Where is the matter in a black hole?

[Grinkle]

Green Dwarf -

I am pretty sure that you and I share the same befuddlement. I have posted threads that ask how black holes of different mass can exist in my now and be observable by me in my now if also in my now its impossible for me to ever see any mass crossing an EH. I have never gotten responses more satisfying than "learn more math", which I accept, but am still frustrated by.

Your description of a black hole really being an accretion of more and more matter at the EH is also where my musings end up.

I expect I'd have enjoyed having you as a teacher!

 

[Nugatory]

I have posted threads that ask how black holes of different mass can exist in my now and be observable by me in my now if also in my now its impossible for me to ever see any mass crossing an EH. I have never gotten responses more satisfying than "learn more math", which I accept, but am still frustrated by.

It's not as complicated as some of the answers make it out to be. You'll never see any mass crossing the event horizon because light from that event will never reach your eyes or your detectors. That doesn't mean it didn't happen - all sorts of things happen every day that we don't see. We do observe the increase in the size of the black hole as a result of the increased mass, so we can reasonably conclude that the mass did cross the event horizon even though we didn't see it happen.

 

[Grinkle]

Nugatory -

Thanks for the response.

You'll never see any mass crossing the event horizon because light from that event will never reach your eyes or your detectors. That doesn't mean it didn't happen

I read your response as saying that mass never crossing the event horizon to my measurement is an optical illusion, not proper time dilation. Is that a fair summary? If so, how long do I need to let my clock tick to be confident that the matter has crossed the EH and what I am observing is the illusion?

We do observe the increase in the size of the black hole as a result of the increased mass, so we can reasonably conclude that the mass did cross the event horizon even though we didn't see it happen.

I struggle to get past the above as an if-then proposition. If I see black holes of different size, then it follows that mass must cross the EH in less than infinite time by my clock. My struggle comes from my perhaps incorrect understanding that GR predicts I will never observe mass crossing an EH in finite time.

How can one outside the EH tell the difference between matter that has crossed the EH and matter that is approaching and very close to the EH?

 

[Bernie G]

No, and until we have a solid theory of quantum gravity, we are not likely to understand what really goes on at the center. An infinitely dense point of zero dimensions containing all of the mass is not generally believed to be physical and that's why we call it a "singularity"

What if space isn't curved in the singularity? Maybe pressure overcomes gravity in the singularity.

 

[anorlunda]

What if space isn't curved in the singularity? Maybe pressure overcomes gravity in the singularity.

That is speculation.

 

[phinds]

What if space isn't curved in the singularity? Maybe pressure overcomes gravity in the singularity.

It's called a "singularity" because we don't know what's going on there. You can speculate anything you like, but this forum is not a good place to do that.

 

[zsolmanz]

How can one outside the EH tell the difference between matter that has crossed the EH and matter that is approaching and very close to the EH?

The broader question here is:
"How does relativity work"

For instance, if an object travels at 0.9c and oscillates its coefficient of reflectivity from 0 to 1 every 1s in proper time (its own reference time), at what frequency does a static observer see it flash?
What if it traveled at 0.99c? 0.999c?
Eventually the object will be traveling so fast that although it continues to oscillate in proper time, there will be no observable change in reflectivity in coordinate time. At this point, how does that change in reflectivity have any influence on external observers? If it has no observable change, then from the perspective of the observer it hasn't happened...

Similarly, if matter approaching a black hole cannot be *observed* to fall into the black hole in any way shape or form, how does the black hole change properties (as in externally-observable properties) over time?

Bonus question:
If the moving object above were quantum-entangled with a static one (they have linked reflectivity), at what frequency would the static object oscillate?

 

[Nugatory]

What if space isn't curved in the singularity? Maybe pressure overcomes gravity in the singularity.

It's meaningless to speak of whether space is curved at the singularity or not, because the singularity only appears as a result of calculating the curvature at the point of the singularity.

However, I expect that you're trying to say something else, that perhaps some as-yet-unknown physics comes into play under those conditions of extremely high density across extremely short distances, and that prevents the collapse down to a point of infinite density and curvature. That's speculation, but it's pretty good speculation; no one will be surprised if that's how it turns out. However...

That is speculation.

