Hollow spherical blackhole thought experiment

[Instine]

I have a thought experiment for anyone interested. All replies welcome:


Imagine if you will, a large spherical body e.g. a moon, about the surface of which are placed many large thermonuclear devices. Deep inside the moon sits an intrepid/foolish experimental physicist. When the the devices are triggered, the surface of the moon is crushed so quickly and uniformly and with such force as to create a spherical black hole. However the critical density is reach first, only by the 'crust' of the moon. meaning the fool/heroic physicist is, for an instance at least, completely surrounded by black hole.

It is my belief that this puts him beyond our universe. And we, beyond his. My first question is, if the black hole then 'evaporated', where/when would our fool/hero and his/her moon's interior reappear, if at all?

Although this is all highly improbable to the point of absurdity, its worth noting, that in theory the fool/hero would not be crushed by the gravitational field of the spherical black hole surrounding him (do the vector analysis if you like), unlike anyone unfortunate enough to fall through a wormhole.

Thoughts anyone?

 

[AlphaNumeric]

I would imagine that the crust wouldn't form a black hole (no matter how powerful the nukes) because it would be 'easier' for the crust to force itself down into the Moon than be crushed into a black hole, in that the Moon's rock would not be able to apply enough pressure to make a black hole.

It's an interesting notion though, being completel surrounded by a black hole without actually being torn apart. It is probably prohited by Penrose's 'Cosmic Censorship Hypothesis' because if you were in a spherical shell of black hole material (whatever that might be) you'd be able to see the material since there'd be no horizon between you and it.

 

[Instine]

I would imagine that the crust wouldn't form a black hole (no matter how powerful the nukes) because it would be 'easier' for the crust to force itself down into the Moon than be crushed into a black hole, in that the Moon's rock would not be able to apply enough pressure to make a black hole.

Sure enough this is almost certainly true. So I guess my second question is, cxan anyone think of a practical, or at least theretically possible way to produce this scenario?

It's an interesting notion though, being completel surrounded by a black hole without actually being torn apart. It is probably prohited by Penrose's 'Cosmic Censorship Hypothesis' because if you were in a spherical shell of black hole material (whatever that might be) you'd be able to see the material since there'd be no horizon between you and it.

No, I think you wouldn't be able to 'see' the event horizon, as the same oneway effect of light that comes into contact with the EH would apply, regardless of it weird geometic nature. As far as I can see. Cheers for the response though. Keep them coming

 

[Tzemach]

I can't get this to work, how could you create a "hollow" black hole? As soon as you remove sufficient matter from a given area you no longer have the required density to maintain a black hole. The black hole must start by having a sufficiently dense core to draw the matter into begin the collapse.

 

[JesseM]

I don't think an oddly-shaped black hole would be possible--the no-hair theorem says that no matter what the shape of the original collapsing object, all black holes will be identical from the outside except for their mass, charge, and angular momentum (and the size of a black hole depends on its mass, so you can't have two black holes which are identical in these three respects but differ in size because one was formed from a large hollow shell while the other was formed from a more compact object).

As for what happens to someone who falls inside a black hole that later evaporates, see this answer to an FAQ to sci.physics on black holes:

5. What about Hawking radiation? Won't the black hole evaporate before you get there?

(First, a caveat: Not a lot is really understood about evaporating black holes. The following is largely deduced from information in Wald's GR text, but what really happens-- especially when the black hole gets very small-- is unclear. So take the following with a grain of salt.)

Short answer: No, it won't. This demands some elaboration.

From thermodynamic arguments Stephen Hawking realized that a black hole should have a nonzero temperature, and ought therefore to emit blackbody radiation. He eventually figured out a quantum- mechanical mechanism for this. Suffice it to say that black holes should very, very slowly lose mass through radiation, a loss which accelerates as the hole gets smaller and eventually evaporates completely in a burst of radiation. This happens in a finite time according to an outside observer.

But I just said that an outside observer would *never* observe an object actually entering the horizon! If I jump in, will you see the black hole evaporate out from under me, leaving me intact but marooned in the very distant future from gravitational time dilation?

You won't, and the reason is that the discussion above only applies to a black hole that is not shrinking to nil from evaporation. Remember that the apparent slowing of my fall is due to the paths of outgoing light rays near the event horizon. If the black hole *does* evaporate, the delay in escaping light caused by proximity to the event horizon can only last as long as the event horizon does! Consider your external view of me as I fall in.

If the black hole is eternal, events happening to me (by my watch) closer and closer to the time I fall through happen divergingly later according to you (supposing that your vision is somehow not limited by the discreteness of photons, or the redshift).

If the black hole is mortal, you'll instead see those events happen closer and closer to the time the black hole evaporates. Extrapolating, you would calculate my time of passage through the event horizon as the exact moment the hole disappears! (Of course, even if you could see me, the image would be drowned out by all the radiation from the evaporating hole.) I won't experience that cataclysm myself, though; I'll be through the horizon, leaving only my light behind. As far as I'm concerned, my grisly fate is unaffected by the evaporation.

All of this assumes you can see me at all, of course. In practice the time of the last photon would have long been past. Besides, there's the brilliant background of Hawking radiation to see through as the hole shrinks to nothing.

