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tgoolsby2
2011-May-24, 03:42 AM
For example, If we could somehow compress the sun to its schwarzschild radius, once it turned into a black hole would it stay that way under its own gravity?
As you compress the sun smaller and smaller, do you need more and more energy to continue to compress it, or does it require less and less energy to compress it?
I imagine that you would need more energy to continue to compress it, like a balloon. Balloons are easy to squeeze at first, but the smaller it gets, the harder it is to squeeze.
But for the sun, what happens at the point where you squeezed it down to its schwarzschild radius? What happens to all that pressure?

Solfe
2011-May-24, 04:12 AM
Once enough material has been forced into the object to create an event horizon, no further force is needed to maintain a black hole. All of the material used to squish the object remains inside the black hole and its event horizon.

As I understand it, black holes do have a temperature so eventually they will evaporate.

Of course, you could "feed" more matter into the black hole and the event horizon would get bigger and the black hole would be more massive, but that is not required.

I am sure someone will be along with more details and depth.

EDIT - Typo - typed "passive" instead of "massive".

Ken G
2011-May-24, 04:54 AM
If you externally crushed the Sun by doing work but not adding heat (or letting any heat escape), the internal kinetic energy in the Sun would scale like 1/R^2 as the radius R got small. The gravitational potential energy would scale only like 1/R, so the Sun would tend to want to re-expand once you let it go, due to all that trapped kinetic energy. So your question is a good one-- in Newtonian gravity, the Sun would always want to re-expand after any amount of compression like that.

However, Newtonian gravity isn't right. Once you compress past the Schwarzschild radius, there's no re-expansion, it falls into a singularity never to return.

caveman1917
2011-May-24, 05:14 AM
Once you compress past the Schwarzschild radius, there's no re-expansion, it falls into a singularity never to return.

Not necessarily. Solutions that incorporated pressure in the collapse of a star (as opposed to the standard collapsing shell of pressureless dust), and using reasonable initial conditions, have been known to sometimes not form any event horizon and get a naked singularity, or even sometimes not form a singularity at all. I'm not sure anyone has ever done it including a downwards force field like the scenario in the OP, but the other results show that it might not be such a given truth.

Ken G
2011-May-24, 06:03 AM
I can't say much about what solutions might be possible, but pressure is another source of gravity, so including it would not seem to me to make the situation better for re-expansion once we reach the scale of the Schwarzschild radius. Normally a high pressure is good for re-expansion because it means the particles are moving faster and therefore curve less under gravity, but when the gravity is strong enough to change the spacetime topology until light itself cannot escape, then no amount of high speed can ever help produce escape either.

Astron
2011-May-24, 07:32 AM
All of the material used to squish the object remains inside the black hole and its event horizon.

Aren't they devoured?
Cause from my understandings black holes doesn't work like massive storage space for anything you throw to them.

WayneFrancis
2011-May-24, 07:36 AM
For example, If we could somehow compress the sun to its schwarzschild radius, once it turned into a black hole would it stay that way under its own gravity?
As you compress the sun smaller and smaller, do you need more and more energy to continue to compress it, or does it require less and less energy to compress it?
I imagine that you would need more energy to continue to compress it, like a balloon. Balloons are easy to squeeze at first, but the smaller it gets, the harder it is to squeeze.
But for the sun, what happens at the point where you squeezed it down to its schwarzschild radius? What happens to all that pressure?

Once there is enough mass it it will form the black hole and by their nature will not "snap back"

It isn't like if you could take a tablespoon of neutron star away from the actual neutron star then electron degeneracy pressure would dominate over gravity again.
With the black hole if you tried to get a spoon full of the black hole you'd have no where to take it to because you are forever inside the event horizon.

Good question.

Strange
2011-May-24, 11:29 AM
Aren't they devoured?

I guess it depends what you mean by "devoured"...

Cause from my understandings black holes doesn't work like massive storage space for anything you throw to them.

Well, it does in the sense that anything you throw in increases the mass of the black hole. Not a very useful storage space though, as you can never get anything out again :)

caveman1917
2011-May-24, 02:10 PM
I can't say much about what solutions might be possible, but pressure is another source of gravity, so including it would not seem to me to make the situation better for re-expansion once we reach the scale of the Schwarzschild radius. Normally a high pressure is good for re-expansion because it means the particles are moving faster and therefore curve less under gravity, but when the gravity is strong enough to change the spacetime topology until light itself cannot escape, then no amount of high speed can ever help produce escape either.

Yes, but strictly speaking the schwarzschild geometry is for an eternal black hole. The formation process of star collapse is not described through the schwarzschild geometry, it's not a static solution. You are right that when the black hole has formed, the spacetime becomes static and the schwarzschild radius represents the event horizon and anything beyond that can never escape, even given infinite acceleration. The question is however, in the dynamic scenario in the OP, will an event horizon form in the first place? What i mean is that it's not a given that this specific dynamic situation of star "compressing" will end up in the schwarzschild geometry, where we then can use standard black hole reasoning. It might give a naked singularity, or perhaps no singularity at all, it has been encountered in models with a realistic equation of state for the collapsing matter, so we can't just rule it out by fiat.

Ken G
2011-May-25, 04:53 PM
The way I interpret the OP is that the star is squeezed in a giant (presumably adiabatic) piston that is able to hold the star at any desired radius, and then ultimately the star is released at the new radius and we ask if it springs back or not. The star can be held as long as necessary to establish an essentially static environment, prior to releasing it. The basic question seems to be, is there a point you can compress an object such that its natural tendency to re-expand once released is overcome by its own gravity. That would seem to hold true at something like the Schwarzschild radius, but I grant you that if you are interested in the dynamics of how a real compression process might unfold (like perhaps a core-collapse supernova), you are probably going to have to worry about more complicated transient effects.

caveman1917
2011-May-25, 11:16 PM
The star can be held as long as necessary to establish an essentially static environment, prior to releasing it.

I think this assumption is unrealistic. Either it forms an event horizon and black hole as you are pushing it down, or it doesn't. I don't see why it would wait until you release it to decide wether to form an event horizon or not. There's also the force field itself that is pushing it down that would need to be taken into account, it will have a (presumably large) effect on the geometry. Considering that contribution it seems it would form an event horizon, but much earlier than the point where everything is below the schwarzschild radius. It's the turning on and off of this force field (or piston if you want) that's the unphysical bit here, making statements about wether the event horizon forms or not difficult if not impossible.

