The Paradoxical Nature of Black Holes

[Slinkey]

Over the years I have read a lot about Black Holes (BH) and the associated Event Horizon (EH). Two statements about black holes strike me as worringly in contention with each other and they lead to a conclusion that seems to make the traditional BH a mockery. Here we go.....

 

According to accounts I have read by various notables (such as Stephen Hawking and Kip Thorne) these two statements stand out:

 

Statement 1. An outside observer watching an object fall into a BH will never see it cross the EH. The explanantion is that the light from the object will become redshifted the closer it gets to the EH and we will simply not get any visible light back from it.

 

That's fair enough, but let's ignore this for a moment (and tidal forces and spaghettification). What would we see if we could see it approach the EH?

 

Let's pretend it is a clock.

 

As we watch the clock approach the EH the time on the clock would slow down. The closer the clock moves to the EH the slower it would appear to "tick" until it would appear to stop entirely. It won't have actually stopped as it will still be moving towards the EH but it would appear to stick on the EH and no one would see it cross the EH.

 

Statement 2. According to Stephen Hawking a BH will not exist forever. Mr Hawking has invoked a process now dubbed "Hawking Radiation" that allows a BH to evaporate.

 

It would take an extraordinarily long time for a BH to evaporate but according to Hawking the temperature of a BH is inversely proportional to it's mass. Simply put the more massive the BH the slower it evaporates. However, during evaporation it would lose mass and slowly heat up until presumably it would explode in a flash of gamma radiation.

 

Conclusion???

If we can't see something cross the EH of a BH, and a BH does not exist forever, then if we could watch long enough the BH would evaporate before an object will be seen to cross the EH.

 

It would appear that nothing, despite a BH having massive gravitational attraction at its EH, can enter a BH or even cross the EH.

 

Therefore BHs can only evaporate and never gain mass.

 

Is this correct?

[Klaynos]

Let's consider statement one. Which is purely about red shifting...

 

Now near the edges of of eyes range the efficiency of the eye drops off. So as something with the same luminosity changes frequency towards being out of our visual range, we see it fade, and if there is nothing else illuminating it, it will fade and disappear, so surely this is what a human observer would see? But you must remember that just because it is not perceivable by one measurement device (the eye) then it doesn't mean it doesn't exist.

[iNow]

Kip's first scenario about the person never crossing the EH relative to an outside observer was meant only to describe infinite redshift. I believe he also referred to the fact that russians used to call BHs "frozen stars" for this very reason.

 

It was not, however, a scenario intended to be 100% reprsentative of actual BHs. It was a tool to explain the infinite redshift. Perhaps your concern would evaporate had Kip started his comments with, "If a blackhole existed forever, and never evaoporated, THEN a traveller would never appear to cross the EH relative to an outside observer due to infinite redshift..."

 

 

 

Last... just because we on the outside of a BH cannot see anything pass the EH does NOT mean that nothing ever crosses the EH and enters the BH (as you reasoned toward the end of your post)... It's just that we struggle to observe things which are infinitely redshifted.

[CPL.Luke]

the object never crosses the black hole to a stationary outside observer. this is a consequence of your particular reference frame, this does not require redshift in order to explain it, just the geometry of spactime. If the observer is falling into the blackhole, then nothing wierd would happen, you would see the other object fall to the center, and shortly thereafter you would fall to the center.

[Slinkey]

Let's consider statement one. Which is purely about red shifting...

 

Now near the edges of of eyes range the efficiency of the eye drops off. So as something with the same luminosity changes frequency towards being out of our visual range, we see it fade, and if there is nothing else illuminating it, it will fade and disappear, so surely this is what a human observer would see?

 

Indeed. That is the accepted version of events. Any signal from the object would be redshifted to infinity at the EH.

 

But you must remember that just because it is not perceivable by one measurement device (the eye) then it doesn't mean it doesn't exist.

 

Exactly my point, which is why I want to discuss what is happening to the object whilst ingoring the effects of gravitational redshifting, tidal forces, and spaghettification. I want to ascertain whether the object would appear to be frozen on the EH if we could see it.