(Due to considerations I won't go into here, some physicists think that the black hole won't disappear completely, that a remnant hole will be left behind. Current physics can't really decide the question, any more than it can decide what really happens at the singularity. If someone ever figures out quantum gravity, maybe that will provide an answer.)

 

[RandallB]

So I guess my second question is, cxan anyone think of a practical, or at least theretically possible way to produce this scenario?

Any such theoretical method of building such a thing would still be “highly improbable to the point of absurdity” as you said in OP. But it might be practical to think of such a construction for the purpose of considering the potential reality of something we can never see - that is looking behind an event horizon. Since no one else has seen behind that horizon, no one can be said to know what is correct.

Since you have given FP (the Foolish Physicist) extra-natural powers let's allow him to clean up a few details from his center position of this sphere by doing even more of the impossible. Since he needs much more mass than the moon; let's allow him to simply place a black hole some distance R from himself. Although not inside this black hole, to avoid being pulled immediately into it FP also places an identical black hole on his opposite side. With the gravity vectors canceling he remains weightless in space and unharmed between them. In like manner he keeps adding identical black holes , always keeping his lab weightless in the center, but increasing the total mass of all the black holes added to the sphere structure radius R until it has the mass of a super-blackhole of radius R.

Now externally we can only see one large black hole – with no hope of “seeing” inside to prove what it looks like in there. But assuming FP can hold this structure together for some time. How would his reference frame in this type of “center” compare to the reference frame of a distant deep space vacuum (roughly equivalent to our own)?
Obviously the Mass density would not be the same as that in the real black holes on the surface of the sphere but it would have some value significantly greater than a vacuum.
What would be the comparative rate of time be verses the stopped time of the small black hole horizons or the vacuum outside?
How about the measure of distance? Backwards? Imaginary?
How would these change as FP’s lab is moved away from the center by a fourth or half of R?

 

[JesseM]

Any such theoretical method of building such a thing would still be “highly improbable to the point of absurdity” as you said in OP. But it might be practical to think of such a construction for the purpose of considering the potential reality of something we can never see - that is looking behind an event horizon. Since no one else has seen behind that horizon, no one can be said to know what is correct.

Perhaps not, but you can say what would be correct according to the theory of general relativity.

Since you have given FP (the Foolish Physicist) extra-natural powers let's allow him to clean up a few details from his center position of this sphere by doing even more of the impossible. Since he needs much more mass than the moon; let's allow him to simply place a black hole some distance R from himself. Although not inside this black hole, to avoid being pulled immediately into it FP also places an identical black hole on his opposite side. With the gravity vectors canceling he remains weightless in space and unharmed between them. In like manner he keeps adding identical black holes , always keeping his lab weightless in the center, but increasing the total mass of all the black holes added to the sphere structure radius R until it has the mass of a super-blackhole of radius R.

If he is within a shell of black holes which itself has enough mass so that each of them lie within the event horizon of a super-black hole, then according to GR it should be inevitable that they will all fall together and form a common singularity, and that the scientist too must be crushed by this singularity in a finite time.

Now externally we can only see one large black hole – with no hope of “seeing” inside to prove what it looks like in there. But assuming FP can hold this structure together for some time.

He can't hold the black holes apart, if that's what you mean. Not according to GR anyway.

Obviously the Mass density would not be the same as that in the real black holes on the surface of the sphere but it would have some value significantly greater than a vacuum.

The no-hair theorem says that as long as two black holes have the same mass, charge, and angular momentum, they must have the same size. So this super black hole originally formed from a shell of smaller black holes could not be any larger than a regular black hole formed from a star with the same mass as the total mass of the small black holes in the shell, meaning that its average mass density would not be any different either.

 

[RandallB]

He can't hold the black holes apart,

Well of course he can with absurd extra-natural powers – obviously the OP is speculating on a Black Hole with no Singularity.
All I did was set up his scenario a little clearer.
If you have no speculation on what that may mean within the unseen boundary of the horizon that’s fine if you have no comment.
But what is the point of just telling the OP the idea doesn’t fit your favorite theory or scientist’s ideas so don’t think about that any more?

Nether GR QM or “no-hair theorem” have a conclusive answer to define singularity as the infinity problem at the center remains. Their resolutions are just a little less speculative than this one.

 

[JesseM]

Well of course he can with absurd extra-natural powers – obviously the OP is speculating on a Black Hole with no Singularity.

Sure, but I don't think the OP was supposing any extra-natural powers--I think the poster just didn't realize that the idea of a black hole shaped like a hollow shell (formed by compressing matter into a shell of huge density) would fundamentally violate the laws of physics as we know them.

Nether GR QM or “no-hair theorem” have a conclusive answer to define singularity as the infinity problem at the center remains. Their resolutions are just a little less speculative than this one.

I think most physicists would say that even though GR is going to give bad predictions at the singularity, its predictions can probably be trusted far from the singularity where you're not dealing with Planck-scale densities and energies. So based on this, my guess is that the no-hair theorem is unlikely to be overturned, at least not at macroscopic scales (micro-black holes whose mass is close to the Planck mass might be a different story).

 

[pervect]

I have a thought experiment for anyone interested. All replies welcome:Imagine if you will, a large spherical body e.g. a moon, about the surface of which are placed many large thermonuclear devices. Deep inside the moon sits an intrepid/foolish experimental physicist. When the the devices are triggered, the surface of the moon is crushed so quickly and uniformly and with such force as to create a spherical black hole. However the critical density is reach first, only by the 'crust' of the moon. meaning the fool/heroic physicist is, for an instance at least, completely surrounded by black hole.