Solfe
2011-May-26, 12:24 AM
I wouldn't use the word devour for a stellar mass black hole, instead I sort of picture that word being applied to very massive black holes that can break up items that get too close. The victim ends up in a disc of material that the black hole "devours" like a snack.

In fact, I don't know why I didn't think of this first:
This is a pod cast (http://www.astronomycast.com/astronomy/ep-213-supermassive-black-holes/) from www.astronomycast.com about supermassive black holes. These types of black holes are much "heavier" the stellar black hole you asked about, it is a great listen.

In fact there are many shows on astronomycast.com that you may enjoy. There is a series called "Mystery of..." that touches on black holes and star types which may be of interest too.

John Mendenhall
2011-May-26, 12:30 AM
I guess it depends what you mean by "devoured"...

Well, it does in the sense that anything you throw in increases the mass of the black hole. Not a very useful storage space though, as you can never get anything out again :)

This is a general truth, as anyone who has rented a storage unit can tell you. The only one of mine that was emptied was hit by a tornado (true story).

Ken G
2011-May-26, 05:40 PM
I think this assumption is unrealistic. Either it forms an event horizon and black hole as you are pushing it down, or it doesn't. I don't see why it would wait until you release it to decide wether to form an event horizon or not.I'm not saying it does. I'm saying if you compress the star to a radius larger than the Schwarzschild radius, hold it as long as you like (adiabatically), and release it, it will spring back to its original size. But if you compress it smaller than the Schwarzschild radius, hold it for awhile, then release, it won't spring back, regardless of exactly when it creates an event horizon. At what point the transients die away enough to give a classical Schwarzschild solution is a kind of unnecessary detail, as would be accounting for the angular momentum that would no doubt be present. Those are issues for actual stellar collapse models, the OP is asking for only a particular idealized and isolated element of the whole process.

There's also the force field itself that is pushing it down that would need to be taken into account, it will have a (presumably large) effect on the geometry.Not necessarily, one can imagine a spherical piston, able to support itself at a given radius regardless of the internal stresses. It's just an idealization to able to ask the OP question, what purpose the OPer has in asking the question, I presume, is purely conceptual rather than physical.

Considering that contribution it seems it would form an event horizon, but much earlier than the point where everything is below the schwarzschild radius. It's the turning on and off of this force field (or piston if you want) that's the unphysical bit here, making statements about wether the event horizon forms or not difficult if not impossible.That could be true, it might be like asking what happens if a star instantly disappears, which is relativistically impossible so you can't apply relativity to it. Maybe an idealized spherical piston of arbitrary radius violates some rule of GR, or maybe it doesn't, I really couldn't say.

tommac
2011-May-26, 07:26 PM
How about past the EH ... lets say once an EH forms ... must the star collapse to a singularity? Or could there be a structure inside of the EH ( of course you would need to pass the EH to see it )

Hornblower
2011-May-26, 07:53 PM
How about past the EH ... lets say once an EH forms ... must the star collapse to a singularity? Or could there be a structure inside of the EH ( of course you would need to pass the EH to see it )

If we ever succeed in unifying general relativity and quantum mechanics, we might be able to answer that question.

caveman1917
2011-May-26, 10:55 PM
I'm not saying it does. I'm saying if you compress the star to a radius larger than the Schwarzschild radius, hold it as long as you like (adiabatically), and release it, it will spring back to its original size.

I'm just not sure how one would describe such a situation.
For example the standard internal schwarzschild solution develops a pressure singularity even for a radius a bit above the schwarzschild radius.

But if you compress it smaller than the Schwarzschild radius, hold it for awhile, then release, it won't spring back, regardless of exactly when it creates an event horizon.

If the process results in a naked singularity rather than a schwarzschild black hole, there is no restriction on the outwards geodesics for it not to spring back.

At what point the transients die away enough to give a classical Schwarzschild solution is a kind of unnecessary detail

Not necessarily since the transition between the regimes must be smooth.
We can't just wait a bit and then consider it a schwarzschild geometry. The ultimate question is wether the geometry describing the compression will develop into the schwarzschild geometry or something else.

Those are issues for actual stellar collapse models, the OP is asking for only a particular idealized and isolated element of the whole process.

But even in an idealized and isolated consideration there are problems. The solution for a spherically symmetric perfect fluid of radius r breaks down before r even gets to the schwarzschild radius. I don't know how we could idealize it more than that.

Not necessarily, one can imagine a spherical piston, able to support itself at a given radius regardless of the internal stresses.

Fair enough, but that doesn't remove the main problem.

It's just an idealization to able to ask the OP question, what purpose the OPer has in asking the question, I presume, is purely conceptual rather than physical.

There's a big difference between "if this much mass is within the schwarzschild radius do i have a black hole" and "if i start compressing a star will i make a black hole".
I'm not sure which of the two the OP had in mind, but i've been considering the latter.

Maybe an idealized spherical piston of arbitrary radius violates some rule of GR, or maybe it doesn't, I really couldn't say.

As far as i know(!) the idealized piston doesn't violate any rule of GR, but the description of the compressing of the star and answering the question as to what geometry will be the result of that is fraught with issues.

caveman1917
2011-May-26, 10:57 PM
How about past the EH ... lets say once an EH forms ... must the star collapse to a singularity? Or could there be a structure inside of the EH ( of course you would need to pass the EH to see it )

If you got a black hole, anything inside the event horizon must collapse towards the singularity in finite (quite little in fact) proper time. There is no possibility of structure. At least for a schwarzschild black hole. This doesn't apply to a kerr black hole, where you can develop structure within the inner cauchy horizon. But then again, that region is unstable.

Ken G
2011-May-27, 01:26 AM
I'm just not sure how one would describe such a situation.
For example the standard internal schwarzschild solution develops a pressure singularity even for a radius a bit above the schwarzschild radius.Yes, one can only be approximate with general statements-- somewhere close to the Schwarzschild radius is where you'd start to get problems, but perhaps not exactly it. That becomes especially true when one includes angular momentum, or the kinds of detailed internal dynamics you are talking about.

If the process results in a naked singularity rather than a schwarzschild black hole, there is no restriction on the outwards geodesics for it not to spring back.
Some might say that if the theory produces a naked singularity, the theory has done something wrong.

