Detecting matter falling into a Black Hole

[Logan5]

Hello to all !

I wanted to ask a question in this forum. I am french, and I have discussed this topic in a french physics forum, but with no clear conclusion. I hope I'll have another insights in this forum, which seems very well frequented.

I know the underlying subject has been discussed in this forum already (with no clear conclusion either !) : can an infalling object in a black hole ever enter the horizon before the end of the universe, or before the BH evaporates ? But I'll try to formulate the problem in a new way, trying to avoid traditionnal pitfalls and shortcomings, and particulary without using the simultaneity concept (or the question WHEN the object enter the horizon ?), which is very tricky in this context.

Here is a mind experience and the question :

Let a regular BH, generating a Schwartzschild metric. Let an observer O at fixed Schw. distance from the BH, in near Minkowski metric and time. The observer sees an infalling object passing near it at his Minkowski time T1 (radial free fall in the BH). Mass of object and observer is negligible compared to the mass of the BH.

The object will disappear from the detecting instruments of O (which does not mean that the object have crossed the horizon) at observer/Minkowski time T2. When (at whatever moment) the object crosses the horizon, the horizon is disturbed, the BH "loose his hair" and emit gravitational waves.

The observer O detects the gravitational waves at his time T3. The question is : what is this time T3 ?

Here are some possible answers :

1. Never (T3 = infinite)
2. At some finite Minkowski time T3. In this case what is the formula which gives T3 ?
3. The GW will not be detectable (for example infinitly expanded), or GW are detectable but with no clear signal at horizon cross, so this mind experience cannot give clue about horizon crossing (this answer is fundamentally different from answer 1).
4. This mind experience has some flaw in his description or assumptions so there is no answer (please kindly explicit the flaws).
5. GR is not sufficient to give the answer. We must take into account quantum or tunnel effects when matter reaches Planck distance from the horizon.
   
6. Some other answer ?

My own answer is something like 3. But in this case, I wonder what is the exact signification of articles like http://kipac.stanford.edu/kipac/black-holes-eating-stars-and-making-waves (there are a lot of such articles). If the answer is 3, we can only detect matter approaching horizon, but we can never say that matter have crossed the horizon and have been "eated" by BH.

The final question if the answer is 3 (or 1 BTW) is : what are the facts and measures, or mind experience, which can invalidate the "frozen star"model (Lifchits model for example) of BH, with matter infinitly approaching horizon but never crosses it in our referential ?

Thanks in advance for your answers !

 

[phinds]

The EH is not a physical thing. Matter falling into the BH is not aware of the existence of the EH. The extra gravity of the BH due to an unfailing particle is measured as increasing as soon as the infalling object is closer to the BH than the observer is because the "gravity of a BH" for the purposes of any observer is the gravity of everything inside the sphere centered on the BH and reaching out to the observer (assume for simplicity that there are no other object inside that sphere other than the BH).

 

[ShayanJ]

The EH is not a physical thing.

This is wrong. EH is surely physical. But it can't be detected locally.

 

[phinds]

This is wrong. EH is surely physical. But it can't be detected locally.

Oh? Why do you think the EH is "surely" physical, particularly if it can't be detected locally? If it can't be detected where it is, how can it be physical?

 

[ShayanJ]

Oh? Why do you think the EH is "surely" physical, particularly if it can't be detected locally? If it can't be detected where it is, how can it be physical?

"it can't be detected locally" is much different from "it can't be detected". Its true that an infalling observer doesn't notice anything strange when passing the horizon, but hey, if the horizon wasn't physical, what would be the meaning of the observer passing it?
The horizon is the surface of infinite redshift, the border of no return, and most importantly, the border after which you're doomed to be sunk in the singularity.(Don't take me wrong, that's not what I wish for you.)
Read here for more explanations!

 

[phinds]

"it can't be detected locally" is much different from "it can't be detected". Its true that an infalling observer doesn't notice anything strange when passing the horizon, but hey, if the horizon wasn't physical, what would be the meaning of the observer passing it?
The horizon is the surface of infinite redshift, the border of no return, and most importantly, the border after which you're doomed to be sunk in the singularity.(Don't take me wrong, that's not what I wish for you.)
Read here for more explanations!

The link you gave is beyond me but I don't see how "can't be detected locally" does not extrapolate to "can't be detected". There is nothing physical there. Yes, there are events that occur there because it is the surfice of infinite redshift and consequently LOOKS to be physical to a remote observer but that is an "optical illusion" exactly as is the fact that the remote observer can't see the infalling object fall in. The object doesn't care about that remote observer.

 

[Logan5]

Thanks for these first answer which tends towards answer 3 also (I think, but this is not clear). If the mind experience is correctly described, there must be an experimental answer, whatever it is.