It is my belief that this puts him beyond our universe. And we, beyond his. My first question is, if the black hole then 'evaporated', where/when would our fool/hero and his/her moon's interior reappear, if at all?

Although this is all highly improbable to the point of absurdity, its worth noting, that in theory the fool/hero would not be crushed by the gravitational field of the spherical black hole surrounding him (do the vector analysis if you like), unlike anyone unfortunate enough to fall through a wormhole.

Thoughts anyone?

To do this with only a moon, you'd need a very tiny physicist.

For an object the mass of the Earth's moon, for instance (pretty large as far as moons go), the Schwarzschild radius is about 100 microns.

So we'd have to compress the Earth's moon into a sphere of about 100 microns radius to turn it into a black hole, while somehow leaving a tiny space at the center for the physicist (who would have to be much smaller than 100 microns for this to work).I don't think there's really any great mystery about what's going to happen to the (tiny) physicist though. Assuming that he's inside an object made out of normal matter, the walls of whatever it is that is keeping him from being crushed will fail. It takes "exotic matter" to have a pressure greater than c^2 times the density, and only exotic matter could exert enough pressure to protect the physicist.

I think this is the main point the OP is missing, that there is a limit to the strength of non-exotic matter.

The rest is a matter of timing and defintions. The fate of the physicist is known (he will be crushed). One gets into arguments about "apparent horizons" vs "absolute horizons". Both of these defintions of horizons (the bounday of the black hole) have counterintiutive poperties when their evolution with time is studied.

"apparent horizons" can shift instantaenously, and are observer dependent. "Absolute" horizons are the same in all reference frames (observer independent), but are not causal. See Kip Thorne's book "Black Holes & Time Warps", pg 416, for more details.

Anyway, depending on the details of the defintions of the boundary of the black hole (i.e. the location of the horizon) one might be able to claim that the physicist was "inside a black hole" a bit before he was crushed. However, that isn't particularly odd, anyone can do that by jumping into a normal black hole. They will survive for a time before they die at the singularity.

 

[Instine]

Nice progression

Great reply pervect!

So if we want our FP to survive, how big do you say the moon/planet/body should be?

And if all you wanted to do was envelope a 1 meter wide probe, how big does the body need to be?

I don't think there's really any great mystery about what's going to happen to the (tiny) physicist though. Assuming that he's inside an object made out of normal matter, the walls of whatever it is that is keeping him from being crushed will fail. It takes "exotic matter" to have a pressure greater than c^2 times the density, and only exotic matter could exert enough pressure to protect the physicist.

Not quite so. Imagine you are inside the sphere of black hole. Just as the net force felt by a charged particle within a charged sphere is zero, the net gravitational effect of the black hole, as long as it is perfectly spherical (or cylindrical for that matter), would be zero. Like I say, do the vector analysis

 

[Instine]

If he is within a shell of black holes which itself has enough mass so that each of them lie within the event horizon of a super-black hole, then according to GR it should be inevitable that they will all fall together and form a common singularity, and that the scientist too must be crushed by this singularity in a finite time.

Nice imagery. My question was though, supposing the shell evaporated before it collapsed, however... And now its gets interesting although there is reason for the black hole shell to collapse, as seen from 'outside', is there equal reasoning from the inside?

If you're inside, everything ~X meters away from you is event horizon, so why would physics be working on the other side? How deep would the shell be? Thin enough to evaporate? or as deep as should be expected due to the history perceived by our FP? Why? The time line has been severed. Thick enough not to evaporate and collapse in on our poor FP? On what grounds? The deciding factors on FP's survival don't exist in FP's universe anymore. I believe this is a paradox. I'd like to call it Teare's, unless someone can tell me why its not valid, or not news.

Cheers for the replies, and keep them coming.

 

[pallidin]

Perhaps I am wrong here, but I thought that the centered singularity of a black hole is the source of the extreme gravitational field. As such, how would it even be possible to create a "void" within the center of an infinitesimally small singularity?
On the other hand(just speculating), what would stop such a singularity from forming a "bubble"?

 

[Instine]

Perhaps I am wrong here, but I thought that the centered singularity of a black hole is the source of the extreme gravitational field. As such, how would it even be possible to create a "void" within the center of an infinitesimally small singularity?
On the other hand(just speculating), what would stop such a singularity from forming a "bubble"?

Another nice reply. However, the bubble is not being created within the singularity, the black hole is being created around the bubble.

 

[pervect]

Great reply pervect!

So if we want our FP to survive, how big do you say the moon/planet/body should be?

And if all you wanted to do was envelope a 1 meter wide probe, how big does the body need to be?

The Schwarzschild radius is 2GM/c^2.

So the Schwarzschild radius of Jupiter, for instance, would be 2.8 meters. Thus if you could compress Jupiter into a hollow sphere with a circumference of less than 2*Pi*2.8 meters, it would be a black hole, leaving you enough room inside for a probe or physicist.