Not necessarily since the transition between the regimes must be smooth.
We can't just wait a bit and then consider it a schwarzschild geometry. The ultimate question is wether the geometry describing the compression will develop into the schwarzschild geometry or something else.Yes, Schwarzschild geometry is the gravitational geometry of a point mass, so only applies if we already have a black hole. However, we can imagine a transition from the Newtonian limit of a spherically symmetric mass distribution to the relativistic limit of a point mass, and say approximately where the gravitation will lead to permanent collapse. We can't be precise without a more detailed GR model, and as I understand it, analytic solutions of the GR equations are only available in a few idealized situations that we use as points of reference (like Schwarzschild). Perhaps that is basically what you are saying here.

But even in an idealized and isolated consideration there are problems. The solution for a spherically symmetric perfect fluid of radius r breaks down before r even gets to the schwarzschild radius. I don't know how we could idealize it more than that.
Yes, there's more complexity than the OPer probably intended!

There's a big difference between "if this much mass is within the schwarzschild radius do i have a black hole" and "if i start compressing a star will i make a black hole".
I'm not sure which of the two the OP had in mind, but i've been considering the latter.
Probably either question depends somewhat on unspecified details, but the overall result is likely to be more or less the same.

As far as i know(!) the idealized piston doesn't violate any rule of GR, but the description of the compressing of the star and answering the question as to what geometry will be the result of that is fraught with issues.No doubt.

caveman1917
2011-May-27, 10:58 PM
Some might say that if the theory produces a naked singularity, the theory has done something wrong.

That may be true, but collapsing fluid models are known to produce them in certain cases, which was my original point.
Since the pressure is so important in the OP scenario, we can't consider it a dust but must consider a fluid solution.
My main point is that we can't just state that the OP scenario will produce a schwarzschild geometry when we already know that the solutions closest to the OP scenario (collapsing fluids) don't always do that.

Yes, Schwarzschild geometry is the gravitational geometry of a point mass, so only applies if we already have a black hole. However, we can imagine a transition from the Newtonian limit of a spherically symmetric mass distribution to the relativistic limit of a point mass, and say approximately where the gravitation will lead to permanent collapse. We can't be precise without a more detailed GR model, and as I understand it, analytic solutions of the GR equations are only available in a few idealized situations that we use as points of reference (like Schwarzschild). Perhaps that is basically what you are saying here.

What i'm basically saying is that the analytic solutions (and numerical methods) that most closely resemble the OP scenario are known to exhibit unexpected behaviour such as the formation of naked singularities without an event horizon.

We can't state by fiat that it will produce a schwarzschild solution when we know that collapsing fluids don't necessarily do.
So although we could indeed imagine a transition from a newtonian limit to a schwarzschild geometry, it is irrelevant since we can't tell wether it will in fact give a schwarzschild geometry or not without doing a full GR treatment of the entire process.

Probably either question depends somewhat on unspecified details, but the overall result is likely to be more or less the same.

You may be right, but i have found that this assumption holds a lot less than one would like when actually doing (well, reading :)) the full GR treatment of similar scenarios.
If there's one thing black hole formation doesn't abide by, it's intuition, even intuition grounded in a good sense of newtonian physics.

Ken G
2011-May-28, 01:09 AM
You may be right, but i have found that this assumption holds a lot less than one would like when actually doing (well, reading :)) the full GR treatment of similar scenarios.
If there's one thing black hole formation doesn't abide by, it's intuition, even intuition grounded in a good sense of newtonian physics.Yes, it is certainly true that any GR-type answer that is not based on rather exhaustive experience with relevant numerical solutions has to be taken with a rather large grain of salt. All the same, that's pretty much all an OPer can really expect here! The issues you raise are valid, but are likely sources of lively debate even at the very frontier of GR dynamics. At some level, the "right" answer to OP questions like that is "nobody knows." Although honest, those types of answers are not terribly satisfying.

caveman1917
2011-May-28, 01:55 PM
Although honest, those types of answers are not terribly satisfying.

Which do you find more satisfying, the truth about our state of knowledge and ignorance, or a false sense of absolute knowledge?

I'd take the former everytime, but i can see how this depends on what one seeks with asking questions.

Ken G
2011-May-28, 08:07 PM
Which do you find more satisfying, the truth about our state of knowledge and ignorance, or a false sense of absolute knowledge?That is a very layered question, and an important one. Basically, any physics question sounds like it is asking "what is the truth", but it is really asking "what is our best current understanding, albeit likely to change either subtly or profoundly in the decades or even centuries ahead." And even that doesn't really cut it, because we must also append "given various idealizations we need to get a precise answer, and subject to whatever mathematical and conceptual level is appropriate for the person asking the question." We don't append those caveats to every question because it would take up a lot of room, but they are always there. I'm not taking Jack Nicholson's approach ("You want the truth? You can't handle the truth!"), I'm saying that scientific truth must be a rather versatile animal.

I know where you are coming from, you are saying that even detailed simulations can't categorically ascertain if a star squeezed to exactly its Schwarzschild radius will re-expand or not, but stars aren't going to be squeezed that way, so the OP is not really asking a physical question, they are asking a hypothetical question that they will use to help them assemble some conceptual point. I think the conceptual point there is that normally, compression causes pressure increases that lead to re-expansion, but gravity does not have to do that because its nonlinear nature allows for compression at some point to overcome pressure and prevent re-expansion, which is ultimately the source of astrophysical black holes-- regardless of the details of how core collapse actually occurs. But I don't say that what you are saying isn't perfectly true.

caveman1917
2011-May-29, 12:19 AM
I know where you are coming from, you are saying that even detailed simulations can't categorically ascertain if a star squeezed to exactly its Schwarzschild radius will re-expand or not

That's not the main point behind my argument.

Suppose that about every simulation of a collapsing perfect fluid produces a black hole. In that case we also cannot categorically ascertain the answer to the OP question but i would have no problem with an answer stating that it should produce a schwarzschild black hole, since it is a likely outcome.

But the fact is that the simulations that we have performed with collapsing fluids show that they do not always produce black holes, especially with high pressure conditions. Knowing that, and seeing that the OP scenario is one with skyrocketing pressure, the answer that it will produce a black hole doesn't seem all that truthful since we know that it is likely that complications will show up influencing the ultimate outcome.

I don't mind that we can't ascertain things categorically including all details. It's only because we know that the scenario is likely to show result-influencing complications why we should be honest and say we don't know.