Don't forget, if your answer tends toward 3 or alike to answer the final question :

what are the facts and measures, or mind experience, which can invalidate the "frozen star"model (Lifchits model for example) of BH, with matter infinitly approaching horizon but never crosses it in our referential ?

 

[ShayanJ]

The link you gave is beyond me but I don't see how "can't be detected locally" does not extrapolate to "can't be detected". There is nothing physical there. Yes, there are events that occur there because it is the surfice of infinite redshift and consequently LOOKS to be physical to a remote observer but that is an "optical illusion" exactly as is the fact that the remote observer can't see the infalling object fall in. The object doesn't care about that remote observer.

OK, I said I didn't wish for you to fall in the singularity but it seems I should throw you into a black hole for explaining things to you.
Let's imagine you invent a curvaturometer, a device that somehow measures the curvature of spacetime in your vicinity. I know your vicinity looks Minkowskian but let's imagine this device can do the measurement by somehow using two far enough events to detect the curvature.(I won't be surprised if someone pops in here and argues somehow that this device is impossible to build but I won't stop because I'd like to hear that argument.)
Now you and I go near a black hole with our spaceship. I give you the device and then throw you out of the spaceship(sorry, but there is a price to pay for learning). Now let's imagine you have a jetpack too. At first you desperately fire your jetpack to escape the black hole. Let's imagine you manage to get a bit far. If you look at your device, you'll see that as you get near the black hole, the curvature increases and as you get further, the curvature decreases. But then your jetpack doesn't work for a moment and you fall into the black hole. As you pass the horizon, you notice nothing strange. Suddenly your jetpack starts working. You know you're in trouble so you try to escape using the jetpack. But then you realize that it doesn't matter which way you go, the device is saying that the curvature increases in all directions. It doesn't matter which direction you go, you will hit the singularity. I think that's much different from outside the horizon.

 

[nitsuj]

"it can't be detected locally" is much different from "it can't be detected". Its true that an infalling observer doesn't notice anything strange when passing the horizon, but hey, if the horizon wasn't physical, what would be the meaning of the observer passing it?
The horizon is the surface of infinite redshift, the border of no return, and most importantly, the border after which you're doomed to be sunk in the singularity.(Don't take me wrong, that's not what I wish for you.)
Read here for more explanations!

A shadow can move ftl, it is not a physical thing, though i can go in it. Remember the joke, "what gets bigger the more you take out of it?" Well a "hole" is a region. An event horizon, like a hole are regions...same with "elsewhere" section of a light cone. Not "physical" things themselves, but simply regions.

Another, as you mentioned, is borders. Though that's just a boundary of a region, not an edge. Like the edge of a cliff.

 

[ShayanJ]

A shadow can move ftl, it is not a physical thing, though i can go in it. Remember the joke, "what gets bigger the more you take out of it?" Well a "hole" is also a region. An event horizon, like a hole are regions...same with "elsewhere" section of a light cone. Not "physical" things themselves, but simply regions.

Another, as you mentioned, is borders. Though that's just a boundary of a region, not an edge. Like the edge of a cliff.

That's not what I meant!

 

[ShayanJ]

Thanks for these first answer which tends towards answer 3 also (I think, but this is not clear). If the mind experience is correctly described, there must be an experimental answer, whatever it is.

Don't forget, if your answer tends toward 3 or alike to answer the final question :

what are the facts and measures, or mind experience, which can invalidate the "frozen star"model (Lifchits model for example) of BH, with matter infinitly approaching horizon but never crosses it in our referential ?

I don't know enough to answer the whole first post. But about this question its easy. Just calculate the proper time it takes for the infalling particle to pass the horizon. Its finite. The distant observer never sees the infalling observer pass the horizon, but for the infalling observer herself, it takes a finite time.

 

[nitsuj]

That's not what I meant!

Ah sorry, I thought it was a proper retort to...

"...if the horizon wasn't physical, what would be the meaning of the observer passing it?"

just because an EH not physical itself, doesn't mean the region of isn't physically significant, like shade on a hot day.

 

[ShayanJ]

Ah sorry, I thought it was a proper retort to...

"...if the horizon wasn't physical, what would be the meaning of the observer passing it?"

just because an EH not physical itself, doesn't mean the region of isn't physically significant, like shade on a hot day.

I meant, if the horizon wasn't physical and only an illusion/mathematical artifact or whatever, then people(physicists) wouldn't talk as such that it actually exists. It does exist but not as a balloon that can be pierced!

