Does time dilation prevent event horizon formation?

[Petr Matas]

I read that time dilation near a black hole's event horizon causes the infalling matter to "freeze" just above the event horizon and never cross it (in a distant observer's frame of reference). Doesn't the same phenomenon prevent the event horizon and singularity from being formed in the first place? I believe that their absence would not change things much, because only time dilation prevents matter from crossing the surface where the event horizon whould be formed. From the outside, everything would look like if the event horizon was actually there.

 

[SerbianQuantum]

That doesn't make much sense. If the event horizon was never formed, therefore the black hole was never formed so what is causing the gravitational time dilatation you speak of?

The answer to you question is no, gravitational time dilatation only comes after a celestial body is "formed" regardless of which type from a star to a planet or even a black hole.

 

[Petr Matas]

The source of gravitation (e.g. a collapsed star) is there, only it is just a tiny bit larger than a black hole of the same mass would be. I expect it to behave like a black hole, even though the actual event horizon does not exist.

 

[phinds]

I read that time dilation near a black hole's event horizon causes the infalling matter to "freeze" just above the event horizon and never cross it (in a distant observer's frame of reference). Doesn't the same phenomenon prevent the event horizon and singularity from being formed in the first place? I believe that their absence would not change things much, because only time dilation prevents matter from crossing the surface where the event horizon whould be formed. From the outside, everything would look like if the event horizon was actually there.

That's like saying that time dilation prevents things from actually falling into a black hole, which is incorrect. You are making the common mistake of thinking that time dilation actually happens to an object rather than being something that is observed by an observer OTHER than the object.

 

[Petr Matas]

That's like saying that time dilation prevents things from actually falling into a black hole, which is incorrect.

I believe that from the distant observer's point of view, time dilation really prevents things from falling into the black hole.
Quoting from https://en.wikipedia.org/w/index.php?title=Black_hole&oldid=748582233#Event_horizon: "To a distant observer, clocks near a black hole appear to tick more slowly than those further away from the black hole. Due to this effect, known as gravitational time dilation, an object falling into a black hole appears to slow as it approaches the event horizon, taking an infinite time to reach it."

 

[phinds]

I believe that from the distant observer's point of view, time dilation really prevents things from falling into the black hole.

Yes, and that is completely irrelevant to the fact that the objects actually DO fall into the black hole.

 

[Petr Matas]

Yes, and that is completely irrelevant to the fact that the objects actually DO fall into the black hole.

They do, from their own perspective. But I am interested in the distant observer's perspective.

 

[phinds]

They do, from their own perspective. But I am interested in the distant observer's perspective.

But you asked whether or not it would prevent the event horizon from forming. I now assume you also meant THAT to be in the FOR of the observer as opposed to the actual formation of the EH.

 

[Petr Matas]

But you asked whether or not it would prevent the event horizon from forming. I now assume you also meant THAT to be in the FOR of the observer as opposed to the actual formation of the EH.

That's right. If you want to discuss the infalling observer's perspective, I would say that from his point of view the event horizon does not form until he reaches it.

 

[phinds]

That's right. If you want to discuss the infalling observer's perspective, I would say that from his point of view the event horizon does not form until he reaches it.

Well, from the in-falling observer's point of view, the EH is irrelevant anyway since there's nothing there and he experiences nothing from the fact that there is a mathematical surface with no physical substance.

 

[mfb]

They do, from their own perspective. But I am interested in the distant observer's perspective.

The distant observer will quickly see the last photon from the object that arrives ever due to redshift / time dilation. While there are coordinate systems (definitions of simultaneity) where the object does not fall in in finite external observer time, this is a purely mathematical artifact - you can also find frames where it does fall in, and you cannot observe the object for long (a statement which does not depend on your choice of coordinates).

 

[Petr Matas]

you can also find frames where it does fall in, and you cannot observe the object for long

That is interesting. Does any of these frames belong to an observer, which never falls into any black hole? Can you provide an example, please?

 

[mfb]

Coordinates in general relativity have a large amount of freedom. The definition of "happens at the same time" is basically completely arbitrary for events not at the same position in space.

Eddington–Finkelstein coordinates are an example constructed to avoid the "infinite time" appearing in Schwarzschild coordinates.