I'm not arguing a simple fact about categorical detailed certainty, but about wether we have knowledge of counterindications or not.

I think the conceptual point there is that normally, compression causes pressure increases that lead to re-expansion, but gravity does not have to do that because its nonlinear nature allows for compression at some point to overcome pressure and prevent re-expansion, which is ultimately the source of astrophysical black holes-- regardless of the details of how core collapse actually occurs.

The difference is that the standard scenario has (or at least is modeled with) vanishing pressure over time whereas the OP scenario has diverging pressure over time, and that difference is very important with regards to the outcome of the process.

Ken G
2011-May-29, 01:42 AM
But the fact is that the simulations that we have performed with collapsing fluids show that they do not always produce black holes, especially with high pressure conditions. Knowing that, and seeing that the OP scenario is one with skyrocketing pressure, the answer that it will produce a black hole doesn't seem all that truthful since we know that it is likely that complications will show up influencing the ultimate outcome.Pressure increases are certainly not insignificant, but again, in high gravity situations the pressure isn't dominant because it controls the speed of the particles moreso than the curvature of inertial paths. The latter is actually increased by pressure, so it's not even clear that high pressure would make the black hole harder to form rather than easier. I really have little doubt that if you compress a star enough in a giant adiabatic piston, it will eventually form something black hole-like that will not re-expand, and this will happen at some point around the Schwarzschild radius, even if it might not be exactly that, and if you might get some additional dynamics along the way (like the envelope blowing off as in a supernova). Of course I could be wrong, but it would seem a pretty inevitable consequence of the nonlinearity of Einstein's gravity. Certainly it is a kind of external squeezing that simply does not happen to stars in practice, so the purpose of the answer is simply to make the point that eventually gravity can become so strong that it cares nothing about the pressure, or is even assisted by the pressure. That seems to me to be the purpose of the OP question, rather than the circumstances whereby you can get a singularity without an event horizon.

tommac
2011-May-31, 08:25 PM
What if there was a force, maybe that we dont know about, that could support or rather stop the collapse? Are you saying that such a force is impossible?

If you got a black hole, anything inside the event horizon must collapse towards the singularity in finite (quite little in fact) proper time. There is no possibility of structure. At least for a schwarzschild black hole. This doesn't apply to a kerr black hole, where you can develop structure within the inner cauchy horizon. But then again, that region is unstable.

WayneFrancis
2011-Jun-01, 02:43 AM
What if there was a force, maybe that we dont know about, that could support or rather stop the collapse? Are you saying that such a force is impossible?

Well might as well ask if it is impossible for invisible pink winged unicorns (IPWU) to stop a star from collapsing. Not knowing the properties of invisible pink winged unicorns neither I or anyone else can say one way or another if they could stop the collapse. What we can say is we don't have any reason to believe that IPWUs actually exist and if they do they don't seem to effect our universe in away that we can measure so they probably will not prevent star from collapsing.

But I agree with Ken G here. While I respect caveman1917's knowledge I think caveman1917 has gone way beyond answering what the original poster was asking and even though technically caveman1917's answers might be right it comes across to me like someone trying to ram the full implications of SR down someones throat when they are asking about the collision of 2 objects each travelling at relative speed of just 30km/hr. This is easy to do in forums where 2 great minds start talking about subjects like this the discussion can get WAY above what the original poster asked.

caveman1917
2011-Jun-01, 05:51 AM
What if there was a force, maybe that we dont know about, that could support or rather stop the collapse? Are you saying that such a force is impossible?

Technically speaking, yes such a force is impossible, at least if you are using the term strictly.

The event horizon (the apparent one), is a null surface of zero expansion. A null surface means that the proper time between events on the surface is zero, an analog in flat spacetime would be an spherical wavefront expanding at c.

Suppose you are in flat spacetime outside a spherical wavefront, let's call this S0. Now suppose at some time S0 passes you and you are inside it. You want to return to the 'outside', what do you have to do? You can use all the acceleration you want, you won't be able to go faster than c to catch up with it again. You can even use infinite acceleration if you want, it won't get you back 'outside', the 'outside' is in your past, it is not in some spatial direction but in a time direction.

If this reminds you of how it's said that the radial dimension turns timelike below the event horizon, good ;)
Back to the black hole, the extra thing we have here is that consecutive 'inner shells' below the event horizon are just as well null surfaces, but even worse, they have inwards expansion (they contract towards the singularity).

So even if you had infinite acceleration (infinite force), it wouldn't matter squat as to your ultimate fate, since the only direction you could apply that acceleration (point your rockets - use the force :)) towards to get out again would be to your past. Even infinite force doesn't cut it anymore once you're below the event horizon, you're going to hit the singularity in finite proper time. Even worse, you'll hit it in less proper time than if you had just let yourself "fall in", since a geodesic maximises proper time.

Jeff Root
2011-Jun-01, 07:22 PM
I am extremely positively impressed with Ken's posts in this thread.
Not only do I agree with his facts, as is virtually always true, but I
agree with and even like all his interpretations of those facts!

My "feeling" is that there is something wrong with a simulation which
ends up in a naked singularity. I don't trust fluid dynamics simulations
any farther than I can throw the thing being simulated! (Think about it.)

What if there was a force, maybe that we dont know about, that could
support or rather stop the collapse? Are you saying that such a force
is impossible?
If general and/or special relativity is correct, such a force is impossible.
If no signal can travel faster than the speed of light, then such a force
is impossible.

The force would have to be enormously strong. It seems very unlikely
that an enormously strong force would exist without any effect of its
existence being detected.

-- Jeff, in Minneapolis

tommac
2011-Jun-01, 08:11 PM
I would think there are at least a handful of people on this board that would disagree with you on this. I will need to dig up the posts but I was just on a thread where someone posts that they dont believe that the mass compresses into a point and this is all just a limitation of the theory of general relativity.

Technically speaking, yes such a force is impossible, at least if you are using the term strictly.

The event horizon (the apparent one), is a null surface of zero expansion. A null surface means that the proper time between events on the surface is zero, an analog in flat spacetime would be an spherical wavefront expanding at c.

Suppose you are in flat spacetime outside a spherical wavefront, let's call this S0. Now suppose at some time S0 passes you and you are inside it. You want to return to the 'outside', what do you have to do? You can use all the acceleration you want, you won't be able to go faster than c to catch up with it again. You can even use infinite acceleration if you want, it won't get you back 'outside', the 'outside' is in your past, it is not in some spatial direction but in a time direction.