 

[phinds]

OK, I said I didn't wish for you to fall in the singularity but it seems I should throw you into a black hole for explaining things to you.
Let's imagine you invent a curvaturometer, a device that somehow measures the curvature of spacetime in your vicinity. I know your vicinity looks Minkowskian but let's imagine this device can do the measurement by somehow using two far enough events to detect the curvature.(I won't be surprised if someone pops in here and argues somehow that this device is impossible to build but I won't stop because I'd like to hear that argument.)
Now you and I go near a black hole with our spaceship. I give you the device and then throw you out of the spaceship(sorry, but there is a price to pay for learning). Now let's imagine you have a jetpack too. At first you desperately fire your jetpack to escape the black hole. Let's imagine you manage to get a bit far. If you look at your device, you'll see that as you get near the black hole, the curvature increases and as you get further, the curvature decreases. But then your jetpack doesn't work for a moment and you fall into the black hole. As you pass the horizon, you notice nothing strange. Suddenly your jetpack starts working. You know you're in trouble so you try to escape using the jetpack. But then you realize that it doesn't matter which way you go, the device is saying that the curvature increases in all directions. It doesn't matter which direction you go, you will hit the singularity. I think that's much different from outside the horizon.

Sorry, you're going to have to hit me on the head with a hammer and THEN throw me out the airlock. I still don't get it. Yes, there is an effect that occurs but I don't get how that makes the EH physical.

 

[Logan5]

I don't know enough to answer the whole first post. But about this question its easy. Just calculate the proper time it takes for the infalling particle to pass the horizon. Its finite. The distant observer never sees the infalling observer pass the horizon, but for the infalling observer herself, it takes a finite time.

I know that. But if "this question" is "what are the facts and measures, or mind experience, which can invalidate the "frozen star"model (Lifchits model for example) of BH, with matter infinitly approaching horizon but never crosses it in our referential ?", this is not an easy question.

Your observation seems to lead to the answer "no facts and measures, no mind experience, can invalidate etc.." so the Lifchits model (frozen star) is possible. But Lifchits model is rejected. So I don't see this question as easy.

 

[phinds]

I meant, if the horizon wasn't physical and only an illusion/mathematical artifact or whatever, then people wouldn't talk as such that it actually exists. It does exist but not as a balloon that can be pierced!

I don't agree w/ this argument at all. People talk about the "observable universe" all the time and that is bounded by a sphere that is not physical but only exists as a mathematical construct. For me, it's a spherical surface of about 49 billion light years radius and centered on my left eyeball (when I've got my right eye closed) but it does not exist physically.

 

[ShayanJ]

Sorry, you're going to have to hit me on the head with a hammer and THEN throw me out the airlock. I still don't get it. Yes, there is an effect that occurs but I don't get how that makes the EH physical.

OK, I think we have a matter of different definitions here. By physical, I mean its a property of spacetime, something really existing out there, not something that depends on our interpretations, mathematical methods, illusions or errors. Now what do you mean by physical?

 

[ShayanJ]

I know that. But if "this question" is "what are the facts and measures, or mind experience, which can invalidate the "frozen star"model (Lifchits model for example) of BH, with matter infinitly approaching horizon but never crosses it in our referential ?", this is not an easy question.

Your observation seems to lead to the answer "no facts and measures, no mind experience, can invalidate etc.." so the Lifchits model (frozen star) is possible. But Lifchits model is rejected. So I don't see this question as easy.

OK, its not easy. But I didn't support the frozen star model! I said it takes a finite proper time for anything to fall into the black hole and that confirms the fact that the star isn't frozen.

 

[phinds]

OK, I think we have a matter of different definitions here. By physical, I mean its a property of spacetime, something really existing out there, not something that depends on our interpretations, mathematical methods, illusions or errors. Now what do you mean by physical?

I mean something that has physical substance, something that is made up of fundamental particles, something that can be detected locally and remotely (at least, if you have the right equipment)

Here's a good dictionary-type definition: physical = of or relating to things perceived through the senses as opposed to the mind; tangible or concrete.

Is it your belief that physicists in general do not subscribe to that definition but use yours instead?

 

[ShayanJ]

I don't agree w/ this argument at all. People talk about the "observable universe" all the time and that is bounded by a sphere that is not physical but only exists as a mathematical construct. For me, it's a spherical surface of about 49 billion light years radius and centered on my left eyeball (when I've got my right eye closed) but it does not exist physically.

OK, by your definition of physically given below(but only the first part of it) neither the horizon nor the boundary of the observable universe are physical. But by my definition, they are physical because they are well-defined in terms of physics and don't depend on humans to survive! They are out there(if our models are correct) whether we exist or not.

I mean something that has physical substance, something that is made up of fundamental particles, something that can be detected locally and remotely (at least, if you have the right equipment)

Your definition of physical has two parts that are not equivalent:

1-something that has physical substance, something that is made up of fundamental particles.
2-something that can be detected locally and remotely.