Not quite so. Imagine you are inside the sphere of black hole. Just as the net force felt by a charged particle within a charged sphere is zero, the net gravitational effect of the black hole, as long as it is perfectly spherical (or cylindrical for that matter), would be zero. Like I say, do the vector analysis

I am not saying that the force in the center would be non-zero if you had a hollow sphere. What I am saying that there is no way to keep the hollow sphere from collapsing under its own weight.

For instance, if you hollowed out a sphere inside the center of the Earth, there would be no gravity in the hollowed out region, but it would take an extremely strong shell to keep that hollowed out cavity from collapsing.

To be specific

http://hypertextbook.com/facts/1999/PavelKhazron.shtml

puts the pressure at the center of the Earth as about 3 million bars (i.e 3 million times the standard atmospheric pressure). So a sphere that could hold the hollowed out region from being smashed close at the center of the Earth would have to be able to support 3 million atmospheres.

You are perhaps thinking "But there is no gravitational force on the inside of the sphere". This is correct, but it doesn't explain what supports all the weight on top of the hollow sphere.

Pressure IS required to support the top part of the sphere, and that pressure is communicated downwards - though the gravity at the center of the Earth becomes zero, the pressure does NOT become zero.

There is no even theoretically possible material of normal (non-exotic) matter that can stop a black hole from collapsing all the way to a singularity once it has been compressed enough to form a black hole.

 

[Instine]

You're totally right that the pressure would be phenomenal, and in real life situations, it already looks like its practically impossible to even get a probe into the 'safe place' in the centre of, say, Jupiter (Cheers for giving us some scale).

However this is a thought experiment, and we don't have to actually make the thing, just prove its possible in theory.

So our FP would gets squished by the pressure of the body. However 'all information' is not destroyed by such forces, even within Jupiter. In theory a probe could be put in the situation where it was completely surrounded by, but not actually touching, event horizon. In which case, what happens next?...

Like I say, whether or not the event horizon evaporates depends on information that does not exist in*the probe's/FP's*universe/space time continuum. Even if the event horizon simply collapses in on poor FP, at what speed would it do this? Again this is dependent on information that does not exist in FP's universe.

 

[pervect]

After the physicist is crushed, the collapse process continues. No known force is strong enough to stop it. The forces attempting to resist collapse are fierce - at this point, matter will be in the form of neutron degenerate matter, i.e. neutronium. However, even these fantastically large nuclear forces aren't large enough to prevent collapse.

Detailed calculations are tricky, but one can look at calculations of simple cases, like a uniform star of constant density, for insight. One can see that in a hypothetical static spherical mass of constant density, above a certain critical radius, the pressure at the center becomes not only large, but infinite.

http://scienceworld.wolfram.com/physics/SchwarzschildBlackHoleConstantDensity.html

IIRC this infinite presssure occurs just when the spherical mass becomes a black hole. The conclusion is that such a static spherical star does not exist - the star must collapse under its own weight.

In a simple spherically symmetric collapse, the physicist becomes part of the central singularity. First the cavity collapses, then you have a spherically symmetrical (but not static) mass that implodes further. Nothing in classical physics can halt the collapse - it proceeds to a mathematical point.

This is according to classical GR. Most theories of quantum gravity suggest that the mass of the black hole does not collapse to a mathematical point (as classical GR predicts), but probably has some Planck-scale size.

There is still some room for argument about the details of what happens even in classical GR for realistic (i.e. non-symmetrical) collapse. Rotating collapse is especially problematical, and is still being studied. However, various singularity theorems show that any black hole must have at least one singularity at its center.

http://en.wikipedia.org/wiki/Penrose-Hawking_singularity_theorems

 

[Instine]

You're still not quite getting my point. From 'outside' the black hole, yes you're right on all accounts, but that's not my issue.

From inside...

If your are surrounded by event horrizon, the depth of the event horizon doesnot exist in your time or space or universe for that matter, only the radious of the event horizon, from the centre of the cavity. From 'inside' the 'event horizon shell', your previous 'outside', doesnot exist. There is no crushing mass beyond. None. The event horizon, is just that. its is the boundry of your universe. And as your universe is not yet crushed out of all existence, why should it be? Why shouldn't the event horizon colapse outwards, evaporate, vanish in a puff of logic etc... There is no beyond. Or that's how I see it. And you've not convinced me otherwise yet.

From 'outside', there is no paradox. It colapses and become a black hole like any other, very quickly. So its easy to say, the FP is crushed, but equally, FP no longer exists to be crushed. But from the perspective of the FP, there is no reason for the event horizon to act in any perticular way. e.g. How fast should it collapse? You can't go by what's 'outside', because outside doesn't exist. Do you see my point? The logical asymatry comes from being able to measure proerties of a black hole from outside (radious, mass, charge...) but from inside a spherical shell of event horizon, none of these measurements can be made, or even implied.

 

[JesseM]

You're still not quite getting my point. From 'outside' the black hole, yes you're right on all accounts, but that's not my issue.

From inside...

If your are surrounded by event horrizon, the depth of the event horizon doesnot exist in your time or space or universe for that matter, only the radious of the event horizon, from the centre of the cavity. From 'inside' the 'event horizon shell', your previous 'outside', doesnot exist. There is no crushing mass beyond. None. The event horizon, is just that. its is the boundry of your universe. And as your universe is not yet crushed out of all existence, why should it be? Why shouldn't the event horizon colapse outwards, evaporate, vanish in a puff of logic etc... There is no beyond. Or that's how I see it. And you've not convinced me otherwise yet.

