Black Hole Event Horizon and the Observable Universe

[MuggsMcGinnis]

1) It's clear that, for the external observer, the event horizon evaporates before anything falls into it.

2) For the external observer, the distance to the event horizon is always less than 5.8 light-days. The only way for the laser pulse to require more than 11.6 days, round-trip, is for light to travel slower than the speed of light. By the way, I'm not willing to accept the possibility that, for any observer, light travels through vacuum at any speed other than c. No valid interpretation of general relativity can require this.

Also, GR requires universality: Observations made by any observer must be compatible with those of any other observer.

The problem here is, how can one reconcile these two statements?

1. The infalling object quickly (less than 580 days, in this example) falls below the event horizon.
2. The observer can interact (bouncing light off of the object & detecting the return) with the in-falling object for more than 10⁶⁶ years.

 

[xantox]

Each pulse sent to the in-falling sphere travels, for all observers, at the speed of light. The return from each pulse will be received in less than 5.8 days. [..] I am arguing that it is not a valid transformation because it yields results that are logically incompatible with the original, untransformed reference frame. [..] The problem here is, how can one reconcile these two statements? [..]

The photon emitted at the limit of the horizon will be received in infinite time measured by the distant observer, ie. never (supposing the purely classical case without evaporation). You're apparently considering this problem within special relativity, but that only allow to talk about flat spacetime with no gravity, where black holes do not exist indeed. I friendly recommend a reading of the beautiful and accessible introductory text by James Hartle, "Gravity: An Introduction to Einstein’s General Relativity", Addison Wesley (2002) (available on Amazon).

Can you please expand on your statement, "photons which can be greatly slowed down"? Under what circumstances does General Relativity predict that light will be slowed down?

I was supposed to mean that in terms of the distant observer clock, the photons which he would expect to receive much sooner if the spacetime was flat, will be received much later. This is again a manifestation of spacetime curvature, not a modification of properties of light which always move locally at the speed of light c. That the travel time of light increases within a strong gravitational field is one of the classic tests of general relativity which has been confirmed experimentally with a precision of about 0.1%.

When the computation was done of the time it takes for an infalling object to reach the event horizon, was the radius of the EH assumed to be fixed for the duration of that time?

Yes, since on that short timescale compared to the one of evaporation it may be considered fixed. But we may simplify the problem by ignoring evaporation, so the radius will never shrink. Also, another computation can be done of the time it takes for a star to collapse into a black hole, which gives again a finite (and short) result.

Unlike two observers traveling at relativistic velocities relative to each other and who both observe the others clock is running slow, an observer in curved spacetime and one in flat spacetime both agree whose clock is running slow, the one in curved spacetime. I think it is reasonable to assume that given the extreme time dilation very close to the EH, that the BH may evaporate as fast as the object falls toward it.

The event horizon may be considered a surface of infinite time dilation relative to the distant observer in flat spacetime. This does not mean that the infalling clock is stopping when it reaches the horizon, or that inward photons become freezed there. Inward photons continue to move at c at the horizon, infalling observers clocks do not stop at the horizon.

I agree that some photons may take a very long time to return but instead of saying they were greatly slowed down can we say that they traveled a much greater distance due to the contraction of spacetime near the horizon?

Perhaps you mean space contraction? but if space would contract then the distance would be smaller..

 

[skeptic2]

"This does not mean that the infalling clock is stopping when it reaches the horizon, or that inward photons become freezed there. Inward photons continue to move at c at the horizon, infalling observers clocks do not stop at the horizon."


True, clocks in their own reference frame do not stop but we are not talking about clocks in their own reference frame nor the time it takes an object to fall to the EH in its own reference frame. We are and we have been talking about observing an infalling object from the reference frame of flat space. So yes, for an object falling into a BH from its own reference frame it happens quickly in finite time. But for us in flatspace we see the object being affected by dilated time and contracted space. These effects become infinite at the EH. It would take an eternity to cross the EH and as Woody Allen once said, "Eternity is a long time, especially towards the end."

Are you suggesting that the reference frame of the infalling object is somehow the 'real' reference frame and what we in flat space see is only an illusion caused by gravitational distortion?

We have been talking about something happening quickly in one frame of reference and not happening at all in another. Perhaps it doesn't really happen in either frame of reference. In both frames of reference the BH evaporates before the object can cross except that in the infalling object's frame the BH evoporates very rapidly because of the extreme dilation of time. This is the problem with calculating the time to fall to the EH in the object's own reference frame. It ignores the fact that the BH is slowly evaporating in nondilated time and very much more rapidly in the dilated time of the object.