If this reminds you of how it's said that the radial dimension turns timelike below the event horizon, good ;)
Back to the black hole, the extra thing we have here is that consecutive 'inner shells' below the event horizon are just as well null surfaces, but even worse, they have inwards expansion (they contract towards the singularity).

So even if you had infinite acceleration (infinite force), it wouldn't matter squat as to your ultimate fate, since the only direction you could apply that acceleration (point your rockets - use the force :)) towards to get out again would be to your past. Even infinite force doesn't cut it anymore once you're below the event horizon, you're going to hit the singularity in finite proper time. Even worse, you'll hit it in less proper time than if you had just let yourself "fall in", since a geodesic maximises proper time.

tommac
2011-Jun-01, 08:13 PM
The force would have to be enormously strong. It seems very unlikely
that an enormously strong force would exist without any effect of its
existence being detected.

The other alternative is that an infinite amount of mass can be infinitely compressed into a point.

Grey
2011-Jun-01, 09:17 PM
The other alternative is that an infinite amount of mass can be infinitely compressed into a point.Well, a finite amount of mass infinitely compressed into a point, right? Nobody is suggesting there are infinitely massive black holes around. As far as we know, an electron might be a finite amount of mass that's a point object, too.

Jeff Root
2011-Jun-01, 09:41 PM
Although I think that an electron is a fundamentally different
kind of thing from a black hole, I think the comparison is good.
No measurement has shown an electron to be anything other
than "point-like". The mass which collapses to form a black
hole would similarly become "point-like". In both cases, we
can't say that the mass is actually all located at a point, but
there is no compelling reason to say that it isn't. It is just a
very strange thing to try to imagine.

I will mention what has been said before, that a black hole
is forever collapsing: The matter is forever becoming more
dense as it collapses, so it doesn't reach infinite density in
finite time. Infinite density is just the theoretical end state
after infinite time. I suspect that uncertainty obscures the
significance of the matter's size anyway, when it reaches
sub-atomic spatial dimensions.

-- Jeff, in Minneapolis

Ken G
2011-Jun-01, 09:50 PM
Actually it isn't accurate to say that a black hole requires an infinite time to reach an infinite density. It's just not that easy to be real precise when talking about the time it takes a black hole to do something. Presumably, the best way to talk about the time it takes a black hole to do something is to look at the proper time of its constituents, and its constituents reach the central singularity in a rather small proper time. So it depends on who you ask-- if you ask the things that are part of the black hole, they would say (if they could survive the experience) that they made it to the central singularity rather quickly. If you ask the person who remains far from the black hole, the very meaning of time inside the black hole for that person outside is not really a physically meaningful kind of time-- it's more like an arbitrary coordinate choice with no particular physical significance. The most natural way to coordinatize time for such a distant observer behaves very strangely-- what we think of as time inside the black hole gets replaced by what we normally think of as a concept of distance, and that stays finite too. What goes infinite is the outside person's interpretation of how long it takes an object to reach the event horizon, but if there's an event horizon, there's already a singularity.

Mouser
2011-Jun-01, 10:50 PM
Once there is enough mass it it will form the black hole and by their nature will not "snap back"

Except shrinking the sun (by some unspecified means) would not give it mass.

tommac
2011-Jun-01, 11:04 PM
Why only a finite amount? What is the max limitation?

Well, a finite amount of mass infinitely compressed into a point, right? Nobody is suggesting there are infinitely massive black holes around. As far as we know, an electron might be a finite amount of mass that's a point object, too.

tommac
2011-Jun-01, 11:07 PM
I suspect that uncertainty obscures the
significance of the matter's size anyway, when it reaches
sub-atomic spatial dimensions.
This statement hints that there is a maximum compressed state.

tommac
2011-Jun-01, 11:09 PM
This part of the thread was about what happens inside the EH for the local observer and if there can be additional compression.

Actually it isn't accurate to say that a black hole requires an infinite time to reach an infinite density. It's just not that easy to be real precise when talking about the time it takes a black hole to do something. Presumably, the best way to talk about the time it takes a black hole to do something is to look at the proper time of its constituents, and its constituents reach the central singularity in a rather small proper time. So it depends on who you ask-- if you ask the things that are part of the black hole, they would say (if they could survive the experience) that they made it to the central singularity rather quickly. If you ask the person who remains far from the black hole, the very meaning of time inside the black hole for that person outside is not really a physically meaningful kind of time-- it's more like an arbitrary coordinate choice with no particular physical significance. The most natural way to coordinatize time for such a distant observer behaves very strangely-- what we think of as time inside the black hole gets replaced by what we normally think of as a concept of distance, and that stays finite too. What goes infinite is the outside person's interpretation of how long it takes an object to reach the event horizon, but if there's an event horizon, there's already a singularity.

WayneFrancis
2011-Jun-02, 12:48 AM
Actually it isn't accurate to say that a black hole requires an infinite time to reach an infinite density. It's just not that easy to be real precise when talking about the time it takes a black hole to do something. Presumably, the best way to talk about the time it takes a black hole to do something is to look at the proper time of its constituents, and its constituents reach the central singularity in a rather small proper time. So it depends on who you ask-- if you ask the things that are part of the black hole, they would say (if they could survive the experience) that they made it to the central singularity rather quickly. If you ask the person who remains far from the black hole, the very meaning of time inside the black hole for that person outside is not really a physically meaningful kind of time-- it's more like an arbitrary coordinate choice with no particular physical significance. The most natural way to coordinatize time for such a distant observer behaves very strangely-- what we think of as time inside the black hole gets replaced by what we normally think of as a concept of distance, and that stays finite too. What goes infinite is the outside person's interpretation of how long it takes an object to reach the event horizon, but if there's an event horizon, there's already a singularity.

I like the descriptions that emphasizes that these are coordinate system choices. If GR is correct, I have no reason to doubt it, then the concept of comparing clocks not in the same location can be very arbitrary. If you think of the vectors in the stress energy tensor it becomes obvious that using parallel transport will only lead to a consistent result if space is perfectly flat. Through curved space the path 1 vector is taken to compare to another vector determines the the final comparison. Like wise comparing distances across an event horizon, to me, is utterly meaningless.