But the event horizon must contain the matter that was compressed into a black hole, that's not "beyond the boundary of your universe" if you're inside. And inside the event horizon, you can still use the same laws of general relativity to predict how this matter will behave--if you compressed a hollow shell into a black hole as you suggested, general relativity says the shell must collapse inwards until it has all gathered at a single point, the singularity.

 

[Instine]

But the event horizon must contain the matter that was compressed into a black hole.

Why? It is not linked to you through time or space. Nor can any information pass through it to you. But nor (and this is the crux) can you imply any properties beyond it, through observation. Why should your past influence it? Time is no longer shared by FP and the that which is beyond the shell.

And inside the event horizon, you can still use the same laws of general relativity to predict how this matter will behave

"still" is the give away. There is no still, beyond the event horizon. There is continuity in the usual sense from outside a 'normal' black hole, because the influence of the black hole on an observer's universe gives away properties, such as mass. These properties give that which is contained within the singularity a continuous implied history to an external observer. Not so if you're in the shell. I realize this is very much bordering on philosophy, but dismissing it as such would render most of Relativity beyond consideration.

It is my belief, though I could easily be very wrong, that the event horizon would have to vanish, as otherwise it would be paradoxical. The FP must then reemerge into a universe, but not the one he was in before, as in that one, he was crushed.

Thoughts...?

 

[JesseM]

But the event horizon must contain the matter that was compressed into a black hole.

Why? It is not linked to you through time or space. Nor can any information pass through it to you.

You seem to be talking about what's beyond the event horizon here, but what I meant was that the matter that was compressed into a black hole will be inside the event horizon at the moment it forms*. An event horizon forms because a certain critical mass has been collected inside a certain volume, so naturally the mass must lie within the horizon.

As an aside, why do you say "nor can any information pass through it to you"? A black hole's event horizon is only a one-way barrier, information can certainly pass from the outside to the inside, it does so every time a new object falls into the black hole.

And inside the event horizon, you can still use the same laws of general relativity to predict how this matter will behave

"still" is the give away. There is no still, beyond the event horizon.

Why do you say that? According to general relativity there is no problem extending the worldline of objects falling into the black hole past the event horizon to see what happens to them, it's only at the singularity that you run into problems. There is nothing magical about event horizons, all they mean is that light-signals from beyond the horizon cannot reach you. There is another type of event horizon defined by the expansion of the universe, for example, because for distant enough events, the space between them and us is expanding faster than light can move towards us, so unless the expansion slows down the light from those events can never reach us. Do you think there is any reason to think the laws of physics don't work the same way beyond the observable universe? (Keep in mind that each galaxy would have a different definition of what is 'beyond the observable universe', centered on themselves.) If not, why should the events inside the event horizon of a black hole be any different?

These properties give that which is contained within the singularity a continuous implied history to an external observer.

What do you mean by "contained within the singularity"? The singularity is just a point, it can't have any internal differentiation.

It is my belief, though I could easily be very wrong, that the event horizon would have to vanish, as otherwise it would be paradoxical.

What would be paradoxical about it?
*I do remember from Kip Thorne's book Black Holes and Time Warps that there is some subtlety in defining when the horizon forms--one definition assumes an event horizon can only form or grow when the mass necessary for a black hole that size would already lie inside it, which implies that the event horizon can jump discontinuously, while another definition assumes the event horizon can grown in anticipation of something that will soon fall in, which allows its growth to be more continuous but treats the event horizon as having a sort of "foreknowledge". I guess I'm assuming the first definition here, although even under the second definition I think the shell should lie within the event horizon at the same time that the event horizon first appears under the first definition.

 

[pervect]

Matter does fall into the black hole. The isolation is only one way - matter and signals can go into the black hole, though they can't get back out. So the idea of the black hole as a "separete universe" doesn't quite work right. The outside universe can and does affect what happens inside the black hole.

In GR, we can treat the inflowing matter as a fluid. We can follow the "lines of flow" of this fluid. The "fluid-flow lines" will be ordinary, timelike worldlines even after the event horizon formes.

 

[Instine]

You both seem to be forgetting that time itself stretches infinitly at the EH. So no. Information never quite reaches the singularity. So information cannot flow in or out. The properties of a black hole, are not the properties of a black hole, but the properties of our own universe coping with a local singularity.

As an aside, why do you say "nor can any information pass through it to you"? A black hole's event horizon is only a one-way barrier, information can certainly pass from the outside to the inside, it does so every time a new object falls into the black hole.

I think your confusing (or I'm confusing ) your in's and outs. But as I mentioned above this is mute. Information never reaches beyond an event horizon from either direction. Always remember the effect of time. Without time, there are no events, and thereby no information.

What would be paradoxical about it?

Like I say, the phyiscal properties of the singularity causing the shell surrounding you, can not be measure or observed in any way, nor can they be implied, other than by your own memory, which is based on your timeline, which is nolonger connected to the singularity, and thereby 'was never' connected to the singularity. This truly puts the 'outside' beyond your universe completely, and a 'probability singularity' (if you like) occurs. Or in other words, a paradox.