If what I described in post #8 is a valid thought experiment, then you can use it to determine where was the horizon. But not locally. You should at first be out of the horizon then pass the horizon and find out that you did, and then remember when was the first time you noticed the change. So you did detect the horizon but nonlocally. Also you detected something not made of particles, so the above two parts of your definition aren't equivalent.

 

[phinds]

You make a good point, but I think we need a different word for what you are describing so that "physical" stays with the dictionary definition.

 

[jimgraber]

The gravitational wave signal will increase with an inverse power law as it gets closer to the center of the black hole. (It goes to infinity, or would go to infinity, at the center, not the horizon. It is still finite at the horizon.) But as it gets close to the horizon, it begins to decrease exponentially and is very soon arbitrarily close to zero, but it never reaches zero, in the classical approximation. So you get a totally negligible tail of radiation extending to future infinite time. But the peak of the radiation arrives very close to the time you would expect from your Minkowski approximation.This is basically your answer 2. The formula for T3 can be computed arbitrarily precisely, but to a very good approximation, it will be equal to the flat space answer.
Jim Graber

 

[Logan5]

OK, its not easy. But I didn't support the frozen star model! I said it takes a finite proper time for anything to fall into the black hole and that confirms the fact that the star isn't frozen.

But it is possible (even probable ?) that, at a finite proper time Tau1, while approaching the EH, the external universe ends, or the BH himself evaporates, or all observers has decayed. So for all practical purposes the BH can be a frozen star, no ?

 

[Logan5]

The gravitational wave signal will increase with an inverse power law as it gets closer to the center of the black hole. (It goes to infinity, or would go to infinity, at the center, not the horizon. It is still finite at the horizon.) But as it gets close to the horizon, it begins to decrease exponentially and is very soon arbitrarily close to zero, but it never reaches zero, in the classical approximation. So you get a totally negligible tail of radiation extending to future infinite time. But the peak of the radiation arrives very close to the time you would expect from your Minkowski approximation.This is basically your answer 2. The formula for T3 can be computed arbitrarily precisely, but to a very good approximation, it will be equal to the flat space answer.
Jim Graber

Thank you for your answer. Can you give me a source where I can see this formula and how it can be obtained ? What is typical T3 for a dozen Solar Mass BH and say 1000 LY distance ?

 

[ShayanJ]

But it is possible (even probable ?) that, at a finite proper time Tau1, while approaching the EH, the external universe ends, or the BH himself evaporates, or all observers has decayed. So for all practical purposes the BH can be a frozen star, no ?

This is different from the frozen star model!

 

[nitsuj]

It does exist but not as a balloon that can be pierced!

Perhaps that is the same use of physical that Phinds was using.

 

[Logan5]

This is different from the frozen star model!

OK. I give you this point. But the question remains intact : at the proper time when the objects crosses the horizon, has the black hole evaporated, or does the universe still exists ? OK this question is too far from the original one (from post 1), and has pitfalls I wanted to avoid. Let's stick with T3. Do you have an opinion about T3 ?

 

[ShayanJ]

OK. I give you this point. But the question remains intact : at the proper time when the objects crosses the horizon, has the black hole evaporated, or does the universe still exists ?

This isn't easy to answer. Also not a good question I think. But anyway, I don't think you can take something like frozen star model out of it!

Let's stick with T3. Do you have an opinion about T3 ?

As I and other people stated several times in this thread, there is nothing special about the horizon locally. So why should the object emit GWs when passing it?

 

[Logan5]

As I and other people stated several times in this thread, there is nothing special about the horizon locally. So why should the object emit GWs when passing it?

Because this source http://kipac.stanford.edu/kipac/black-holes-eating-stars-and-making-waves (and numerous others) seems to say so, and also Jim Graber in this thread. And because crossing EH is a major "hair" (hair are deformation of the horizon, aren't they ?) that should be shaved with a major GW emission, shouldn't it ? And because some theories (like firewall) doesnot agree and leads to the "5" family of answer to this question, which should not be too quickly dismissed ?

 

[phinds]

And because crossing EH is a major "hair" (hair are deformation of the horizon, aren't they ?) that should be shaved with a major GW emission, shouldn't it ?

That would only be true (if at all) if the EH were significant locally and has been said repeatedly in this thread, it is not.

 

[Logan5]

That would only be true (if at all) if the EH were significant locally and has been said repeatedly in this thread, it is not.

But a deformation is not locally detectable (or significant) either. A deformation is a global artefact, which extends in space and time. If we consider a single point, there is no deformation. So this is not incompatible ? GW emission is a global phenomenon not a local one.