It's called a "singularity" because we don't know what's going on there. You can speculate anything you like, but this forum is not a good place to do that.

As phinds and anorlunda suggest, this is not the place to speculate about what that as-yet-unknown physics might be. When something makes it into a peer-reviewed journal, then there will be a theory to discuss here.

 

[Dr Wu]

Although I'm strictly an armchair observer in all this, I tend to agree with Green Dwarf. Yes, I can well understand that any infalling phenomenon - whether it be a cow or the zippiest neutrino - crossing the event horizon of a black hole will very rapidly reach the singularity. Nonetheless, this 'rapidity' would seem to be entirely relative to what is doing the moving and who is doing the thinking about it from the other side of the horizon. In other words, while it might take a shaving of a nanosecond to reach the centre of a given BH, that same temporal shaving, as far as the rest of the universe is concerned, could conceivably last for aeons. And then what? That's what I want to know.

 

[phinds]

Although I'm strictly an armchair observer in all this, I tend to agree with Green Dwarf. Yes, I can well understand that any infalling phenomenon - whether it be a cow or the zippiest neutrino - crossing the event horizon of a black hole will very rapidly reach the singularity. Nonetheless, this 'rapidity' would seem to be entirely relative to what is doing the moving and who is doing the thinking about it from the other side of the horizon. In other words, while it might take a shaving of a nanosecond to reach the centre of a given BH, that same temporal shaving, as far as the rest of the universe is concerned, could conceivably last for aeons. And then what? That's what I want to know.

Nugatory answered that in post #19

 

[yoron]

Just another thought following on from my last post. In the picture I painted, from the perspective of the outside observer, the cow will never reach the center of the black hole to become part of a singularity; and yet from the perspective of the cow, it does. This seems to be a contradiction. This is probably because there's a flaw in my logic. But is it possible that the space inside the event horizon becomes a different universe which can have a different (and seemingly contradictory) history?

It's not a contradiction, it's a logic bound to mass, speed, and 'time'. If you define 'c' as a local constant, then define time as connected to your local measurement of 'c', as per counting oscillations of some 'light clock'. Then locally measured 'time' never stops, neither does 'c'. And as far as I know there is no way for 'time' to tick backwards, it just 'stops' at most, as measured by you relative some black hole. Although there exist the idea of https://en.wikipedia.org/wiki/Closed_timelike_curve . And it's no illusion to me, what you see is what you get so to speak. On the third tentacle, time as such, locally measured, only have one direction as I think of it, into a future.

 

[Dr Wu]

I chanced upon this comment, which I found via a link posted by another contributer to this interesting thread (I am unable to locate it at present). It would appear then that there are exclusions to what appears from my current state of unknowing to be a counterintuitive reading of how GR operates above, upon and within a black hole. NB. The italics are my own.

"Remark 4. In Reissner-Nordstr¨om and Kerr black holes under their event horizons (which are quite similar to Schwarzschild’s) there is another remarkable surface — the Cauchy horizon. And that horizon does have the property in discussion: an astronaut falling into the black hole reaches the Cauchy horizon in a finite proper time and crosses it in a point p that contains in its causal past the whole “external universe”. Such an astronaut, indeed, will be able to see the death of stars and galaxies."

In the meantime, unable to find an easily digestible account of how Krustal diagrams figure in the (internal?) structure of black holes, I am at present seeking some illumination by reading up on Penrose diagrams.

 

[Zentrails]

Can we know that? Can we observe anything at all of the singularity?

I understand that the mass and charge of the BH are detectable from outside the BH, but that tells us nothing about the possible radius of the core/singularitty; does it?

A spinning BH is theorized to cause frame dragging. That may be a way to indirectly make some singularity measurements. Course, we haven't even been able to detect gravity waves yet.

 

[Zentrails]

The event horizon is a coordinate surface that has no physicality. Putting aside the fact nothing is actually there,

Not saying you are wrong, but doesn't Hawking believe the EH contains information?

 

[Grinkle]

Not saying you are wrong, but doesn't Hawking believe the EH contains information?

My understanding of Hawking's description of the event horizon (or some horizon around a singularity, if not really the EH) is that it is a surface that to an outside observer is geometrically defined by having a specific consistent-throughout-the-surface temperature and except for the black-body radiation resulting from the >0K temperature, to be completely opaque. To me, that qualifies as being something. I don't know what we all precisely might mean by something vs nothing though.