So complaining that to an external point of view the event horizon can never form is, to me, meaningless because I don't care if something is in my infinite future because that IS an event horizon. IE no matter how long I travel I'll never be able to reach something beyond that event horizon. I think people get to tied up thinking that they should be able to compare clocks all the time and there are times when comparing clocks is not even hypothetically possible.

WayneFrancis
2011-Jun-02, 12:52 AM
Once there is enough mass it it will form the black hole and by their nature will not "snap back"Except shrinking the sun (by some unspecified means) would not give it mass.

What I should have said was "Once there is enough mass within a given volume it will form the black hole and by their nature it will not 'snap back'

all objects have enough mass for a black hole...that mass just isn't within a small enough volume to produce a black hole. But I get your point that the sun doesn't have enough mass to form a black hole normally but we aren't talking about forming a black hole via normal means.

WayneFrancis
2011-Jun-02, 01:03 AM
This statement hints that there is a maximum compressed state.

I don't see any problem with a singularity. Think about it this way. We aren't saying the matter stays as fermions and must obey the Pauli exclusion principle. At some point I'd expect that the fermions start reducing to pure energy. Now if they are just photons you might think that they'd be able to travel away at the speed of light but remember this, to that mass's proper time, is already, as caveman1917 points out very eloquently in post #28 (http://www.bautforum.com/showthread.php/115876-If-you-compressed-something-to-a-black-hole-do-you-have-to-keep-compressing-it?p=1896436#post1896436) within a region where the photons can't get "out" because "out" is in the past. There is no problem packing energy into a point beside getting that energy. So you can think of the singularity as some compressed state but really what are you comparing it to? Some distance measurement outside of the event horizon? How can you do that...you can't compare clocks or rulers at that point.

caveman1917
2011-Jun-02, 03:09 AM
My "feeling" is that there is something wrong with a simulation which
ends up in a naked singularity.

This is not just some computer glitch in numerical simulations, naked singularities show up all over the place in analytical collapse solutions.
You don't even need a fluid solution (even though that would be more appropriate to the OP question), a collapsing dust that's not homogeneous will already do.
It's plain GR, not just a numerical approximation error. The belief in the weak cosmic censorship hypothesis may be popular, but it is not supported by theoretical research.

The force would have to be enormously strong.

Not even that, it could be infinite if you want. The problem is that all paths lead towards the singularity, you have no direction to apply this force to that will do anything else than make you (or whatever structure you're trying to maintain within the EH) reach the singularity faster.

caveman1917
2011-Jun-02, 03:14 AM
I would think there are at least a handful of people on this board that would disagree with you on this. I will need to dig up the posts but I was just on a thread where someone posts that they dont believe that the mass compresses into a point and this is all just a limitation of the theory of general relativity.

If you want to include hypothetical theories that haven't been discovered yet, who knows indeed..
It's not possible in GR at least.

caveman1917
2011-Jun-02, 03:17 AM
Why only a finite amount? What is the max limitation?

The two aren't contradictory.
If i say "give me an integer", the reply will always be finite, even though there's no max limitation.

Strange
2011-Jun-02, 10:51 AM
I would think there are at least a handful of people on this board that would disagree with you on this. I will need to dig up the posts but I was just on a thread where someone posts that they dont believe that the mass compresses into a point and this is all just a limitation of the theory of general relativity.

That seems like a good "common sense" argument. On the other hand, if the radial dimension becomes time-like, that does rather mean that the concept of being" compressed to a point" doesn't have its common sense meaning; instead it seems to mean compressed to zero time. Although it is not clear what that means in physical terms either....

tommac
2011-Jun-02, 01:18 PM
Is it timelike for the local freefaller? Or just the external observer?

That seems like a good "common sense" argument. On the other hand, if the radial dimension becomes time-like, that does rather mean that the concept of being" compressed to a point" doesn't have its common sense meaning; instead it seems to mean compressed to zero time. Although it is not clear what that means in physical terms either....

tommac
2011-Jun-02, 01:22 PM
BUt if I asked what is the max integer could you provide a true answer? The point I was making is that if everything could compress to a point then in theory there would be no limit to the amount of energy you could fit into 0 volume. While this may work out in mathmatical terms for GR ... it doesnt seem that it could work out in the real world. Maybe one question I would have is what is the most energy that can fit into a local ( at the point of observation ) planck length.

The two aren't contradictory.
If i say "give me an integer", the reply will always be finite, even though there's no max limitation.

tommac
2011-Jun-02, 01:23 PM
Yes ... but I think it is generally agreed that GR breaks down at the planck scale.

If you want to include hypothetical theories that haven't been discovered yet, who knows indeed..
It's not possible in GR at least.

Grey
2011-Jun-02, 01:42 PM
Why only a finite amount? What is the max limitation?There's no maximum limitation, but that's not the same as having an infinite amount of mass. There is no highest integer, but there is also no integer equal to infinity. Similarly, there is no upper limit to the size of a black hole, but there are also no black holes of infinite mass.

caveman1917
2011-Jun-02, 01:51 PM
Is it timelike for the local freefaller? Or just the external observer?

External observer.

caveman1917
2011-Jun-02, 01:54 PM
Yes ... but I think it is generally agreed that GR breaks down at the planck scale.

Semi-classical gravity (combining quantum mechanics with a weak-field approximation of GR) breaks down at the planck scale, GR itself does just fine all the way down.

Grey
2011-Jun-02, 02:02 PM
BUt if I asked what is the max integer could you provide a true answer? The point I was making is that if everything could compress to a point then in theory there would be no limit to the amount of energy you could fit into 0 volume. While this may work out in mathmatical terms for GR ... it doesnt seem that it could work out in the real world.That's always going to be true. There are plenty of solutions to the field equations of general relativity that don't necessarily apply to the real world. As far as general relativity is concerned, there really is no upper limit to the amount of energy that can be contained in a given volume. For the real universe, we're limited to the amount of matter we could actually go out and collect and throw into a black hole. The biggest ones seem to be on the order of a few billion solar masses.