 

Kip's first scenario about the person never crossing the EH relative to an outside observer was meant only to describe infinite redshift. I believe he also referred to the fact that russians used to call BHs "frozen stars" for this very reason.

 

Frozen in the sense that if you could see something as it approached the EH then it would appear to slow down?

 

It was not, however, a scenario intended to be 100% reprsentative of actual BHs. It was a tool to explain the infinite redshift. Perhaps your concern would evaporate had Kip started his comments with, "If a blackhole existed forever, and never evaoporated, THEN a traveller would never appear to cross the EH relative to an outside observer due to infinite redshift..."

 

My concern is a bit deeper than that. Consider: if an object cannot be seen to cross the EH due to the time dilation present at that point in spacetime (again ignoring redshift, tidal forces and spaghettification), and if we could observe events for the required time, then the BH would evaporate before the object crosses the EH and we would observe it emerge from where the BH once was.

 

 

Last... just because we on the outside of a BH cannot see anything pass the EH does NOT mean that nothing ever crosses the EH and enters the BH (as you reasoned toward the end of your post)... It's just that we struggle to observe things which are infinitely redshifted.

 

Indeed. However, if we could observe events we would see the BH evaporate before any object crosses the EH. No?

 

the object never crosses the black hole to a stationary outside observer. this is a consequence of your particular reference frame, this does not require redshift in order to explain it, just the geometry of spactime.

 

So, from a staionary observers point of view nothing can cross the EH. Then from a stationary observers POV and if they could watch for long enough, the BH would evaporate before any object can cross the EH?

 

If the observer is falling into the blackhole, then nothing wierd would happen, you would see the other object fall to the center, and shortly thereafter you would fall to the center.

 

Now that's interesting. Why would the situation be different if the observer is moving relative to the BH?

[CPL.Luke]

unfortunately I am not sure how black hole evaporation figures into it, my guess would be that the geometry is no longer purely schwarschild or thats something we need quantum gravity to deal with.

 

fortunately its hard to find stationary observers with respect to black holes.

 

the difference between the free falling observer and the stationary observer is that one of them is being accelerated (to fight the black hole) accelerated observers always have horizons and in this case they correspond to the event horizon of the black hole.

[thedarkshade]

Oh, the thread I was looking for!

 

Lately I had a discussion with someone related to black holes.

He says that black holes have size zero. But I have seen the term "radius" many many times when reading about black holes.

 

Now how can you measure the radius of something that has size zero?

Or do black holes have zero size after all?

[timo]

Lately I had a discussion with someone related to black holes.

He says that black holes have size zero. But I have seen the term "radius" many many times when reading about black holes.

 

Now how can you measure the radius of something that has size zero?

Or do black holes have zero size after all?

The zero refers to the extension of the mass-distribution in coordinate space and probably (not exactly sure about this) the measure of the volume occupied by the mass. The non-zero Schwarzschild radius belongs to a standard coordiante system (Schwarzschild coordinates) and defines a spherical shell at which this coordinate system breaks down. The non-zero Schwarzschild-radius is a description of the gravitational field generated by a mass, not a description of its spacial extent (e.g., the SR of the sun is ~3 km, that certainly is not the size of the sun - sidenote: In the case of the sun, the simple Schwarzschild solution fails at the edge of the mass-distribution, already).

[thedarkshade]

OK, thanks Atheist, your post is absolutely great and it matches with what I have recently read.

 

But what I need is a yes/no answer. Does a black holes have size zero?

[Slinkey]

unfortunately I am not sure how black hole evaporation figures into it, my guess would be that the geometry is no longer purely schwarschild or thats something we need quantum gravity to deal with.

 

My hunch (unscientific as that is) is that the BHs we find in GR will "evaporate" once we have a working GR-QM theory. My hunch is that we will find something entirely different at the center of galaxies, and thus far we conclude they are BH due to the lack of QM involved in calculations. A geometrical dead-end if you will.

 

fortunately its hard to find stationary observers with respect to black holes.