 

[sophiecentaur]

If the ship entering the black hole were to send regular pulses (regular by the shipboard clock) of RF to a distant observer, the time intervals between the received pulses would get longer and longer (frequencies in the signal would also get lower). Until they spaghettified, the crew would just see their clock giving regular pulses (in time with their heart beats and all the other regular functions in the ship. Eventually the time situation at one end of the ship would be different from the situation at the other end and they would probably have ceased any interest the progress of their experiments.

 

[DrStupid]

I read that time dilation near a black hole's event horizon causes the infalling matter to "freeze" just above the event horizon and never cross it (in a distant observer's frame of reference). Doesn't the same phenomenon prevent the event horizon and singularity from being formed in the first place?

I can't show you how the event horizon actually forms but I can at least tell you why this argumentation fails. What you usually read about the "freezing" of the infalling matter from the view of an external observer applies to a static black hole with Schwarzschild metric. Any significant amount of matter outside the event horizon changes this situation. That means that you must not conclude from a small test mass in the gravitational field of a black hole to a gravitational collaps.

 

[Chronos]

An event horizon is observer dependent. Theory suggests it comprises the entire observable universe to an interior observer. To an external observer, it is only region forever unobservable. It has been proposed this suggests our observable universe may reside inside a black hole. I think it only suggests we have much more to learn before we can draw any logical conclusions.

 

[Petr Matas]

Coordinates in general relativity have a large amount of freedom. The definition of "happens at the same time" is basically completely arbitrary for events not at the same position in space.

Eddington–Finkelstein coordinates are an example constructed to avoid the "infinite time" appearing in Schwarzschild coordinates.

In an attempt to falsify your statement, I tried to show that a photon sent into the black hole to chase an infalling object can reach the object before crossing the event horizon, reflect off the object and return from the black hole, although extremely delayed and red-shifted. Using the Eddington-Finkelstein coordinates, it turned out that if a sufficiently long head start is given to the object, the photon will not hit the object before they both cross the event horizon.

Maybe I am going to accept that my original question is a bit irrelevant, but here is another question:

Black holes evaporate due to Hawking radiation. Will not the black hole completely evaporate and disappear before an infalling object crosses the event horizon, thanks to time dilation?

 

[mfb]

Using the Eddington-Finkelstein coordinates, it turned out that if a sufficiently long head start is given to the object, the photon will not hit the object before they both cross the event horizon.

I would expect that this sufficiently long head start is of the order of the Schwarzschild radius (/c). That would be the natural scale and I don't see how a different scale could come into the calculation.

Hawking radiation of big black holes (>>Planck mass) doesn't matter on any relevant timescale, although firewalls are still discussed.

 

[DrStupid]

Will not the black hole completely evaporate and disappear before an infalling object crosses the event horizon, thanks to time dilation?

No, but I would expect that it will evaporate before the object reaches the singularity in the center. That could mean that there would be no singularity at all - even without quantum efects.

 

[phinds]

No, but I would expect that it will evaporate before the object reaches the singularity in the center. That could mean that there would be no singularity at all - even without quantum efects.

I don't get how that makes any sense. The object reaches the singularity pretty quickly after entering the EH but the BH doesn't evaporate for a HUGELY long time.

 

[DrStupid]

I don't get how that makes any sense. The object reaches the singularity pretty quickly after entering the EH but the BH doesn't evaporate for a HUGELY long time.

From the view of the same observer?

 

[phinds]

From the view of the same observer?

Ah. OK. we're still on the POV of the remote observer.

There was a discussion about exactly this sometime fairly recently and I believe the consensus was that if you hang around long enough (a totally unrealistic amount of time for any living organism, but forget that for the moment) you actually WOULD see the person evaporate (or something like that) as the BH got smaller and the EH shrank to a size smaller than a person. Of course, by then the wavelength would be so long you'd need a galactic scale instrument with almost impossible sensitivity to detect any light.

 

[Chronos]

Only photons attempting to retreat become time dilated as an infaller approaches a black hole. The infaller remains right on schedule for a date with oblivion. What you see is not what the infaller gets. The infaller is not retreating so remains unaffected.