Maybe one question I would have is what is the most energy that can fit into a local ( at the point of observation ) planck length.We have no idea. We are sure that if you take the whole universe and compress it down to that size, that our current understanding of physics is not sufficient to describe how it will behave. It's also probably true that even if you have less than the whole universe in a volume that small, our understanding of how it behaves is pretty limited. But as far as we can tell, it turns out that this isn't as much of a problem as you'd think, since compressing even a moderate amount of energy into a volume that small produces an event horizon, which strongly limits how the energy in that volume can interact with the outside world. So we can't do experiments to find out exactly what happens to the matter inside a black hole, whether it's really compressed to a point, or something else happens instead. But the details don't matter, because they won't make a difference to the universe outside the black hole anyway.

tommac
2011-Jun-02, 02:55 PM
Remember though we are talking about the local observer not the external observer. We all agree that the External observer cant see past the EH. But as a freefaller or one that will hit the singularity there is no limit to the amount of energy

We have no idea. We are sure that if you take the whole universe and compress it down to that size, that our current understanding of physics is not sufficient to describe how it will behave. It's also probably true that even if you have less than the whole universe in a volume that small, our understanding of how it behaves is pretty limited. But as far as we can tell, it turns out that this isn't as much of a problem as you'd think, since compressing even a moderate amount of energy into a volume that small produces an event horizon, which strongly limits how the energy in that volume can interact with the outside world. So we can't do experiments to find out exactly what happens to the matter inside a black hole, whether it's really compressed to a point, or something else happens instead. But the details don't matter, because they won't make a difference to the universe outside the black hole anyway.

Shaula
2011-Jun-02, 03:17 PM
Remember though we are talking about the local observer not the external observer. We all agree that the External observer cant see past the EH. But as a freefaller or one that will hit the singularity there is no limit to the amount of energy
Irrelevant to the point that physics breaks down so the answer to your question is "we have no idea because we have no consistent model for energy densities that high"

Grey
2011-Jun-02, 03:47 PM
Remember though we are talking about the local observer not the external observer. We all agree that the External observer cant see past the EH. But as a freefaller or one that will hit the singularity there is no limit to the amount of energyI don't understand your point. Yes, there is no theoretical limit to the amount of energy compressed into a small volume. But again, that is not the same as saying that there is an infinite amount of energy compressed into a small volume.

Jeff Root
2011-Jun-02, 04:56 PM
Is it timelike for the local freefaller? Or just the external observer?
External observer.
Tom's question was very good, and the answer is most interesting.
It fits my understanding, yet I hadn't really thought about it.

I asserted that objects falling to the center of a black hole fall
forever. That is because there is nothing to stop the fall, and
because the "gravity well" keeps getting deeper and deeper,
without limit. This increasing depth is in the time dimension.
Everything is squeezed together in the horizontal direction and
stretched apart in the radial direction. But I don't quite know
what that means. Is everything stretched out in time?? If so,
what does that mean? Kip Thorne says that everything falling
into a black hole gets farther and farther apart in the radial
direction, but to what extent is that a stretching in/of space,
and to what extent is it a stretching in/of time? How does this
fit with the prediction which Ken pointed out, that infalling
objects "reach the singularity" in a finite, very short time?
I know it must fit because both predictions result from the
same calculations. So it appears to be just a matter of
describing the predictions correctly and understandably.

-- Jeff, in Minneapolis

caveman1917
2011-Jun-02, 06:58 PM
I asserted that objects falling to the center of a black hole fall
forever. That is because there is nothing to stop the fall, and
because the "gravity well" keeps getting deeper and deeper,
without limit. This increasing depth is in the time dimension.

There's the singularity to stop the fall, so i'm not quite sure where you're getting the "increasing depth without limit" idea.
But it's not something that's sitting there at some location, it is an event in the future of the infaller, just as unavoidable as death or taxes :)

Everything is squeezed together in the horizontal direction and
stretched apart in the radial direction. But I don't quite know
what that means.

An infalling extended object will be subjected to tidal forces, and there's nothing wrong as far as he is concerned.

Is everything stretched out in time?? If so,
what does that mean?

So the question is, how do tidal forces inside the event horizon make sense to the outside observer?

Kip Thorne says that everything falling
into a black hole gets farther and farther apart in the radial
direction, but to what extent is that a stretching in/of space,
and to what extent is it a stretching in/of time? How does this
fit with the prediction which Ken pointed out, that infalling
objects "reach the singularity" in a finite, very short time?
I know it must fit because both predictions result from the
same calculations. So it appears to be just a matter of
describing the predictions correctly and understandably.

Good question. I suppose we could consider it somewhat like how seperations between participants in a race are given, as differences in time wrt to some reference point rather than spatial differences (the second runner is 5 seconds behind the leader, instead of 10 meter). So we could say the feet of an infaller are 5 seconds ahead of his head at first (in the sense that it will hit the singularity 5 seconds earlier). But this increases during the fall, so some time later we'll say the feet are 10 seconds ahead, and so on.
All of this is pretty moot since to an external observer nothing reaches the event horizon in the first place, but a good question nevertheless.

Jeff Root
2011-Jun-02, 08:10 PM
My understanding is that at the event horizon, the time aspect
of spacetime has been increased so much (compared to "flat"
spacetime) that it is "equal to" the spatial aspect. Outside the
event horizon, space dominates. Inside, time dominates. The
closer you get to the center, the more dominant time becomes.

But an infaller below the event horizon would still see space
and time close to him as pretty much the same as it looks in
"flat" space. His feet would still be about the same distance
from his head until he gets close enough to the center for the
tide to pull his head and feet off of his body. Superman,
whose body has a tensile strength somewhat exceeding that
of a high-grade steel, would be able to observe closer to the
center, and would find that he still sees things extending in
the radial direction. Objects that fell in just before him, or
that he throws down, are visible to him as they fall farther
and farther away from him, toward the center. He would not
be able to see any object reach the center, though, because
the only light he can see from objects below him is light
which was emiited or reflected by those objects when they
were farther from the center than Superman's eyes are when
the light reaches his eyes.

I'm pretty sure the feet of an infaller could not be 5 seconds
ahead of the infaller's head until the infaller is pulled apart.
More like 5 nanoseconds or less. But two objects dropped
into the black hole, one after the other, would appear to an
infaller to move steadily apart as they fall, due to the tide.

How do you imagine the singularity would stop an object
from falling any further? If a particle reaches the singularity,
it increases the "depth" of the "gravity well". Which is to
say it increases the curvature at the black hole's center.
So the particle has a tiny bit farther to fall. Any particles
that fall in after that particle also have farther to fall. And
all the mass-energy which reached the singularity before
that particle also has a tiny bit farther to fall, as a result
of that particle's reaching the singularity. That is a lot of
mass-energy, so when it falls that little bit, it increases
the depth of the gravity well even further... We have a
runaway increase in "depth" of the gravity well. The
curvature of spacetime at the center approaches infinite
more and more closely as the mass-energy approaches
infinite density more and more closely. There is nothing
to stop it.