 

[Naty1]

What bothers me is that the presumption that something can fall to (much less, through) an event horizon in finite time depends upon there being a `true reality' that contradicts the observable reality.

If you accept in general that observers in different reference frames don't always agree on observed time,distance,mass,etc, elsewhere seems like this one should also also be accepted.

 

[skeptic2]

Naty1

I raised the question of how an object is able to cross the event horizon because I don't understand how it happens and what seems logical to me is at odds with the widely accepted interpretation of black hole geometries. Certainly I accept that observers in different reference frames don't always agree on observed time,distance,mass,etc. but I also believe that events in one reference frame can be mathematically transformed into any other reference frame to explain what those observers see. To suggest that simply because observers in different reference frames disagree about time, distance or mass, is sufficient reason to accept an ad hoc instance of differing observations without providing some sort of transformation between the reference frames is less than scientific.

I also raised the question hoping that someone here could point out the errors in my logic. The references I've seen, like xantox's posts, don't address the issue of the evaporation of the black hole during the extremely dilated time an object experiences as it falls towards the event horizon. Briefly put, is time infinitely dilated at the event horizon and if so, how does an object cross that event horizon in finite time? If it crosses in finite time in one frame of reference but not in another, what is the transformation between those reference frames that permits that?

 

[Chalnoth]

Briefly put, is time infinitely dilated at the event horizon and if so, how does an object cross that event horizon in finite time? If it crosses in finite time in one frame of reference but not in another, what is the transformation between those reference frames that permits that?

It doesn't. Basically in the case of a static black hole without any Hawking radiation, this means that it is impossible to do a transformation between the observer that has already passed the event horizon and an observer outside the event horizon. This is, in fact, what is meant by an event horizon in the first place: observers on different sides of an event horizon are causally disconnected, and it is therefore no longer possible to translate between their reference frames.

However, I'm beginning to think that with Hawking radiation, an infalling observer won't actually ever observe the interior of the black hole, but will instead just see the black hole evaporate to nothing, until the observer itself exits the black hole as Hawking radiation.

 

[skeptic2]

Basically in the case of a static black hole without any Hawking radiation, this means that it is impossible to do a transformation between the observer that has already passed the event horizon and an observer outside the event horizon.

Of course not. I guess I should have been clearer. I meant a transformation between an observer very close to the EH where time is extremely dilated and flat space.

However, I'm beginning to think that with Hawking radiation, an infalling observer won't actually ever observe the interior of the black hole, but will instead just see the black hole evaporate to nothing, until the observer itself exits the black hole as Hawking radiation.

Exactly, and this is the crux of my problem. If nothing can pass through the horizon, how can there be large black holes? (Small black holes may still be possible.) If the weight of all the matter can be supported by the EH, why is there required to be a singularity at the center?

 

[xantox]

Briefly put, is time infinitely dilated at the event horizon and if so, how does an object cross that event horizon in finite time? If it crosses in finite time in one frame of reference but not in another, what is the transformation between those reference frames that permits that?

The infalling body falls only in one place, not two. His path in that one place is finite, as it may be calculated by integrating the proper time on his worldline. So, the infalling body reaches the horizon, and enters the black hole, and fast. However, when this same path is measured by a distant observer, and since he is not in the same curved spacetime, he will use as a result coordinates having a radically different meaning. So he may well obtain an infinite result since his clock is not measuring the same thing that the infalling body calls "time".

Maybe this metaphor can help get a very rough and partial image: if you can only measure your shadow, then when the sun approaches noon exactly above you, the shadow will approach zero length, while at sunset it will become longer and longer, until going ideally to infinity. This does not mean your height is infinite, but just that it has been projected in some way onto different coordinates.

 

[Chalnoth]

Exactly, and this is the crux of my problem. If nothing can pass through the horizon, how can there be large black holes? (Small black holes may still be possible.) If the weight of all the matter can be supported by the EH, why is there required to be a singularity at the center?

Well, ultimately, I think that describing what a black hole actually is would require an understanding of quantum gravity. And we know that there isn't going to be a real singularity at the center: that's a feature of General Relativity, and a signature that General Relativity is wrong.

 

[Chronos]

GR may not be complete, but, nobody has proven it wrong. That hits my hot button. Show me the math before prophetizing.

 

[Chalnoth]

GR may not be complete, but, nobody has proven it wrong. That hits my hot button. Show me the math before prophetizing.

Let me be clear with what I mean. We know that GR must break down at some point, because it provides nonsensical predictions (singularities). But we don't yet know where it breaks down, because so far all experiments and observations are exactly in line with the theory's predictions.

