Black Hole Event Horizon and the Observable Universe

[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

 

[skeptic2]

Thank you xanox and Chalnoth. I saw the Penrose diagram but I still fail to understand why the path of the infalling object leads to the young black hole instead of asymptotically approaching the event horizon.

Nevertheless I recognize there is a problem with claiming that a black hole must evaporate before an object can penetrate the event horizon. Evaporation itself depends upon one of the two virtual particles created at the event horizon falling past the event horizon.

 

[stevebd1]

Regarding Hawking radiation and crossing the event horizon, you might also find this of interest from Usenet Physics FAQ-

'What about Hawking radiation? Won't the black hole evaporate before you get there?'
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html
(scroll down to the fouth FAQ)

 

[Chalnoth]

Thank you xanox and Chalnoth. I saw the Penrose diagram but I still fail to understand why the path of the infalling object leads to the young black hole instead of asymptotically approaching the event horizon.

Nevertheless I recognize there is a problem with claiming that a black hole must evaporate before an object can penetrate the event horizon. Evaporation itself depends upon one of the two virtual particles created at the event horizon falling past the event horizon.

Well, if you look at the Penrose diagram in fig. 3 of the paper I linked above, you should see a wavy, light-blue dashed line on the bottom of the graph. This is the event horizon of the evaporating black hole. The second point of interest is the singularity, which is the nearly-horizontal red line on the left: anything that hits that is squashed.

The thing to recognize here is that the event horizon is a horizon for outgoing light rays: if you start a light beam somewhere along that horizon traveling outward, it will travel straight along the horizon. If, however, I start a light beam traveling inward, it will just go and smack right into the singularity. So, what if I'm just a plain object? Well, if I was traveling inward I would just go right on through the event horizon and smack the singularity. The only way to prevent this occurring would be if the event horizon were also a horizon for inward-traveling light rays as well as outward-traveling ones. This clearly does not appear to be the case.

 

[Phrak]

Thank you xanox and Chalnoth. I saw the Penrose diagram but I still fail to understand why the path of the infalling object leads to the young black hole instead of asymptotically approaching the event horizon.

Nevertheless I recognize there is a problem with claiming that a black hole must evaporate before an object can penetrate the event horizon. Evaporation itself depends upon one of the two virtual particles created at the event horizon falling past the event horizon.

Virtual particles are not constrained to time-like world lines.

 

[Chalnoth]

Update on the falling into a realistic black hole with Hawking radiation:

My old GR professor got back to me, and pointed out something that I had forgot to consider: it depends upon whether or not a singularity forms before the black hole evaporates. If the singularity forms, then yes, some of the matter will travel in and smack the singularity before evaporation. If not, then indeed, infalling matter will see the black hole evaporate before it. Apparently the question as to whether or not the singularity will form in an evaporating black hole is still open.

 

[Phrak]

Update on the falling into a realistic black hole with Hawking radiation:

My old GR professor got back to me, and pointed out something that I had forgot to consider: it depends upon whether or not a singularity forms before the black hole evaporates. If the singularity forms, then yes, some of the matter will travel in and smack the singularity before evaporation. If not, then indeed, infalling matter will see the black hole evaporate before it. Apparently the question as to whether or not the singularity will form in an evaporating black hole is still open.

By 'infalling', I hope you mean 1) matter that is present in the interior when the event horizon forms, or 2) exterior matter that will find itself within the horizon if the Swarzchild radius increases, for instance.

 

[Chalnoth]

By 'infalling', I hope you mean 1) matter that is present in the interior when the event horizon forms, or 2) exterior matter that will find itself within the horizon if the Swarzchild radius increases, for instance.

Naturally, yes. At least it would in the idealized black hole that was already fully-formed. If there is no singularity, apparently, there is no true event horizon.

 

[MuggsMcGinnis]

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.

Yes, this is the crux of my problem with this. I can't get my head around the idea that reality is different for different observers. By this I mean that, the laws of physics are different, which is what this requires.

If anything can fall through an event horizon, then a single universe can have multiple realities that are logically, causally inconsistent.

For one observer, all causal contact is lost with the outside universe while, from another perspective, the in-falling object can be interacted with forever (until the black hole evaporates).

 

[MuggsMcGinnis]

By 'infalling', I hope you mean 1) matter that is present in the interior when the event horizon forms, or 2) exterior matter that will find itself within the horizon if the Swarzchild radius increases, for instance.

Presuming that it's possible to have "matter that is present in the interior <of an> event horizon" sort of bypasses the whole core of any discussion of whether it's possible to fall through an event horizon.

 

[MuggsMcGinnis]

Naturally, yes. At least it would in the idealized black hole that was already fully-formed. If there is no singularity, apparently, there is no true event horizon.

Chalnoth

How are these things incompatible?

Why can you not have an event horizon (which isn't really a "thing" so much as a geometrical definition) if you don't have a singularity?

Thanks