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Falling into BH question

by nicksauce
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skeptic2
#37
Jan9-09, 05:10 PM
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Quote Quote by Chalnoth View Post
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.

Quote Quote by Chalnoth View Post
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
#38
Jan9-09, 06:21 PM
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Quote Quote by skeptic2 View Post
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
#39
Jan10-09, 01:03 AM
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Quote Quote by skeptic2 View Post
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
#40
Jan10-09, 01:46 AM
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GR may not be complete, but, nobody has proven it wrong. That hits my hot button. Show me the math before prophetizing.
Chalnoth
#41
Jan10-09, 02:13 AM
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Quote Quote by Chronos View Post
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
#42
Jan10-09, 04:58 AM
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Quote Quote by Chalnoth View Post
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
#43
Jan10-09, 05:48 AM
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Quote Quote by atyy View Post
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
#44
Jan10-09, 05:49 AM
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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
#45
Jan10-09, 05:52 AM
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Quote Quote by Phrak View Post
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
#46
Jan10-09, 10:27 AM
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Quote Quote by Chalnoth View Post
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
#47
Jan10-09, 10:56 AM
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These lecture notes by Kim Griest might be of interest-
http://physics.ucsd.edu/students/cou...161.8feb07.pdf

In all cases, [itex]r_s=2Gm/c^2[/itex]


'..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: [itex]dr/d\tau=\pm\sqrt{2Gm/r}=\pm\sqrt{r_s/r}[/itex], and [itex]dt/d\tau=\left(1-r_s/r\right)^{-1}[/itex], 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:

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

We see again that as r→rs, v→0. The far away observer never sees the person fall in..'


The following is based on [itex]dr_{shell}=dr\left(1-r_s/r\right)^{-1/2}[/itex] and [itex]dt_{shell}=dt\left(1-r_s/r\right)^{1/2}[/itex]


'..We can also find the speed measured in the shell frame:

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

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

[tex]v_{shell}=\frac{dr_{shell}}{dt_{shell}}=-\sqrt{\frac{r_s}{r}}[/tex]

This gives the result that to a shell observer, sitting at r=rs, the falling objects goes by at vshell=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
#48
Jan10-09, 11:59 AM
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Quote Quote by xantox View Post
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
#49
Jan10-09, 12:38 PM
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Quote Quote by Chalnoth View Post
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
#50
Jan10-09, 04:10 PM
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Quote Quote by xantox View Post
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
#51
Jan10-09, 05:17 PM
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Quote Quote by Chalnoth View Post
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
#52
Jan10-09, 05:57 PM
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Quote Quote by Phrak View Post
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
#53
Jan10-09, 06:13 PM
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Quote Quote by Chalnoth View Post
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
#54
Jan10-09, 06:36 PM
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Quote Quote by Phrak View Post
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.

Quote Quote by Phrak View Post
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.


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