And how to interpret all these sources which talks about GW emission when a BH "eats" matter (eat = the matter cross the horizon)

 

[ShayanJ]

Because this source http://kipac.stanford.edu/kipac/black-holes-eating-stars-and-making-waves (and numerous others) seems to say so, and also Jim Graber in this thread. And because crossing EH is a major "hair" (hair are deformation of the horizon, aren't they ?) that should be shaved with a major GW emission, shouldn't it ? And because some theories (like firewall) doesnot agree and leads to the "5" family of answer to this question, which should not be too quickly dismissed ?

Well, eating another star isn't comparable to eating just a small object. The star surely has a size and mass comparable to the black hole and so its passage from the horizon can't be called local. This is much different from what we've been talking about in this thread. There may be many things causing the gravitational waves that are different from what you think. At least I can talk about such a situation.
I should also say that the no-hair conjecture is not yet proved, let alone a hair-shaving theorem!

 

[PeterDonis]

The observer O detects the gravitational waves at his time T3. The question is : what is this time T3 ?

The short answer is (2); jimgraber's post gave the basic explanation of why.

But it is possible (even probable ?) that, at a finite proper time Tau1, while approaching the EH, the external universe ends, or the BH himself evaporates, or all observers has decayed. So for all practical purposes the BH can be a frozen star, no ?

No. We have had a lot of threads in this forum on this; it's a common misconception, but it's still a misconception.

It's important to keep distinct the time according to the distant observer, who always stays far away from the hole, and the proper time of an observer who falls into the hole. They are not the same.

If the distant observer sets up his most "natural" time coordinate (which is just the Schwarzschild time coordinate), and tries to extend it to the horizon, he finds it giving an infinite value of $t$ to any event on the horizon. But the horizon is not just one event; it contains a lot of different events, so a coordinate chart that labels them all with the same value is not valid there. This is usually described as Schwarzschild coordinates having a coordinate singularity at the horizon.

For an observer falling into the hole, however, it only takes a finite amount of his proper time to fall to the horizon. And if he sets up his most natural time coordinate, the one that matches his proper time to fall to the horizon, he finds that this coordinate chart can cover the region at and inside the horizon just fine, all the way down to the singularity at $r = 0$. And according to this time coordinate, the end of the external universe (if there even is one--according to our best current model, our universe will expand forever), or the evaporation of the black hole (if we include quantum effects--but note that for the hole to evaporate, it has to be colder than the CMBR, which even most supermassive holes are not at this point), will be very, very far in the future at the time the infalling observer crosses the horizon.

As for which coordinate is "right", they're both just coordinates, and coordinates in GR have no direct physical meaning. But there is a clear sense in which the infalling observer's coordinates give a better picture of what's happening: those coordinates label distinct events on the horizon with distinct times, and give a clear time ordering to those events, which matches the "natural" time ordering of events on the horizon. So this ordering is invariant, and it says that the evaporation of the hole is, as I said above, far to the future of the event where the infalling observer crosses the horizon.

 

[PeterDonis]

That would only be true (if at all) if the EH were significant locally and has been said repeatedly in this thread, it is not.

First of all, the implication here is not true: if matter falls into a black hole, and the infall process is not perfectly spherically symmetric, then GWs will be emitted. This has been known since the 1970s and has been confirmed by many calculations.

Second, this whole question of whether the EH is "significant locally" is a red herring, because, as Logan5 pointed out, GW emission is itself not a "local" process. To even tell that GWs are being emitted, you have to look on a distance scale comparable to the wavelength; for GWs emitted by a black hole as an object falls in, the wavelength will be on the order of the hole's Schwarzschild radius. From a global perspective, the GW emission process can just as easily be viewed as the horizon (i.e., the boundary of the region that can send light signals to infinity) changing shape from its original spherical shape, to a deformed spherical shape, to a new spherical shape with a larger area.

eating another star isn't comparable to eating just a small object.

True; the amplitude of the GWs will be much larger if the hole eats a star. But in principle they will be there even if the hole eats a small object.

 

[ShayanJ]

True; the amplitude of the GWs will be much larger if the hole eats a star. But in principle they will be there even if the hole eats a small object.

Could you explain why is there any GW at all?

 

[PeterDonis]

Could you explain why is there any GW at all?

Heuristically, it's because the infall process is not perfectly spherically symmetric, so when the infalling object passes through the horizon, the horizon gets deformed. But a stationary black hole horizon must be spherical, so the deformation will get radiated away as GWs. Kip Thorne's Black Holes and Time Warps has a good non-technical discussion. The original discovery of this was by Richard Price in 1972: see here:

http://en.wikipedia.org/wiki/Richard_H._Price

Note that Price's theorem is actually a theorem, even though the no-hair result that it helps to justify is still only a conjecture since it has not been rigorously proven.