So, what is the measure of "reaching the singularity"?
What is meant by that phrase?

-- Jeff, in Minneapolis

caveman1917
2011-Jun-02, 11:32 PM
How do you imagine the singularity would stop an object
from falling any further? If a particle reaches the singularity,
it increases the "depth" of the "gravity well".

Yes, by a tiny little bit (depending on how much mass exactly you're throwing in).

We have a runaway increase in "depth" of the gravity well.

You might be taking the "depth of the gravity well" analogy a bit too strict.
The interval between events (such as the particle being some distance from the singularity and the particle hitting the singularity) is given by the proper time along a geodesic connecting those events.
Either way, if we had a runaway increase in this interval as you claim, it means we have a runaway increase in the mass of the black hole, which isn't the case.

So, what is the measure of "reaching the singularity"?
What is meant by that phrase?

It is that event through which geodesics cannot be extended anymore, ie the worldlines of particles "end" there.
Which incidentally is also the problem with them, since we cannot determine the future through them (cannot extend worldlines beyond them), so if we got naked singularities we'd in general (barring some technical details) have a spacetime section that cannot be determined.

Jeff Root
2011-Jun-03, 12:52 AM
We have a runaway increase in "depth" of the gravity well.
You might be taking the "depth of the gravity well" analogy a
bit too strict.
Maybe, but I don't think so. There isn't anything to stop the
inward fall of matter. As the matter falls into an ever-smaller
volume, the density keeps rising. There isn't anything to stop
the increase in density, so the spacetime curvature keeps
increasing. Runaway feedback loop with no limit. It tends
toward infinite density and infinite curvature at the center, but
would only reach infinite density and infinite curvature after
infinite time.

The interval between events (such as the particle being some
distance from the singularity and the particle hitting the singularity)
is given by the proper time along a geodesic connecting those events.
Either way, if we had a runaway increase in this interval as you claim,
it means we have a runaway increase in the mass of the black hole,
which isn't the case.
No, the mass doesn't increase, just the density.

-- Jeff, in Minneapolis

WayneFrancis
2011-Jun-03, 02:47 AM
Remember though we are talking about the local observer not the external observer. We all agree that the External observer cant see past the EH. But as a freefaller or one that will hit the singularity there is no limit to the amount of energy

I don't get what you mean here? To a freefaller the amount of energy they have available to them is very limited. The amount of energy that has fallen into the singularity is also finite. The amount of energy that could fall into the black hole after the freefaller is also finite even if the universe is infinite in size. So even though I don't understand your statement I'm inclined to say that there is a limit to the amount of energy but again there is nothing preventing theoretical upper limit to the amount of energy in a given volume just a practical one.... I think I'm understanding your question now and I think I answered it...I'm sure someone will/has answered it more eloquently then I.

WayneFrancis
2011-Jun-03, 02:49 AM
Irrelevant to the point that physics breaks down so the answer to your question is "we have no idea because we have no consistent model for energy densities that high"

Just saying what I said about there being no apparent upper limit fits with this. IE we don't have a model that precludes it just a model that can't answer it.

WayneFrancis
2011-Jun-03, 02:53 AM
Tom's question was very good, and the answer is most interesting.
It fits my understanding, yet I hadn't really thought about it.

I asserted that objects falling to the center of a black hole fall
forever. That is because there is nothing to stop the fall, and
because the "gravity well" keeps getting deeper and deeper,
without limit. This increasing depth is in the time dimension.
Everything is squeezed together in the horizontal direction and
stretched apart in the radial direction. But I don't quite know
what that means. Is everything stretched out in time?? If so,
what does that mean? Kip Thorne says that everything falling
into a black hole gets farther and farther apart in the radial
direction, but to what extent is that a stretching in/of space,
and to what extent is it a stretching in/of time? How does this
fit with the prediction which Ken pointed out, that infalling
objects "reach the singularity" in a finite, very short time?
I know it must fit because both predictions result from the
same calculations. So it appears to be just a matter of
describing the predictions correctly and understandably.

-- Jeff, in Minneapolis

This gets into the holographic principal and besides some general and, on my part, gross analogies, that I'd probably butcher, I couldn't do it justice.

WayneFrancis
2011-Jun-03, 02:58 AM
Yes, by a tiny little bit (depending on how much mass exactly you're throwing in).

You might be taking the "depth of the gravity well" analogy a bit too strict.
The interval between events (such as the particle being some distance from the singularity and the particle hitting the singularity) is given by the proper time along a geodesic connecting those events.
Either way, if we had a runaway increase in this interval as you claim, it means we have a runaway increase in the mass of the black hole, which isn't the case.

It is that event through which geodesics cannot be extended anymore, ie the worldlines of particles "end" there.
Which incidentally is also the problem with them, since we cannot determine the future through them (cannot extend worldlines beyond them), so if we got naked singularities we'd in general (barring some technical details) have a spacetime section that cannot be determined.
CC At least for me your description of the geodesics is working well.

WayneFrancis
2011-Jun-03, 03:09 AM
Maybe, but I don't think so. There isn't anything to stop the
inward fall of matter. As the matter falls into an ever-smaller
volume, the density keeps rising. There isn't anything to stop
the increase in density, so the spacetime curvature keeps
increasing. Runaway feedback loop with no limit. It tends
toward infinite density and infinite curvature at the center, but
would only reach infinite density and infinite curvature after
infinite time.

To me your view is moot and well not really a big deal. No matter will every hit the singularity. Tidal forces will change that matter into energy long before that happens. The matter will turn in to energy in a very finite amount of time. Will the energy reach the singularity? Well ... who cares. There isn't anything that gives a crap about "time" at those scales if there is even anything like the concept of time at those energy levels and scales.

IE nothing can follow it down to see if your right. To me the "singularity" doesn't have to be a singularity in size because, at this point and to my knowledge, it doesn't matter. It might have great meaning to theoretical particle physicist and the like but this probably has to do more with them understanding elementary particles better and maybe some unified theory of gravity. Alice would cease to exist as Alice in a very finite amount of time.