the gradient is not noticeable to people, so for nearly all purposes we can simply say that it is a uniform field and ignore the gradient in every day life. Also, remember that gravity attracts ALL of your body, so in a uniform field every single subatomic particle that makes up your body would be pulled in a certain direction equally as hard. When a gradient exists the field isn't uniform and will pull parts of your body at different strengths.
Now we must look at the differences between the Earth and a black hole. First, the Earth is not very massive compared to a black hole, so it's gravitational strength is not very high. Second, a black hole with the mass of a few suns is VERY small. The event horizon is only 60 km across! (That's about 37 miles) In contrast, a supermassive black hole with a mass around 1 billion suns has a diameter of about 10 au. (1 au is the distance between the Sun and the Earth)
Now why does the size of the black hole matter? Well, it doesn't really. The size is actually the diameter of a spherical event horizon. Remember that event horizon is NOT a physical object. If you were to fall into a black hole you would encounter an increasing force from gravity. At a certain distance this force would be strong enough to keep light from leaving. However if you keep falling in, which of course you will, the force simply gets stronger as you continue to fall.
Let's assume that the model of a black hole where we have all mass packed into an infinitely small point is correct. For supermassive black holes around 1 billion solar masses that means that as you fall towards it the distance where light cannot escape is much greater than a black hole of around 10 solar masses. Which of course is as it must be if we remember that more mass equals a larger force at any given distance.
But that doesn't explain the whole story yet. For that we need to discuss the gradient. Now a gradient, as I said before, is a difference in strength between two points in a field. (Such as a gravitational field) The thing about a gradient is that it is steeper as we get closer to the singularity. (that means that the difference in strength between points of equal distance is greater as we get closer) For a supermassive black hole we are VERY far away from the singularity when we pass the event horizon, so the gradient is very shallow, like walking up long slope to the top of a hill. For a small black hole, since we are much much closer to the singularity when we pass the event horizon, the gradient is very very steep, like trying to walk up the steep slope of a mountain. However, if you were to fall into a supermassive black hole, you would pass the event horizon just fine. But remember that the force just keeps on increasing, as does the gradient, as we get closer to the singularity. So when you get very very close to the singularity the gradient would be extremely steep and you would be ripped apart.
So in either case, falling into a singularity of the type we looked at would eventually result in you being ripped apart.