Originally Posted by

**kojax**
It seems that the issue here is that, in Special Relativity, every observer believes their own clock is the fast one. But, in General Relativity, the observer with the slower clock knows their clock is slower (or rather, knows the other observer's clock is the fast one). The two situations are different animals.

The picture I'm starting to envision of black holes is that none of them have ever quite formed yet. The matter is all still sitting there right at the event horizon waiting to fall in. They think it will happen in 0.0000000......01 seconds. We observe that it may be billions of years away (or never happen). If there's matter already inside the outer event horizon, the matter outside the horizon doesn't count toward the Schwarzchild radius for it, so it could still be outside the event horizon that applies to it. You know, like in the same way as how the gravity is less and less as you get closer to the center of the Earth, until you reach the core and it is zero because of all the mass canceling out.

At this point, I just don't get what part of the picture I'm missing. Taking all the information available, it seems likely that this would be the way of things, but some very prominent scientists have said there is such a thing as matter collapsing inside the Scharzchild Radius. I'm just curious to understand how it is that they think this is possible.

kojax, thank you for bringing this up, it is an interesting conundrum, isn't it ??

The main point here is that we are dealing with a full GR scenario; as such it needs to be clear that there is

**no** absolute frame of reference on which our two observers ( the stationary one and the in-falling one ) can agree. This means, as we shall see, the two observers seeing different outcomes of the experiment.

The most important concept in this case is that time cannot be defined

*globally,* but only

*locally* - time as the observers see it ( clocks ) will

*not* agree. The stationary observer ( let us assume he is far from the black hole ) sees

*coordinate time*, whereas the in-falling observer measures

*proper time*. Coordinate time, as the name implies, depends only the specific choice of coordinate system, whereas proper time depends on the physical geometry of space-time ( mathematically it is a function of the metric tensor ); it is immediately obvious now that these only coincide if space-time is sufficiently flat, which unfortunately isn't the case for a black hole. Let's do the maths, starting with the stationary observer who measures coordinate time

*t(coord)* :

wherein F and C are constants following from the starting conditions of the observer's state of motion. The derivation of the above integral is beyond the scope of this post, but I can give the required references if anyone needs them; basically it follows from a solution of the geodesic equations from of the Schwarzschild Metric. What the above means is that, from the frame of reference of a far-away observer, anything falling into the black hole will

*appear* to need infinite time to reach the event horizon; this is just like kojax has pointed out.