 

[atyy]

Let me be clear with what I mean. We know that GR must break down at some point, because it provides nonsensical predictions (singularities). But we don't yet know where it breaks down, because so far all experiments and observations are exactly in line with the theory's predictions.

What exactly is so bad about a singularity, since it doesn't seem to be preventing predictions?

 

[Chalnoth]

What exactly is so bad about a singularity, since it doesn't seem to be preventing predictions?

Beyond the difficulties of having an actual infinity in the theory, General Relativity has a fundamental energy scale (the Planck scale). Singularities necessarily go far beyond that energy scale. And the reason why it's a problem for General Relativity is because GR predicts such singularities under very general conditions.

To put it another way, even with this fundamental energy scale sitting in the theory, if there was no reason to believe that the energy density could ever get high enough to contest this energy scale we might well think that the theory could potentially be absolutely correct.

And, of course, there are the incompatibilities with quantum mechanics to consider.

 

[Phrak]

I don't know what you all are talking about, but the horizon can't be crossed in finite time in the refererence frame of the exterior universe. So is it crossed, or is the question a nonsequiter?

Are we talking physics here, or UFOs?

 

[Chalnoth]

I don't know what you all are talking about, but the horizon can't be crossed in finite time in the refererence frame of the exterior universe. So is it crossed, or is the question a nonsequiter?

In basic General Relativity with no Hawking radiation, the answer is a definitive yes, because the proper reference frame to consider is not the reference frame of an external observer, but rather the observer falling into the black hole.

I think that the definitive answer to how this works in reality may potentially require an understanding of quantum gravity, which we don't yet have.

 

[xantox]

In basic General Relativity with no Hawking radiation, the answer is a definitive yes, because the proper reference frame to consider is not the reference frame of an external observer, but rather the observer falling into the black hole.

The answer is a definitive yes -also- with Hawking radiation for any macroscopic black hole. For a free falling body starting at rest in the distant flat spacetime, the time it takes on the body's own stopwatch to go from say 3x(horizon radius) to the horizon is around 100 microseconds – rather small compared to the evaporation timescale into a surrounding vacuum of such black hole of around 10^68 years, so that such effect may be ignored.

 

[stevebd1]

These lecture notes by Kim Griest might be of interest-
http://physics.ucsd.edu/students/courses/winter2007/physics161/Lectures/p161.8feb07.pdf

In all cases, r_s=2Gm/c^2'..Suppose we take the case where someone starts from rest at ∞ and falls into the hole.. as viewed from far away the person’s time slows down and then stops as it enters the Schwarzschild radius. The calculation is done starting from radial and time equations: dr/d\tau=\pm\sqrt{2Gm/r}=\pm\sqrt{r_s/r}, and dt/d\tau=\left(1-r_s/r\right)^{-1}, where we used conserved energy E=m which is valid starting at rest from infinity. Dividing these equation we find the relation between r and t, that is the speed as seen from from away:

v_{far\ away}=\frac{dr}{dt}=-\left(1-\frac{r_s}{r}\right)\sqrt{\frac{r_s}{r}}

We see again that as r→r_s, v→0. The far away observer never sees the person fall in..'The following is based on dr_{shell}=dr\left(1-r_s/r\right)^{-1/2} and dt_{shell}=dt\left(1-r_s/r\right)^{1/2}'..We can also find the speed measured in the shell frame:

v_{shell}=\frac{dr_{shell}}{dt_{shell}}=\left(1-\frac{r_s}{r}\right)^{-1}\frac{dr}{dt}

For the person falling in from far away, we put in the result for dr/dt above to find:

v_{shell}=\frac{dr_{shell}}{dt_{shell}}=-\sqrt{\frac{r_s}{r}}

This gives the result that to a shell observer, sitting at r=r_s, the falling objects goes by at v_shell=1, the speed of light! Isn’t it strange that the same object doing the same thing can be moving at 0 speed or c from different vantage points..'

Steve

 

[Chalnoth]

The answer is a definitive yes -also- with Hawking radiation for any macroscopic black hole. For a free falling body starting at rest in the distant flat spacetime, the time it takes on the body's own stopwatch to go from say 3x(horizon radius) to the horizon is around 100 microseconds – rather small compared to the evaporation timescale into a surrounding vacuum of such black hole of around 10^68 years, so that such effect may be ignored.

Remember that the important metric for determining whether or not the observer sees itself passing the event horizon is the lifetime of the black hole in the infalling observer's frame, as opposed to an outside observer's frame. Because any reference frame is a valid reference frame for computing the results, provided that you're not attempting to talk about behavior beyond an event horizon from your reference frame, and because from the outside observer's point of view an object never falls beyond a black hole's event horizon, it's beginning to look to me that the black hole will always evaporate before the observer passes the event horizon, when considered by an outside observer.