Again, I give the example of, how fast does the EH collapse in on FP, as perceived by FP? This depends on how much mass is contained in the singularity. How much is? You don't know. You can't measure it, and you can't induce it (unlike being 'outside' a black hole, where you can measure its gravitational effect, and radious). You can't say, it contains the mass you saw going in before you were surrounded, because your 'before' is no longer connected to the singularity.

 

[JesseM]

You both seem to be forgetting that time itself stretches infinitly at the EH.

Not true. Although observers outside will never see an object cross the event horizon, this is because each successive light signal closer and closer to the horizon takes longer and longer to climb out, general relativity still predicts that the amount of "proper time" (time as measured on the clock of the infalling observer) to reach the event horizon is finite, as is the time to hit the singularity. See this answer from the Usenet Physics FAQ:

Won't it take forever for you to fall in? Won't it take forever for the black hole to even form?

Not in any useful sense. The time I experience before I hit the event horizon, and even until I hit the singularity-- the "proper time" calculated by using Schwarzschild's metric on my worldline-- is finite. The same goes for the collapsing star; if I somehow stood on the surface of the star as it became a black hole, I would experience the star's demise in a finite time.

On my worldline as I fall into the black hole, it turns out that the Schwarzschild coordinate called t goes to infinity when I go through the event horizon. That doesn't correspond to anyone's proper time, though; it's just a coordinate called t. In fact, inside the event horizon, t is actually a spatial direction, and the future corresponds instead to decreasing r. It's only outside the black hole that t even points in a direction of increasing time. In any case, this doesn't indicate that I take forever to fall in, since the proper time involved is actually finite.

At large distances t does approach the proper time of someone who is at rest with respect to the black hole. But there isn't any non-arbitrary sense in which you can call t at smaller r values "the proper time of a distant observer," since in general relativity there is no coordinate-independent way to say that two distant events are happening "at the same time." The proper time of any observer is only defined locally.

A more physical sense in which it might be said that things take forever to fall in is provided by looking at the paths of emerging light rays. The event horizon is what, in relativity parlance, is called a "lightlike surface"; light rays can remain there. For an ideal Schwarzschild hole (which I am considering in this paragraph) the horizon lasts forever, so the light can stay there without escaping. (If you wonder how this is reconciled with the fact that light has to travel at the constant speed c-- well, the horizon is traveling at c! Relative speeds in GR are also only unambiguously defined locally, and if you're at the event horizon you are necessarily falling in; it comes at you at the speed of light.) Light beams aimed directly outward from just outside the horizon don't escape to large distances until late values of t. For someone at a large distance from the black hole and approximately at rest with respect to it, the coordinate t does correspond well to proper time.

So if you, watching from a safe distance, attempt to witness my fall into the hole, you'll see me fall more and more slowly as the light delay increases. You'll never see me actually get to the event horizon. My watch, to you, will tick more and more slowly, but will never reach the time that I see as I fall into the black hole. Notice that this is really an optical effect caused by the paths of the light rays.

This is also true for the dying star itself. If you attempt to witness the black hole's formation, you'll see the star collapse more and more slowly, never precisely reaching the Schwarzschild radius.

Now, this led early on to an image of a black hole as a strange sort of suspended-animation object, a "frozen star" with immobilized falling debris and gedankenexperiment astronauts hanging above it in eternally slowing precipitation. This is, however, not what you'd see. The reason is that as things get closer to the event horizon, they also get dimmer. Light from them is redshifted and dimmed, and if one considers that light is actually made up of discrete photons, the time of escape of the last photon is actually finite, and not very large. So things would wink out as they got close, including the dying star, and the name "black hole" is justified.

As an example, take the eight-solar-mass black hole I mentioned before. If you start timing from the moment the you see the object half a Schwarzschild radius away from the event horizon, the light will dim exponentially from that point on with a characteristic time of about 0.2 milliseconds, and the time of the last photon is about a hundredth of a second later. The times scale proportionally to the mass of the black hole. If I jump into a black hole, I don't remain visible for long.

Also, if I jump in, I won't hit the surface of the "frozen star." It goes through the event horizon at another point in spacetime from where/when I do.

(Some have pointed out that I really go through the event horizon a little earlier than a naive calculation would imply. The reason is that my addition to the black hole increases its mass, and therefore moves the event horizon out around me at finite Schwarzschild t coordinate. This really doesn't change the situation with regard to whether an external observer sees me go through, since the event horizon is still lightlike; light emitted at the event horizon or within it will never escape to large distances, and light emitted just outside it will take a long time to get to an observer, timed, say, from when the observer saw me pass the point half a Schwarzschild radius outside the hole.)

All this is not to imply that the black hole can't also be used for temporal tricks much like the "twin paradox" mentioned elsewhere in this FAQ. Suppose that I don't fall into the black hole-- instead, I stop and wait at a constant r value just outside the event horizon, burning tremendous amounts of rocket fuel and somehow withstanding the huge gravitational force that would result. If I then return home, I'll have aged less than you. In this case, general relativity can say something about the difference in proper time experienced by the two of us, because our ages can be compared locally at the start and end of the journey.

So no. Information never quite reaches the singularity.

Just to make sure, do you understand the difference between the event horizon and the singularity? The singularity is the point of infinite density at the very center of the black hole, the event horizon is a sphere-shaped boundary (or some kind of ellipsoid shape in the case of a rotating black hole, I believe) between events whose light can escape the singularity and events whose light cannot.

