The question is inspired by a conversation with a friend - Paul Gray. We wonder if we can resolve the problems associated with the singularity if it can be shown that the singularity never actually quite forms.
If we are falling into a black hole and we can see back in the direction from which we have come from, then we observe time speeding up - we would witness the universe accelerate towards its ultimate demise. Presumably, this would also be true of the matter that first formed the black hole. This might mean that the singularity is always on the verge of forming - as if frozen in time.
I believe the answer is observer dependent.
Observers outside the horizon never see the horizon form, much less the singularity.
The only observers who can observe the singularity are those who cross the horizon, and only after crossing the horizon. So arguably, the singularity forms after the horizon. For these observers, the singularity not only forms in a finite amount of time, it is also unavoidable.
"If we are falling into a black hole and we can see back in the direction from which we have come from, then we observe time speeding up - we would witness the universe accelerate towards its ultimate demise."
This is not quite true. While the redshift of the infalling observer goes to infinity from the point of view of a far-away observer, i.e. the infalling observers seems to be slowing down indefinitely, there is no corresponding speed-up of the far-away observer as assessed by the infalling one. In fact, he also sees the far-away observer slow down, albeit not indefinitely. At the horizon, the slow-down factor is 2 for a Schwarzschild black hole. So the infalling observer does not see the whole history of the outside universe.
As to the original question: it is difficult to compare times at a distance. So the question is not necessarily meaningful. In terms of the Schwarzschild time, there is no definite relationship between the time of coming into existence of the singularity and the time of formation of the horizon. The horizon forms at t=infinity in terms of Schwarzschild time. The time of formation of the singularity cannot be measured in Schwarzschild time, as that time does not exist inside the horizon. If you use Kruskal-Szekeres coordinates, the singularity exists from t=0 to t=infinity. One "point" of the horizon exists at t=0, the rest at t=infinity.
Christopher,
In my understanding of this issue the event horizon is a sphere that surrounds the center of any mass and which that mass has to collapse to in order to become a singularity. That sphere exists for all matter. This does not mean that all things shrink to black holes but that the limits exist for all matter.
If you can compress the matter to within the limit it will form a singularity. Any given amount of matter has this event horizon even though for small things it is very very small. The sun would have to drop within a few kilometer sphere to make it a black hole. Even if it were to do that it would not have any more gravity than it does now. Its mass would just be inside a much smaller sphere. Also any energy that would have been escaping from the surface of the sun would not escape from the new surface of the sun as a singularity. This is due to the fact that even light can not escape from the black holes event horizon.
So to answer your question the event horizon is already there. As a body collapses to a singularity its internal structure is compromised and the gravity that exists over comes the energy that the body is putting out. At that point the rotation increases significantly as the mass drops below the event horizon.
This also raises an even bigger issue. Why are not all things black holes, as all things loss energy and all stars should burn out over time.
Our physics does not explain this.
@Van Hoesen: If the wording in your message is changed from "event horizon" to "Schwarzschild radius", then it will go in line with what our physical theories say.
Event horizons do not exist for all matter. An event horizon will form around a chunk of matter, if the extent of that matter becomes smaller than its Schwarzschild radius. The Schwarzschild radius is a number that you can associate with any mass, the event horizon is a surface with certain physical properties. It is null which means that nothing can locally pass beyond that surface. If a piece of matter is bigger than its Schwarzschild radius, no event horizon will form.
By the way, the Planck scale is the wavelength of a photon that is equal to its Schwarzschild radius. If you increase the energy of a photon, its wavelength decreases. At some point the wavelength becomes smaller than the Schwarzschild radius associated with the energy of the photon (corresponding to a certaim mass). For photons of such an energy, our current physical theories break down; photons of a wavelength below the Planck scale are not meaningfully describable within them (as they should immediately vanish behind their own event horizon).
The Schwarzschild Radius is the event horizon that was calculated during WWI by him as the first exact solution of the Einstein Field equations. What I mean is that if a mass of any size falls below its Schwarzschild radius (or event horizon radius) it will by definition become a black hole. In the LHC they are trying to create supper small black holes with this understanding in mind.
This implies that (all matter) has a distance where if it gets smaller than that radius it will become a black hole.
Just because we do not see the black hole does not mean that is not what it is. The influence if a black hole is no different from the original mass as its gravitational force does not change when something falls below the Schwarzschild radius.
Well, I do not know whether they are literally trying to create mini-black holes at the LHC. There were some statements that they might be created (unintentionally), and there wers also some fearful statements that this might be dangerous. There was even an attempt to stop LHC from being started by a court rule.
You are right that the gravitational effect at a distance of an object being compressed below its Schwarzschild radius (and becoming a black hole this way) is not different from that of the object before becoming a black hole. So these mini black holes would not put the planet in danger by eventually "eating it up" as their gravitational effect would be tiny.
You are correct that they should not be dangerous. I understand that they were not trying to create the black holes but may have it happen. As the gravity of such a small particle is very small and no bigger than it had as a particle before collapse it is not a problem.
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