 

Indeed. But something that cannot be ignored in principle even if it cannot truly happen in practice.

 

the difference between the free falling observer and the stationary observer is that one of them is being accelerated (to fight the black hole) accelerated observers always have horizons and in this case they correspond to the event horizon of the black hole.

 

Which is entirely at odds with what the stationary observer would see. This is getting a bit like Schrodingers Cat!

 

Let me explain: if the stationary observer would not see anything cross the EH and BHs evaporate then if we could observe for long enough the BH would evaporate and the object would not enter the BH.

 

Yet, if I am in a ship following an object towards a BH then we will both cross the EH and be crushed out of existence at the singularity (long before that if we include tidal forces and spaghettification).

 

So, similar to Schordingers Cat, we would be both alive and dead depending on who is doing the observing.

 

This cannot be right in my estimation. Something does not ring true to me.

 

Thus far it seems like the scientific community has settled on an agreement whereby we assume something will enter a BH. Hawking radiation added something new into the mix which has thrown up a lot of questions in my mind (hence this thread) and rather seems to thrown up a "hole" in BH theory.

 

I think the most important factor here is gravitational time dilation. Whether we are moving or not relative to a BH both parties would agree that time dilation would be infinite at the EH. Even if I am accelerating towards a BH (either by gravity alone or with my rocket boosters on) I will still be able to take measurements and deduce a location for the EH (a point in space where the escape velocity is equal to c and of infinite time dilation).

 

Would both parties get the same results from their measurements and therefore deduce the same location for the EH?

 

Considering your "free falling" example above where we follow an object towards a BH. We are again in our spaceship hovering at a distance from a BH at a point where the pull on our ship is equal to 1g. We have a clock attached to the underside of our ship. We release the locking clamps and the clock starts falling towards the BH. One second later we cut our rocket boosters and start falling towards the BH as well.

 

Let's round off 1g to 10m/s. After 1sec the clock is moving at 10m/s relative to our startpoint. After 2sec the clock is moving at 20m/s and we are moving at 10m/s and so on. The clock is accelerating away from us. As it hurtles towards the EH we would notice the clock slowing down. Somewhere near the EH it would slow to a virtual stop, yet we are still behind it! This would not be due to our movement but to the difference in gravitation each of us are experiencing. Our relative positions would be spaghettified!

 

As we haven't seen the clock cross the EH (it's basically a stopped clock from our perspective) how can we cross the EH ourselves?

 

Please feel free to point out any errors in my reasoning here as that is the purpose of this thread. I don't think that me, a layman with little mathematical training, can come to this conclusion without missing something and I want someone to give me a reality check! This thing has been bugging me for about 3 years and thus far I haven't found anyone who can explain this to me.

 

....But what I need is a yes/no answer. Does a black holes have size zero?

 

As far as I remember the singularity is a "point". Similar to the focus of a circle. You know where the center of a circle is but it has no size.

[thedarkshade]

Great Slinkey, thanks! After reading that, something real strong came to my mind! That guy is dead:cool:!

 

Cheers,

Shade

[CPL.Luke]

we'll watch the clock fall to the center alright, because we are also falling and as such we don't see an event horizon, although we can figure out the schwarschild radius.

 

its not so much a schrodingers cat phenomenon, as while a stationary observer on the outside of the black hole will never see you cross the EH he will agree on the time it took you personally to fall into the center. GR provides the set of transformations such that we can not only predict how your going to move in one frame of reference, but how your going to move in all frames of reference

[foodchain]

Well according to the laws of our known universe could everything pulled into a blackhole exist as matter or energy as we know it? I mean if everything that made up Jupiter fell into a blackhole it would eventually become or enter the singularity. So my guess means that something very weird has to happen there, or spacetime as understood such as representing the fabric of space is lacking something. Is a black hole hot or cold? I never understood how that works in regards to thermodynamics or if such a term is even applicable to them. As far as any quantum thought on the issue, I would have no idea what a quantum world would look like if the environment was a blackhole, I mean could you even have momentum in a singularity?

[iNow]

Try to remember, foodchain...