 

[dreens]

Hey Green Dwarf,

At time t0 on earth, a cow is sent off toward the black hole in the center of the galaxy. Does there exist a finite time t1 on earth, after which even the most powerful conceivable rocket could not rescue the cow? Based on your shell argument, I imagine you might think "NO". This is what I used to think for a few years in between taking GR for the first time and sitting across a desk from a black hole theorist for a few hours.

However the answer is "YES". To convince yourself of this, think from the cow's perspective. The cow can still watch things on Earth after it crosses the EH, for a brief time before it hits the singularity. So if the rescue rocket is sent off at an Earth time t2 such that the cow sees CNN's coverage of the rocket launch just after it has crossed the EH in its own frame, the rescue mission is going to fail despite JPL's efforts.

The Earth time interpretation of the cow's experience (lingering near the EH) is irrelevant as soon as you are interested in a dynamical activity that involves interplay between the Earth and the cow, such as a rescue mission. General Relativity frees us to think in the coordinate system most appropriate to a given scenario. Earth time is not useful for objects approaching an EH, and indeed leads to misperceptions such as one I had for many years, that the cow is always salvageable.

 

[zerospin]

I don't believe in a singularity, what we call a singularity is caused by our incomplete understanding of how matter and energy work. Nature does not deal with infinite amounts or values. It is far more likely, that inside a black hole, somewhere below the event horizon, the matter that fell inside is stopped, once again, by some yet unknown form of pressure that prevents a collapse to a point of no dimensions. Perhaps dark energy pressure stops it, or something that involves dark matter or something completely different. We barely understand a little about how the visible matter and energy works, and we know almost nothing about 95% of the stuff that makes the Universe, so out theories are incomplete and flawed by definition.

So my answer is, the "matter" or what is left of it, forms a ball of finite and non-zero radius below the event horizon, and a yet unknown form of pressure is preventing further collapse. To me this makes far more sense than something with infinite density and 0 radius.

Furthermore, the matter that falls in never breaks the speed of light before reaching the surface of this ball, and therefore time never stops.

 

[Green dwarf]

However the answer is "YES". To convince yourself of this, think from the cow's perspective. The cow can still watch things on Earth after it crosses the EH, for a brief time before it hits the singularity. So if the rescue rocket is sent off at an Earth time t2 such that the cow sees CNN's coverage of the rocket launch just after it has crossed the EH in its own frame, the rescue mission is going to fail despite JPL's efforts.

If the picture I painted is correct, then wouldn't the cow see the CNN coverage of the launch before it crossed the EH, not afterwards? The coverage photons and the rescue ship should have an infinite amount of time to reach the cow before the cow crosses the horizon. Once the cow does cross the EH, it would still see the outside universe, but it would be seeing a universe more than an infinite time into our future, long after it had suffered heat death or whatever. CNN probably won't be broadcasting then.
This is all assuming of course that it is possible to rescue a cow from a few millimetres outside the EH.

 

[Green dwarf]

I don't believe in a singularity, what we call a singularity is caused by our incomplete understanding of how matter and energy work. Nature does not deal with infinite amounts or values.

Have we actually proved that or is it just that the maths gets too hard for our present capabilities when things become infinite?

I know this is a bit different, but I understand that, if the universe is flat, then it must also be infinite. No one seems to have too much trouble with this infinity.

What boggles my mind is that, if the universe is infinite, then it would have been infinite at the time of the Big Bang too. Our whole observable universe would have been contained in a sphere maybe 10^-15 m in diameter. 1 cubic metre of this material would have contained 10^45 universes like our own, 1 cubic light year 10^93 of our universes. Yet 1 cubic light year would be an infinitesimal part of the whole universe. I'm not trying to make any particular point here - just being awe struck.

 

[Green dwarf]

I'm fascinated by the discussion. Thanks to everyone who has contributed.

 

[anorlunda]

I think this is relevant to the OP's question. I would like some clarity on the boundary between theoretical versus obervational science on the title of this thread.

Can we ever observe, directly or indirectly, the distribution of mass inside the EH of a BH?

Changing the word mass to energy is probably a better way to state the question, thus ...