I think your confusing (or I'm confusing ) your in's and outs. But as I mentioned above this is mute.

"moot"

Information never reaches beyond an event horizon from either direction.

Again, simply not true according to general relativity.

Like I say, the phyiscal properties of the singularity causing the shell surrounding you, can not be measure or observed in any way, nor can they be implied, other than by your own memory, which is based on your timeline, which is nolonger connected to the singularity, and thereby 'was never' connected to the singularity.

From your perspective inside, the singularity has not even formed yet until the shell has collapsed to a single point at the center of the volume enclosed by the event horizon. But again, when the event horizon forms, the matter in the shell will be inside it, not outside it.

Again, I give the example of, how fast does the EH collapse in on FP, as perceived by FP?

The event horizon doesn't collapse at all, it's just a boundary whose size is constant as long as the amount of mass within it is constant. The physical shell is not the same thing as the event horizon. I don't know exactly how long it would take to collapse, but it could be calculated using GR, depending on the mass and size of the shell.

This depends on how much mass is contained in the singularity.

Again, the singularity is not even present until all the mass in the shell has collapsed to a single point.

How much is?

The same as the mass of the shell (plus whatever else was in the horizon, like the observer, but we can assume this is negligible).

You can't say, it contains the mass you saw going in before you were surrounded, because your 'before' is no longer connected to the singularity.

According to general relativity, you can certainly track the path of each part of the collapsing shell as it falls inwards towards the center, with the singularity being formed when all these parts meet there at a single point. The proper time for each part to reach hit the singularity can be calculated, and it will be some finite time-interval.

 

[Instine]

OK I made a few gaffs in the last post (it was very early and I got up at 4). Thanks for pointing some out (although I don't need spelling mistakes highlighted, I'm dyslexic, it doesn't help).

The finite propper time to singularity issue is news to me (and shouldn't be), and could be the downfall of my theory :( However I'll have to have a good ponder on it. And initially I don't think its is. Again I think you're not quite picturing my theoretical situation. I'm suggesting there would be a hollow spherical singularity (yes I know the difference, although yes I got confused in the last post - again - tired dyslexic).

No this isn't in textbooks, but not everything is. Why can't you have a 'point thick' shell of singularity? Apart from the obvious "because that's not a singularity", I mean why can't you have such a construct?

Re the gaffs, I meant to say information never passes beyond a singularity (all physics as we no it is destroyed). But our shell of singularity is like an uber event horizon. A reality horizon if you like. A true information boundry (both ways).

So my paradox, re FP's universe not 'knowing' enough information to sustaing the shell, IMO, still holds.

Thanks for the info re propper time, and please forgive my sloppyness.

Keep 'm coming.

 

[pervect]

You both seem to be forgetting that time itself stretches infinitly at the EH.

Only for a hovering observer. An infalling observer will cross the horizon in finite proper time. Furthermore, for an observer falling into a black hole from infinity, light falling from infinity will be redshifted by a finite amount (corresponding to finite time dilation). The redshift factor for radially falling light is 50% for an observer freely falling into a black hole from infinity, see for instance

https://www.physicsforums.com/archive/index.php/t-104577.html

As I mentioned before, in a case where we have matter infalling into a black hole, there will be some specific frame where said matter is at rest.

Time dilation will be finite in this frame. Basically, infalling coordinates like this (I believe they are called Novikov coordiantes) will be much better behaved than Schwarzschild coordinates. Metric coefficients will remain finite and not exhibit the singular behavior of Schwarzschild coordinates as per the previous example in which the time dilation factor was 50% corresponding to a g_00 of .25.

See also Chris Hillman's remarks in

http://www.lns.cornell.edu/spr/1999-05/msg0016149.html

See the
discussion of Lemaitre, Kruskal-Szekeres, Penrose, or Novikov coordinates.
These are all fairly intuitive, but the Lemaitre coordinates are
mathematically the easiest to derive, and the KS coordinates are not much
harder and have the benefit of covering the maximal completion, which the
Lemaitre coordinates do not. However, the Lemaitre coordinates are
perfectly adequate for discussion of radial infall, and should help you to
understand that gtr predicts that if you drop your watch near a black
hole, it can drop through the horizon in finite time.

 

[Instine]

Thanks for that, but read above. Sorry, I made a gaff. Was actually reffering to the 'singularity shell', not the event horizon.

But again, good points.

 

[JesseM]

OK I made a few gaffs in the last post (it was very early and I got up at 4). Thanks for pointing some out (although I don't need spelling mistakes highlighted, I'm dyslexic, it doesn't help).

Sorry, didn't mean to be pedantic...I don't usually point out spelling errors, but sometimes when people write things in ways that suggests it might be a misheard phrase rather than an ordinary spelling error (like if someone writes 'for all intensive purposes' instead of 'for all intents and purposes') I point that out just so they know that's not how it's supposed to go.

The finite propper time to singularity issue is news to me (and shouldn't be), and could be the downfall of my theory :( However I'll have to have a good ponder on it. And initially I don't think its is. Again I think you're not quite picturing my theoretical situation. I'm suggesting there would be a hollow spherical singularity (yes I know the difference, although yes I got confused in the last post - again - tired dyslexic).

