Original Post
Ok, with this latest talk about Hawking's ideas and so on, I've been some reading on what has been said about Black Holes. Not that I can understand much or anything of the mathematics of the thing. However, I have understood something about them because the scientists which predicted black holes described it in such simple terms.
Basically, I'm talking about the 'austronaut falling into black hole' example. One description of the many I have found is this, although they all say the same.
Ok, first of all, I don't understand why the phrase it 'second austronaut never actually sees the first austronaut reach Schwarzschild radius', as it is some kind of optical illusion. For any observer outside this radius, the austronaut or anything else never reaches that radius.
Now, what I can't understand at all is, if that's true, then how black holes are even formed. It is said that a star is starting collapsing and there is nothing that keeps the particles of the star to collapse into a singularity. But that same austronaut example says that there *is* something that prevents the austronaut from falling into the singularity, namely time dilation. If the austronaut, or generally any particle, will never reach Schwarzschild radius, how the particles of the collapsing star reach it and go inside? Does it mean that any observer of the collapse of the star will never observe it to form a black hole? If that's so, then the conclusion is that black holes are never formed! Now, obviously I thought(and still think) I have forgot something. However, I found this link that states the same:
I can't imagine a solution to this contradiction. I'm talking with such surprise that I don't understand it, because it's not about the math of the thing, it's what scientists say about the black hole. For every observer outside the black hole, a particle will never fall into it. But, at the same time, a star that we can observe today with the telescope and is more than 2-3 masses, will form a black hole, that is its particles will cross the horizon. I don't see what is the implication. I don't understand the math, but scientiest have categorically stated both that a particle will never cross the horizon for any observer, and that the particles of a collapsing star will cross it and form a black hole. It's not about general relativity or math at all. It's about statements that describe what happens. Those statements seem like they are the exact polar opposites. What the hell am I not seeing here?
Basically, I'm talking about the 'austronaut falling into black hole' example. One description of the many I have found is this, although they all say the same.
Quote:
We assume that the astronaut approaching the black hole can send out signals in various directions, including back to the other astronaut. As the first astronaut approaches the black hole, the first thing the distant astronaut would notice is the redshift in the signals received. The magnitude of the redshift increases as the first astronaut becomes closer to the Schwarzschild radius.
Before the Schwarzschild radius is reached, another effect becomes noticeable. The paths of photons sent out by the first astronaut are not straight lines. They bend. The only direction in which the astronaut can aim a beam and not have it bend is straight up. If the beam is not aimed sufficiently close to the vertical, the bending will be so great that the light will not escape. Only light aimed into a cone about the vertical, called the exit cone, will escape. As the first astronaut moves closer to the Schwarzschild radius, the exit cone becomes smaller. At a distance equal to (3/2)Rs, photons aimed horizontally go into orbit around the black hole. The sphere of orbiting photons is called the photon sphere. If you were to look straight out, along the horizon, you would see the back of your head.
The second astronaut never actually sees the first astronaut reach the Schwarzschild radius. The gravitational time dilation is so great that, as Rs is approached, the second astronaut thinks that it takes the first astronaut an infinite amount of time to reach Rs. The time dilation makes the first astronaut appear to slow down as Rs is approached.
From the point of view of the first astronaut, there is no such respite. The Schwarzschild radius is reached very quickly. If the black hole is of sufficiently small mass, the tidal forces would tear the first astronaut apart. However, if the black hole is massive enough, the tidal forces might be survived and the astronaut crosses Rs. When this happens, we say that the astronaut has crossed the event horizon. If the black hole is massive enough, the astronaut might not notice anything unusual, except that escape is impossible!.
Ok, first of all, I don't understand why the phrase it 'second austronaut never actually sees the first austronaut reach Schwarzschild radius', as it is some kind of optical illusion. For any observer outside this radius, the austronaut or anything else never reaches that radius.
Now, what I can't understand at all is, if that's true, then how black holes are even formed. It is said that a star is starting collapsing and there is nothing that keeps the particles of the star to collapse into a singularity. But that same austronaut example says that there *is* something that prevents the austronaut from falling into the singularity, namely time dilation. If the austronaut, or generally any particle, will never reach Schwarzschild radius, how the particles of the collapsing star reach it and go inside? Does it mean that any observer of the collapse of the star will never observe it to form a black hole? If that's so, then the conclusion is that black holes are never formed! Now, obviously I thought(and still think) I have forgot something. However, I found this link that states the same:
Quote:
The popular story is that in a supernova large amounts of mass can get crushed at the center to form a black hole. Well, general relativity disagrees. Think of a black hole being formed by a certain amount of mass M in the form of a fine dust (debris) collapsing due to gravity. It will become a black hole when all of M falls within a sphere of radius rs = 2GM/c2 as given above. But closer it gets to doing this the greater is the time dilation for the outermost pieces of the debris. The last few pieces that need to fall in to form the black hole will take literally forever (infinite time) to do so. Hence, a star cannot collapse to form a black hole. What it can form is a ball of dust which is close to being a black hole at every spherical layer within it but not quite. In such a star, time dilation is so large for every falling piece of debris that it appears to be "frozen" in time. It can be shown that such a "frozen star" would have a density profile that reduces as the inverse square of distance from the center.
So, the only way the universe can have black holes is if they were there all the time. Of course, this is a conclusion of general relativity which is only a theory and a theory can be wrong. However, if general relativity is wrong and we need to abandon it, we would also have to abandon the definition of black holes that comes from it and there exists no other definition.
I can't imagine a solution to this contradiction. I'm talking with such surprise that I don't understand it, because it's not about the math of the thing, it's what scientists say about the black hole. For every observer outside the black hole, a particle will never fall into it. But, at the same time, a star that we can observe today with the telescope and is more than 2-3 masses, will form a black hole, that is its particles will cross the horizon. I don't see what is the implication. I don't understand the math, but scientiest have categorically stated both that a particle will never cross the horizon for any observer, and that the particles of a collapsing star will cross it and form a black hole. It's not about general relativity or math at all. It's about statements that describe what happens. Those statements seem like they are the exact polar opposites. What the hell am I not seeing here?