 

[Logan5]

The short answer is (2); jimgraber's post gave the basic explanation of why.

I like this answer, but, as I asked to Jim (alas without answer), can you show me a source which gives a formula to compute a finite T3, and how this formula is found ? If your answer is true, it is very precious for me and my understanding.

Also, this answer seems contradictory with other answers in this thread, which denies the possibility to remote detect horizon crossing because "horizon has no signification locally", so no physical phenomenon can be locally emitted when the object cross locally the horizon. Can your position and these positions be reconciliated or are they incompatible ?

 

[Logan5]

No. We have had a lot of threads in this forum on this; it's a common misconception, but it's still a misconception.

I agree, I know that, and it is the reason why I formulated the problem in post 1 (or tried to) in a way which avoids this kind of formulation and time comparison in 2 different referentials. Anyway your summary is very clear and push again in my mind these important concepts.

 

[PeterDonis]

can you show me a source which gives a formula to compute a finite T3

Roughly, it will be $R^{3/2} + R$, where $R$ is the distance of the observer from the hole. I don't have a handy online reference, unfortunately.

 

[PeterDonis]

this answer seems contradictory with other answers in this thread, which denies the possibility to remote detect horizon crossing because "horizon has no signification locally", so no physical phenomenon can be locally emitted when the object cross locally the horizon.

As I noted in a previous post, GW emission is not a "local" phenomenon; you can't pick a particular point on the horizon and say GWs are being emitted from that point. The wavelength of the GWs will be comparable to the Schwarzschild radius of the hole, so the GW emission is really a phenomenon that involves the entire horizon. An observer falling in with the object that adds mass to the hole won't be able to tell that GWs are being emitted as it crosses the horizon. That is only observable on a larger scale.

 

[Logan5]

As I noted in a previous post, GW emission is not a "local" phenomenon; you can't pick a particular point on the horizon and say GWs are being emitted from that point. The wavelength of the GWs will be comparable to the Schwarzschild radius of the hole, so the GW emission is really a phenomenon that involves the entire horizon. An observer falling in with the object that adds mass to the hole won't be able to tell that GWs are being emitted as it crosses the horizon. That is only observable on a larger scale.

I agree. It was the observation I made in post #31.

 

[Logan5]

Roughly, it will be $R^{3/2} + R$, where $R$ is the distance of the observer from the hole. I don't have a handy online reference, unfortunately.

Very unfortunate, indeed ! I have a quest for this formula for years now, but I have not been able to find it, or even to find the theoretical background to justify it. There is something strange here. I will worship your name for ever if you can give me a link or a book title where I can find such things. I am serious

 

[jimgraber]

Logan5, I will try to reply more soon, but it may take a few days. In the meantime, take a look at figure 2 on page 6 of this reference to get a good idea of what I am talking about:

http://arxiv.org/pdf/1106.1021v2.pdfInspiral-merger-ringdown multipolar waveforms of nonspinning black-hole binaries using the effective-one-body formalism
Authors:Yi Pan, Alessandra Buonanno, Michael Boyle, Luisa T. Buchman, Lawrence E. Kidder, Harald P. Pfeiffer, Mark A. Scheelhttp://arxiv.org/abs/1106.1021

best,
a very busy Jim Graber

 

[Logan5]

Logan5, I will try to reply more soon, but it may take a few days. In the meantime, take a look at figure 2 on page 6 of this reference to get a good idea of what I am talking about:

http://arxiv.org/pdf/1106.1021v2.pdfInspiral-merger-ringdown multipolar waveforms of nonspinning black-hole binaries using the effective-one-body formalism
Authors:Yi Pan, Alessandra Buonanno, Michael Boyle, Luisa T. Buchman, Lawrence E. Kidder, Harald P. Pfeiffer, Mark A. Scheelhttp://arxiv.org/abs/1106.1021

best,
a very busy Jim Graber

Thank you very much. I now understand better what you, and probably Peter, meant.

As far as I can understand this document, and your answer in post #22, these elements gives me this information (which is new for me) : GW peak signal does NOT witness horizon crossing, but horizon approaching. BTW, you said in post #22 : "But as it gets close to the horizon, it begins to decrease exponentially and is very soon arbitrarily close to zero, but it never reaches zero"

So my thought experiment is not very good for what I intended. I wanted a remote signal for horizon crossing. But I had no much hope, because I awaited the answer to be 3. and your answer actually implies 3. (or even 4.) not 2. Indeed a peak GW signal reaches the observer at a finite time T3, but this peak signal is not for horizon crossing and the question was all about that.