 

A singularity is a point of infinite density.

It's a point where our currently available math breaks (mostly, AFAIK, b/c of the infinities involved).

 

That is all.

 

Once we find a mathematical system which describes it, many of your (and my) confusions will ameliorate.

 

 

It's not some mythical four leaf clover, nor some unknown with unknowable godly attributes. It's just a place we don't YET understand... that we can't YET fully describe or model.

 

That is all.

 

Cheers, mate.

[Slinkey]

we'll watch the clock fall to the center alright, because we are also falling and as such we don't see an event horizon, although we can figure out the schwarschild radius.

 

My understanding of the S.Rad. is that it is a volume within which there is enough mass to create a BH. Surely if we can figure out the S.Rad. we can deduce the location of the EH and where it would be relative to us as we fall towards the BH?

 

its not so much a schrodingers cat phenomenon, as while a stationary observer on the outside of the black hole will never see you cross the EH he will agree on the time it took you personally to fall into the center.

 

Rather, we could do the math first and then I fly towards the BH and the time it takes me to reach the center is as we calculated. However, as you hint below, even though we can calculate it only one of us could ever find out if it is correct and never be able to divulge that information to anyone outside the EH. The stationary observer would only have a set of equations and no experimental evidence to support it. He would not see me pass the EH although he could reliably predict what he would see as I approach the EH.

 

GR provides the set of transformations such that we can not only predict how your going to move in one frame of reference, but how your going to move in all frames of reference

 

The problem is however that GR leads to a point of infinite density which is not only mathematically intractable within GR but non-sensical. I can accept that QM can be far from common-sensical, but GR is a classical theory. It should, as you state above, be able to make sense in any reference frame, yet the very equations of GR lead to a point that does not make sense within GR.

 

Not only this but combined with Hawking Radiation, a QM theory, we get the possibility of dual and contradictory outcomes depending on who is doing the observing.

 

I'm not saying your conclusions are wrong, but from my perspective there is a giant hole here in science (no pun intended) and our only tool to try and fill this hole, QM, leads to absurdities.

 

The absurdities being that from one reference frame an observation could be made of someone falling towards a BH only to emerge alive as the BH has evaporated billions of years in the future of the RF of the observer. Yet, from the perspective of the person falling into the BH he would be crushed into an infinite point and die.

 

For myself, I currently have more faith in QM than I do in relativistic black holes.

[CPL.Luke]

as I haven't done any work on black holes where we had to take into account hawking radiation I honestly can't answer those questions (although someone may have found the answer already)

 

it seems that you don't really understand what an event horizon is, its a border in space time which you will never see events occurring beyond. for instanc if I look at the space of an accelerated observer, and an inertial observer, and compare them then I will see that there are some events that the stationary observer doesn't see and will never see. feven if he lived an infinite amount of time.

 

now if you look at a black hole the stationary observer will watch the object fall very close to the black hole, but never into it. but the observer who falls into the black hole will see himself cross the schwarschild radius (the radius of the EH) (and there are a number of ways he can deduce that he's crossed this point) and then fall into the center of the black hole.

 

 

Now we are dealing with special observers here as they are actually capable of falling into a black hole (any actual observer would be destroyed), and while the observer who fell in would not be able to ever send a message out to the ones on the outside, the others could fall in after them and find out the results of the experiment.

 

it is interesting that its possible for us on the outside of the black hole to never know what the results of the experiments were, but I think a lack of a result in this case would be evidence for the correctness of our description.

[Slinkey]

Hi CPL.Luke

 

How do you out proper math symbols in the forums?!

 

as I haven't done any work on black holes where we had to take into account hawking radiation I honestly can't answer those questions (although someone may have found the answer already)

 

Fair enough. I've not found anything myself except pages that tell you what it is rather than how it would apply in the circumstances I have described.

 

it seems that you don't really understand what an event horizon is, its a border in space time which you will never see events occurring beyond.

 

Hence the name event horizon. I understand what it is, yes. It is also a point in space where time dilation is infinite. If it were not then it would not be an event horizon because we would be able, in principle, to detect temporal information.