No this isn't in textbooks, but not everything is. Why can't you have a 'point thick' shell of singularity? Apart from the obvious "because that's not a singularity", I mean why can't you have such a construct?

OK, this is helpful, I didn't get from your earlier posts that you were thinking of the observer being surrounded by an actual 2D singularity rather than just a normal event horizon. I'm not sure if sheet-like singularities are possible mathematically in relativity--they may be though, I think I remember a while back that some physicists had thought they could explain the rotation of galaxies without the need for dark matter using a new type of analysis based on GR, but then it was shown that their model contained a planelike singularity through the center of the galaxy which was physically unrealistic. But that would suggest at least that GR allows such things, even if there's not really any natural way they could form. Pervect, do you know anything about this?

 

[Instine]

Lol


I finally manage to explain it, just as I get round to uploading the diagram.

"[URL

Again cheers for the reponses. I've already learned a great deal.

 

[Instine]

I think I remember a while back that some physicists had thought they could explain the rotation of galaxies without the need for dark matter using a new type of analysis based on GR, but then it was shown that their model contained a planelike singularity through the center of the galaxy which was physically unrealistic. But that would suggest at least that GR allows such things, even if there's not really any natural way they could form. Pervect, do you know anything about this?

Any info on this? Sounds very interesting. I've been pondering this one on and off for nearly 9 years, but never got round to really investigating it in earnest. Any like minded researchers who want to chat about it? If you/they have had any theoretical or experimental (modelling) encounters with 2D or 3D singularities, that would be even better.

If anyone stumbles on this and doesn't want to chat on the forum about it (lurkers you know who you are:) feel free to email me at:
philDOTaDOTteareATgooglemailDOTcom* < demangle the address*if you're not a spamb0t

 

[Garth]

I think I remember a while back that some physicists had thought they could explain the rotation of galaxies without the need for dark matter using a new type of analysis based on GR, but then it was shown that their model contained a planelike singularity through the center of the galaxy which was physically unrealistic. But that would suggest at least that GR allows such things, even if there's not really any natural way they could form.

Any info on this? Sounds very interesting.

This has been well discussed in these Forums here: new study shows Dark Matter isn't needed? Relativty explains it? and here: More about the Cooperstock and Tieu model and here: Cooperstock and Tieu Respond to Criticisms.

Garth

 

[Instine]

Now I've got some reading to do. Thanks. This looks like a pefect place to start. Although at very first glance, it looks like these model anomalies are even more exotic still. And very model driven. If that's not a such a big critisism.

Many thanks.

What are your thoughts on the paradox Garth? (remembering this is purly a thought experiment, we're not necessarily expecting this to ever actually happen, or be observed).

Chrs

 

[Garth]

What are your thoughts on the paradox Garth? (remembering this is purly a thought experiment, we're not necessarily expecting this to ever actually happen, or be observed).

I did not realize this was a paradox, just a gedankenexperiment.

The scenario of being inside a shell black hole is not so unrealistic.

The Schwarzschild metric becomes singular at
$$\frac{2GM}{rc^2} = 1$$
so the radius required to make a black hole is proportional to the mass, and therefore the density required is proportional to 1/r².

A solar mass has to be compressed into a sphere of radius ~ 1.5 kms.

An extremely large 10¹²M_solar globular cluster closely packed into a sphere of radius 1.5 x 10¹² kms, (a compact giant elliptical really!), would pinch itself off from the rest of the universe into a black hole from which no light or anything could escape. This would have a density of about one solar mass star every 150 million kms - one solar mass star/AU, close but not impossibly so.

Tidal forces would not be too great either as an unfortunate astronaut passed unsuspecting through the event horizon...

Your question would now be: "What if this globular cluster were hollow?" A impractical situation I know, but nevertheless surpose there were an enormous massive shell around an observer. Would there be an inner horizon as well? I do not think anyone has solved this problem, if anybody knows differently please post links.

As far as your OP evaporating 'hollow BH' scenario is concerned, I would guess the intrepid observer trapped at the centre would reappear, a little bit singed, back into their original universe space-time. (After all it is the only one we can be sure about).

Garth

 

[Instine]

Another great response. Thankyou.

I did not realize this was a paradox, just a gedankenexperiment.

The topic is the thought experiment, and my putative outcomes are based on avoiding a paradox. Namely I don't believe that the 'snipped of' universe is capable of logically sustaining the event horizon surrounding it. Most specifically when the shell is spherical (see prior posts).

If I'm unemotional and a little cautious about it, my response would be as yours. But I'd rather like to be a bit more daring and actually suggest what might happen to poor old Foolish Physicist. To that end I'd say the pinched off universe would have to reappear in a universe that would rationally sustain its 'appearance', but that had no event horizon surrounding FP, and which wasn't the universe that FP was in prior to the experiment (as in that one the black hole swallowed him). But not a specific universe other than that. Random, but rational. If you see what I mean.

But of course this is a guess. Which is all it can ever be. As the one thing that seems for sure, is that the FP is not going to be seen by any external onlookers ever again.

 

[Garth]

Although the BH is pinched off in the sense that nothing can get out, the space-time continuum is continuous through the event horizon.

If Hawking radiation caused the BH to eventually evaporate, then the space-time continuum would simply 'ping' back to a non-singular state.

Garth