The conclusion I draw (for now) from this discussion (and other discussions elsewhere also) is that no actual experience, no signal, no thought experiment, can falsify the "frozen star" model. I don't know if this model is true or not, but I understand it, and I don't understand the model where a BH "eats" matter, which cross the horizon within the time the universe or BH lives. And the Newton shell theorem assure that we confound, for all practical and experimental, or even theoretical purposes, a matter shell (which is a BH in the frozen star model) with a singularity. I am eager to hear about any actual or thought experiment which can falsify this model.

If I am not abusing, I have another question to surround the problem. I place the observer, now, on the falling object. Let this observer look behind the fixed clock. Which is the last Minkowski time the observer on the falling object can see on the remote clock, before the signal becomes too weak and before it crosses the horizon ? This gives a minimal bound for T3 (alas not a maximal bound), and I wonder if this time (let name it T'3 < T3) is large or not, and i wonder also how it compares with the peak GW signal time.

 

[PeterDonis]

GW peak signal does NOT witness horizon crossing, but horizon approaching.

This is not really correct. Yes, the peak signal is effectively emitted from the infalling object before it crosses the horizon; but if the infalling object did not cross the horizon, but instead remained above it (suppose, for example, that there was a large rocket attached to it that fired just before it reached the horizon, and kept it "hovering" there), you would see a different pattern of GWs; also, other observations would be different as well (for example, the light from the object would stop redshifting at some finite wavelength, instead of continuing to redshift to arbitrarily long wavelengths). So, while the GWs and other observations do not directly show you the object crossing the horizon, they are certainly evidence of the object crossing the horizon, since all those observations would be different if the object did not cross the horizon.

The conclusion I draw (for now) from this discussion (and other discussions elsewhere also) is that no actual experience, no signal, no thought experiment, can falsify the "frozen star" model.

This is not correct. The "frozen star" model leads to different observations than the black hole model does. See above.

I don't know if this model is true or not, but I understand it, and I don't understand the model where a BH "eats" matter

Picking a model you can understand over a model you can't is only a viable strategy if both models make the same predictions. That is not the case here. See above.

And the Newton shell theorem assure that we confound, for all practical and experimental, or even theoretical purposes, a matter shell (which is a BH in the frozen star model) with a singularity

I don't understand what you mean by this. The shell theorem says that a spherically symmetric matter distribution outside some region of interest does not cause any spacetime curvature (gravity) inside that region. It says nothing about how gravitational collapse looks to someone outside the collapsing region.

There is a theorem called Birkhoff's theorem that says that any vacuum, spherically symmetric region of spacetime must have the Schwarzschild geometry. But that theorem only applies in the case of exact spherical symmetry; we are talking about an asymmetric case, where an object falls into a black hole along one particular radial trajectory.

 

[PeterDonis]

I place the observer, now, on the falling object. Let this observer look behind the fixed clock. Which is the last Minkowski time the observer on the falling object can see on the remote clock, before the signal becomes too weak and before it crosses the horizon ?

The signal seen by the infalling observer, coming from the fixed clock, does not get infinitely weak at the horizon; it is only redshifted by a factor of about 2 (the exact factor depends on the details of the infall). The time seen by the infalling observer on the fixed clock as he crosses the horizon will be roughly the time on his own clock at that instant minus $R$, i.e., minus the radial coordinate of the fixed clock. (Note that I am using units where $c = 1$.)

 

[Logan5]

This is not really correct. Yes, the peak signal is effectively emitted from the infalling object before it crosses the horizon; but if the infalling object did not cross the horizon, but instead remained above it (suppose, for example, that there was a large rocket attached to it that fired just before it reached the horizon, and kept it "hovering" there), you would see a different pattern of GWs; also, other observations would be different as well (for example, the light from the object would stop redshifting at some finite wavelength, instead of continuing to redshift to arbitrarily long wavelengths).

We have a misunderstanding here. The object which fall does not "hover" : it follow a geodesic of course (free fall). If the object was hovering, or does not follow a geodesic, I agree the GW signal should be a different pattern. But this is not the case. In the "frozen star" model, objects who follow a geodesic asymptotically approches the horizon, never stop or hover, and only cross the horizon at Minkowski time = infinity (as given by well known equations or coordinates).

So, while the GWs and other observations do not directly show you the object crossing the horizon, they are certainly evidence of the object crossing the horizon, since all those observations would be different if the object did not cross the horizon.

Nevertheless, this remark can be correct even if I still don't see clearly what are these evidences. If this remark is correct, do you agree that the thought experiment in post #1 can be modified to measure these "evidences" and determine a finite T3, as soon as the signal is significant of a "crossing horizon" event ?