 

for instanc if I look at the space of an accelerated observer, and an inertial observer, and compare them then I will see that there are some events that the stationary observer doesn't see and will never see. feven if he lived an infinite amount of time.

 

Indeed. Exactly the point I am trying to get across. They will never see anyone cross the EH yet the BH will evaporate given enough time....

 

now if you look at a black hole the stationary observer will watch the object fall very close to the black hole, but never into it. but the observer who falls into the black hole will see himself cross the schwarschild radius (the radius of the EH) (and there are a number of ways he can deduce that he's crossed this point) and then fall into the center of the black hole.

 

I submit that this cannot happen whilst there is a perspective from which a viewer cannot see anything cross the EH of an evaporating BH. These two histories are simply incompatible. It is a vastly different situation to someone sitting on a platform and watching a light being turned on in glass carriaged train moving past us at 0.8c.

 

it is interesting that its possible for us on the outside of the black hole to never know what the results of the experiments were, but I think a lack of a result in this case would be evidence for the correctness of our description.

 

Ah, but us observers outside the EH do get a result. The result is we never see anything cross the EH.

 

The crux of the issue for me is the ingredient of time. No one knows what it is. Thus we have no theory of time to put into our calculations. Although relativity tells us what happens at sub-luminal speeds and outside singularities it tells us nothing about time except that our theories cannot deal with it at c or BHs.

 

I'm more au fait with SR (I can do and understand some of the math!) than GR so my example is from SR here but it should have a counterpart example in GR.

 

d = sqrt(1 - v^2 / c^2)

 

I once stated in a forum that if v = c then d = 0 therefore time would be at a standstill. I was told in response that this is an assumption, and of course it is. When v=c we simply have no more information about time.

 

The corrollary in GR is that anything beyond the Event Horizon is also an assumption. We can map out an increasing gravitational field but we cannot explain what happens in the temporal direction once the field is strong enough to reduce time to zero for any observer except our hero who is falling towards the EH.

[Klaynos]

[ math ] Cos\theta = \frac {a} {b} [ /math ]

[math] Cos\theta = \frac {a} {b} [/math]

 

If you remove the spaces you will get what I wrote.... if you click on any of the formula in a post you will see what LaTeX code they used.

 

 

It should be remembered when talking about blackholes that we're useing incomplete physics to describe them....

[CPL.Luke]

your question is an interesting one and I forwarded it to my GR prof, however if we aren't looking at an evaporating black hole than we can still use classical GR to predict what happens on the inside of the schwarschild radius for instance the fact that nothing could leave once inside it (the time and radial co-ordinate switch) but there are flaws, I personally don't know exactly where these flaws become critically important (does anyone?).

[JHAQ]

If any object hits the event horizon of a black hole , on a relativisyic basis its mass becomes infinite ( at c ) hence the energy release becomes infinite . Infinity is infinity so how come the universe is stll here ?

[foodchain]

your question is an interesting one and I forwarded it to my GR prof, however if we aren't looking at an evaporating black hole than we can still use classical GR to predict what happens on the inside of the schwarschild radius for instance the fact that nothing could leave once inside it (the time and radial co-ordinate switch) but there are flaws, I personally don't know exactly where these flaws become critically important (does anyone?).

 

If you are in the position to have questions answered by a professor the one I always tried to find answered when I could was basically this. During the collapse of say a massive red giant during some super nova, at what point in that does a BH form, I mean does it form at some crucial point of the nova as some reaction to it? When does it actually form? I mean I think it would be kind of weird if the BH formed before the nova, is there any chance of that?

[Martin]

If you are in the position to have questions answered by a professor the one I always tried to find answered when I could was basically this. During the collapse of say a massive red giant during some super nova, at what point in that does a BH form, I mean does it form at some crucial point of the nova as some reaction to it? When does it actually form? I mean I think it would be kind of weird if the BH formed before the nova, is there any chance of that?