Now, I'm not certain on this. The idea just occurred to me in reading this thread, and I haven't heard any GR experts' take on it. But it seems to make sense to me. Perhaps I'll send an e-mail to my old GR professor...

 

[xantox]

because from the outside observer's point of view an object never falls beyond a black hole's event horizon, it's beginning to look to me that the black hole will always evaporate before the observer passes the event horizon, when considered by an outside observer

I fail to understand how you can consider that while without Hawking radiation the observer of the previous example can cross the final gap to the horizon in 100 microseconds, with Hawking radiation he would need to wait 10^68 more years. Or maybe you think the black hole will evaporate for him in 100 microseconds?

 

[Chalnoth]

I fail to understand how you can consider that while without Hawking radiation the observer of the previous example can cross the final gap to the horizon in 100 microseconds, with Hawking radiation he would need to wait 10^68 more years. Or maybe you think the black hole will evaporate for him in 100 microseconds?

That's precisely it. Remember that those 100 microseconds to the infalling observer are beyond positive infinity for the outside observer. So yes, I'm suggesting that perhaps the time dilation really is that extreme.

 

[Phrak]

In basic General Relativity with no Hawking radiation, the answer is a definitive yes, because the proper reference frame to consider is not the reference frame of an external observer, but rather the observer falling into the black hole.

I think that the definitive answer to how this works in reality may potentially require an understanding of quantum gravity, which we don't yet have.

So the answer is, "No, it can't be crosses, as the horizon retreats under Hawking radiation in finite time."

 

[Chalnoth]

So the answer is, "No, it can't be crosses, as the horizon retreats under Hawking radiation in finite time."

Well, maybe. This is my suspicion. I want to verify it, however.

 

[Phrak]

Well, maybe. This is my suspicion. I want to verify it, however.

Your suspicions are valid for a test particle. A massive object that perturbs the event horizon may be different.

In addition to this, a central singularity is often invoked, but not proven nor motivated.

 

[Chalnoth]

Your suspicions are valid for a test particle. A massive object that perturbs the event horizon may be different.

Yeah, I've been wondering about that.

If my suspicion were valid for a massive object that perturbs the event horizon, then this would indicate that a black hole might be thought of as a region of space where lots of matter is colliding, but that it's gotten so incredibly dense that time dilation has slowed the collision to an absurdly slow pace as far as outside observers are concerned.

In addition to this, a central singularity is often invoked, but not proven nor motivated.

Yeah, it seems to me that an actual singularity is just physically impossible. Now, it may be an incredibly dense region of space, but an actual singularity? I don't think so.

 

[Phrak]

Yeah, I've been wondering about that.

Imagine you are halfway between two black holes that are approaching each other. To a observer the horizons merge, with you inside. Apparently the size of the black hole must increase for something to cross an event horizon--which, come to think about it, is nearly a tautalogy, anyway.

If my suspicion were valid for a massive object that perturbs the event horizon, then this would indicate that a black hole might be thought of as a region of space where lots of matter is colliding, but that it's gotten so incredibly dense that time dilation has slowed the collision to an absurdly slow pace as far as outside observers are concerned.

Yeah, it seems to me that an actual singularity is just physically impossible. Now, it may be an incredibly dense region of space, but an actual singularity? I don't think so.

Why should it be dense? At the time of collapse, the mass is not all stuck at one point in space. Put enough air together at standard density and it's a black hole.

 

[Chalnoth]

Imagine you are halfway between two black holes that are approaching each other. To a observer the horizons merge, with you inside. Apparently the size of the black hole must increase for something to cross an event horizon--which, come to think about it, is nearly a tautalogy, anyway.

Right. That's exactly what I was thinking about (well, not exactly...but mostly).

Why should it be dense? At the time of collapse, the mass is not all stuck at one point in space. Put enough air together at standard density and it's a black hole.

Well, I suppose. But this isn't the way that black holes form, and it also ignores the potential dynamics that may be going on in the interior.

My sort of vague suspicion is this: imagine that we form a black hole by accretion of matter. This is closer to the way an actual black hole forms, but certainly isn't exact. As it's forming, the matter starts to bunch up just outside the event horizon. This makes for an effective event horizon that is slightly larger, and more matter bunches up outside of that. If we understand a black hole as a collision frozen by time dilation (which I understand as being a completely wild guess), then the density should be highest near the center, and taper off towards the outer edge.