 

[PeterDonis]

The object which fall does not "hover" : it follow a geodesic of course (free fall).

This is correct. But if the object falls into the hole, through the horizon, it is not "frozen" near the horizon. Similarly, if the hole is formed by collapsing matter, it is not a "frozen star"; the collapsing matter is not "frozen". It collapses all the way to form a singularity at $r = 0$.

In the "frozen star" model, objects who follow a geodesic asymptotically approches the horizon, never stop or hover, and only cross the horizon at Minkowski time = infinity (as given by well known equations or coordinates).

If this is what you mean by the "frozen star" model, then it is not a different model from the black hole model; it is just an incomplete version of the black hole model. It only covers the region outside the horizon. This model does not say the horizon is not there, or that nothing can fall through it. It only says that it cannot describe such events.

What you are missing here is that the "Minkowski time" of an event is just a number; it has no physical significance in itself. The proper time elapsed on the distant observer's clock between two events on his worldline has physical significance; but there is no invariant way of saying which event on that distant observer's worldline happens "at the same time" as some event near, or at, or inside the horizon of the black hole. Your "Minkowski time" is simply one convention for saying which events happen "at the same time"; but it is only a convention. And since it assigns the value "infinity" to events on the horizon, it is a convention that simply does not work there. There is no physical meaning to that "infinity" value. The way to fix it is to adopt a different convention that does not have that problem.

Your question about what time T3, by the distant observer's clock, he will observe GWs from an object falling into the hole does have physical meaning; but note that it is a question about events on that observer's worldline. If I tell you a finite value for T3, that does not tell you, in itself, "what time" the object crossed the horizon, according to the distant observer's clock; answering that question still requires adopting a convention, even if you know T3. Even with a finite T3, you could still adopt the convention that assigns the value "infinity" as the "Minkowski time" of events on the horizon, such as the object crossing it. You might not want to, because it seems unreasonable to you; but "unreasonable" is not the same as "mathematically impossible".

If this remark is correct, do you agree that the thought experiment in post #1 can be modified to measure these "evidences" and determine a finite T3, as soon as the signal is significant of a "crossing horizon" event ?

The answer for the finite T3 that jimgraber gave you already does that. The GW pattern he describes is the "evidence" that the object fell through the horizon. If it hadn't, a different GW pattern would have been observed.

 

[Logan5]

The signal seen by the infalling observer, coming from the fixed clock, does not get infinitely weak at the horizon; it is only redshifted by a factor of about 2 (the exact factor depends on the details of the infall). The time seen by the infalling observer on the fixed clock as he crosses the horizon will be roughly the time on his own clock at that instant minus $R$, i.e., minus the radial coordinate of the fixed clock. (Note that I am using units where $c = 1$.)

I never read somebody who stated that as clearly as that (thank you !). And your statement made me reconsider this kruskal szekeres diagram of a fall : http://www.google.fr/imgres?imgurl=http%3A%2F%2Fi.stack.imgur.com%2FYA5TE.png&imgrefurl=http%3A%2F%2Fphysics.stackexchange.com%2Fquestions%2F111930%2Fschwarzschild-metric-coordinate-sign-change-in-0-leq-r-leq-2gm&h=898&w=658&tbnid=lAyY3AjZjbaIvM%3A&zoom=1&docid=H-7OyVASRlrGbM&ei=mLpLVY31EeejyAOzooDoDg&tbm=isch&iact=rc&uact=3&dur=251&page=1&start=0&ndsp=1&ved=0CCEQrQMwAA

In a KS diagram, photons conveniently follows a constant 45° path (as in Minkowski diagram), and photon path can be reversed. Indeed, if we follow the past photon cone at tau=33.7M (horizon crossing) until the R=3.5M line (say the distant clock is at this distance), this intersects a "t" (minkowski time) line very near of the "t" line where the object was when it was at 3.5M distance. You should be right and you made me realize this. Thank you again.

Well, this fact gives us nothing about the problem, but is worth to be known.

 

[Logan5]

If I tell you a finite value for T3, that does not tell you, in itself, "what time" the object crossed the horizon, according to the distant observer's clock; answering that question still requires adopting a convention, even if you know T3.

This is the very crux of the problem. In fact, I am not interested by a Minkowski time at which I can tell "the object IS in the BH". And I know (and understand) simultaneity is conventional even in simple SR cases, and even more in extreme GR cases ! I am interested by an evidence which can invalidate frozen star model, and you are near to convince me. I am digesting your other statements I carefully read.

I can't help myself to think, if we have a signal significant of an horizon crossing, then this event is the past of this measure (whatever moment in the past, but in the past), but I think you'll tell me we cannot conclude this. There is still an hard difficulty here.