 

I'll tell you what I think and you or Luke can tell me if it's right, when you find out from the professor.

there are a several Supernova scenarios, different types, but one of the most common is the collapse of a massive star at the end of its life, to form a

NEUTRON star. this is more common than where a black hole is formed.

but in some cases it can LEAD to a BH.

 

if you want to understand the timing, you have to picture the collapse of the iron core which forms the NEUTRON star and also blows much of rest of the giant star away in Supernova explosion.

 

this collapse of the dead iron core to form neutron matter can blow everything else away cleanly, in some cases, or, in other cases, the shockwave can stagnate as it travels outwards and do an incomplete job

 

if the SN explosion doesnt blow enough matter away, the leftover remnant is too massive to be stable as a neutron star----it presumably consists of a neutron-matter core overlain by a lot of garbage. THEN it can collapse to form a BH.

 

I have heard of all this stuff happening according to different timetables. Sometimes the initial star is so massive it can have SEVERAL supernova explosions---I read this recently: it was by reliable people although it goes against what I always thought till now. Anyway there are exceptions to whatever general rule.

 

but this is at least one scenario and one i think is fairly common: a one-time supernova results in a neutron star covered by a layer of crud and the whole thing is more massive than usual and forms a BH at the center and subsides into it.

[CPL.Luke]

I gotan email back from my professor

 

*EXCELLENT* question!

 

This is one of the main problem of black hole Physics. It is a bit long to tell by email, but things are even more complicated than you thought.

The point is that black hole evaporation emerges because an observer at a constant distance (even at infinity) is accelerated wrt the BH. If he was not, he would fall into the BH. Now the observation of a thermal spectrum of particles is not a property of the Schwarzschild metric only, but of any metric that has horizons as a consequence of the existence of a set of accelerated observers.E.g., if I put a quantum field on Rindler space, I will see also in this case a thermal spectrum.

 

Bottom line: the fact that the observer outside the BH sees radiation is due to the fact that he is accelerated. An observer freely falling into the BH will see NO radiation!

 

So the situation is even worse. One observer sees evaporation, the other does not! The word invoked in this case is "complementarity". And it concerns the problem of information.

 

The point is roughly speaking that if I sit outside of a classical black hole and I throw a TV set into it, the information about the TV set is lost forever (the classical BH is eternal). Now if I put quantum mechanics into the game the BH evaporates and I can recover information about the TV set by looking at the Hawking radiation (btw this is all matter of (religious) belief, there are no clear calculations showing this). If I throw myself into the BH I will meet the TV set itself, and no need of Hawking radiation to recover the info related to it...

 

Well, I am sure I am not clear (and hoestly this stuff is not clear to me either). Maybe you might want to give a look at

 

Black Holes and the Information Paradox, by Leonard Susskind, Scientific American, April 1997.

 

(I did not read it, but, knowing the author, I think there is good material there).

 

So the problem is unresolved

[Slinkey]

I gotan email back from my professor

 

This bit caught my eye....

 

Bottom line: the fact that the observer outside the BH sees radiation is due to the fact that he is accelerated. An observer freely falling into the BH will see NO radiation!

 

You would've thought that someone falling towards the BH would see more radiation rather than less, or at least, see the radiation coming from the EH as blueshifted, but no. What we see is a BH suddenly frozen by our movement towards it.

 

This can only be as a consequence of the infinite time dilation at the EH im my humble opinion.

 

So the problem is unresolved

 

Indeed. It is both re-assuring to me that I have noticed this problem and it is a known problem within physics, but disturbing that there is such a problem with regard to BHs and that they are widely accepted as existing in reality.

 

I truly belive that BHs will be eradicated once we have a coherent QM/GR theory. I will stick my neck out now and predict that spacetime will become quantized and new rules will be formulated to comprehend incredible densities and their intense gravitational fields.

[Mr Skeptic]

I truly belive that BHs will be eradicated once we have a coherent QM/GR theory. I will stick my neck out now and predict that spacetime will become quantized and new rules will be formulated to comprehend incredible densities and their intense gravitational fields.

 

Well, most people at least expect the singularity inside the black hole to be eliminated.