Now, you might ask, why should it remain frozen once it's inside the event horizon? Obviously this is not what classical General Relativity predicts: since the light cone of any object inside the event horizon inevitably travels towards the singularity at the center, anything within that horizon must collapse into the singularity.

However, what I'm wondering is, what if the information about the existence of these outer layers hasn't yet reached the inner layers, as measured by an outside observer? This might cause the inner layers of the black hole to be essentially frozen in time, at least as far as an external observer is concerned, until they are re-radiated as Hawking radiation later.

I strongly suspect that if this idea is correct even in the most vague sense, it would require a quantum theory of gravity to actually describe in detail.

 

[Phrak]

Right. That's exactly what I was thinking about (well, not exactly...but mostly).


Well, I suppose. But this isn't the way that black holes form, and it also ignores the potential dynamics that may be going on in the interior.

My sort of vague suspicion is this: imagine that we form a black hole by accretion of matter. This is closer to the way an actual black hole forms, but certainly isn't exact. As it's forming, the matter starts to bunch up just outside the event horizon. This makes for an effective event horizon that is slightly larger, and more matter bunches up outside of that.

That certainly sounds better than most of the stuff I read on black holes here (Where are the black hole mentors?) So if I, and a few thousand of my closest friends, all fall toward the event horizon, equally spaced around the black hole, we could end up within an expanded
event horizon.

If we understand a black hole as a collision frozen by time dilation (which I understand as being a completely wild guess), then the density should be highest near the center, and taper off towards the outer edge.

Now, you might ask, why should it remain frozen once it's inside the event horizon? Obviously this is not what classical General Relativity predicts: since the light cone of any object inside the event horizon inevitably travels towards the singularity at the center, anything within that horizon must collapse into the singularity.

However, what I'm wondering is, what if the information about the existence of these outer layers hasn't yet reached the inner layers, as measured by an outside observer? This might cause the inner layers of the black hole to be essentially frozen in time, at least as far as an external observer is concerned, until they are re-radiated as Hawking radiation later.

I strongly suspect that if this idea is correct even in the most vague sense, it would require a quantum theory of gravity to actually describe in detail.

That's an interesting question. I can't answer. But dispite all the talk about a central singularities, the Schwartzchild solution that gives rise to a singularity requires a vacuum condition everywhere within a black hole, except at a single central point. So I'm not likely to believe much talk here about singularites without an explanation as to why the entire mass must always be located at this single central point in the first place.

 

[Chalnoth]

That certainly sounds better than most of the stuff I read on black holes here (Where are the black hole mentors?) So if I, and a few thousand of my closest friends, all fall toward the event horizon, equally spaced around the black hole, we could end up within an expanded
event horizon.

Well, from the point of view of an outside observer, anyway. I'm pretty confident that no matter which way you slice it, any observer falling into a black hole will experience the process in a very finite amount of time.

That's an interesting question. I can't answer. But dispite all the talk about a central singularities, the Schwartzchild solution that gives rise to a singularity requires a vacuum condition everywhere within a black hole, except at a single central point. So I'm not likely to believe much talk here about singularites without an explanation as to why the entire mass must always be located at this single central point in the first place.

That part doesn't so much bother me, because at least in General Relativity without Hawking Radiation, there just isn't any way for the matter to produce enough pressure to support its own weight. So it is forced to collapse. Actually, I'd be rather surprised if this hasn't been proven for a spherically-symmetric body. I just don't have the familiarity with the General Relativity research to determine whether or not this is the case.

 

[xantox]

That's precisely it. Remember that those 100 microseconds to the infalling observer are beyond positive infinity for the outside observer. So yes, I'm suggesting that perhaps the time dilation really is that extreme.

They are not beyond future infinity for the outside observer, since the black hole is evaporating – so the time dilation varies with time until spacetime becomes again flat and there is no more time dilation. Anyway, if you look at the Penrose diagram of a semiclassically evaporating black hole, you will notice that the path of the infalling body leads into the young black hole, and not into the region where it has already evaporated away.

 

[Chalnoth]

They are not beyond future infinity for the outside observer, since the black hole is evaporating – so the time dilation varies with time until spacetime becomes again flat and there is no more time dilation. Anyway, if you look at the Penrose diagram of a semiclassically evaporating black hole, you will notice that the path of the infalling body leads into the young black hole, and not into the region where it has already evaporated away.

Ah, okay, that would seal it, then. Clearly the idea is wrong. I can't believe I didn't think to look up the Penrose diagram of an evaporating black hole. After your comment, I was quickly able to find this article:
http://arxiv.org/abs/0710.2032