Can we ever observe, directly or indirectly, the distribution of energy inside the EH of a BH?

A spinning BH is theorized to cause frame dragging. That may be a way to indirectly make some singularity measurements. Course, we haven't even been able to detect gravity waves yet.

The spinning case is a possible exception. There may be other special cases. But I intend to exclude special cases from my question.

 

[Nugatory]

If the picture I painted is correct...

It's not. When you hear someone saying that it takes an infinite amount of time for the cow to reach the event horizon, they are using a particular convention for defining "at the same time" in the statement "at the same time that the cow is $X$ meters above the event horizon the outside observer's wristwatch reads $T$". That convention is similar to (not exactly the same, but mine is easier to explain) the following:
- At time $T_0$ according to his wristwatch, the outside observer sends a radar/light signal towards the infalling cow.
- This radar signal reaches the cow and is reflected back to the observer, arriving at time $T_1$ according to his wristwatch.
- The round-trip time for the signal was $\Delta{t}=T_1-T_0$ and the signal was moving at the speed of light, so the round-trip distance was $c\Delta{t}$. The one-way travel time was $\Delta{t}/2$ and the one-way distance was $c\Delta{t}/2$.
- Therefore, at the same time that the observer's wristwatch read $T_0+\Delta{t}/2$ the cow was at a distance $c\Delta{t}/2$ away and still hasn't fallen through the horizon (because we're still getting radar returns from it).

Note that $\Delta{t}$ grows without bound as the cow gets closer to the horizon; thus the outside observer finds that any time on his wristwatch, no matter how large, corresponds to a position of the cow outside the horizon and only in that sense can we say that it takes an infinite time for the cow to reach the horizon. However, this is telling us more about what happens to light signals between us and the cow than it is about what's really happening to the cow. The convention is simply refusing to recognize any position of the cow that doesn't produce a radar return; that's a problem with the convention, not the path of the cow through spacetime.

The key to resolving these paradoxes is to adopt a convention for matching the cow's position to the time on the outside observer's watch that works everywhere, not just outside the event horizon. The easiest to visualize are Kruskal coordinates - the math is quite daunting but you can get a satisfactory qualitative understanding understanding just from looking at the spacetime diagrams. You can plot the path of the cow through spacetime, the path of the CNN broadcasts following the cow across the event horizon and into the singularity, and the path of the radar signals that the outside observer is using to determine where the cow is when.

then wouldn't the cow see the CNN coverage of the launch before it crossed the EH, not afterwards? The coverage photons and the rescue ship should have an infinite amount of time to reach the cow before the cow crosses the horizon.

Again, no. The cow crosses the horizon, the CNN broadcast crosses the horizon a moment later. If there's enough time left, the broadcast catches up to the cow a moment before the cow reaches and dies at the central singularity so the cow gets to see it. Any later broadcasts reach the central singularity after the cow, so the cow is dead before it can see them. [/QUOTE]

 

[Nugatory]

Can we ever observe, directly or indirectly, the distribution of mass inside the EH of a BH?

As far as we know, only if we're willing to cross the event horizon to find out - and then we don't get to tell anyone outside.

 

[Nugatory]

I don't believe in a singularity, what we call a singularity is caused by our incomplete understanding of how matter and energy work.

Have we actually proved that or is it just that the maths gets too hard for our present capabilities when things become infinite?

Neither of the above. Zerospin has a very good conjecture, namely that some effect that we don't yet know about prevents the infinities from happening. But it's still a conjecture, not something that we know for sure.

 

[Dr Bee]

By definition the escape velocity of a Black hole is the speed of light but matter cannot travel at the speed of light so matter entering a black hole will not be traveling at the speed of light only very very close, ? It will be falsely observed to slow down and its length immensely shortened but these observations are an illusion , all that is happening is that time has slowed down hugely for the matter which we observe as matter compressing and almost coming to a halt but what does it look like from the matters perspective ? To the matter billions of years pass in milli-seconds as it enters the black hole and its matter fields become entwined in the total matter fields already in the black hole and more importantly the information that attended the matter cannot be destroyed and is retained somehow?

 

[Green dwarf]

Can we ever observe, directly or indirectly, the distribution of mass inside the EH of a BH?

To me, the question is whether the matter/energy in a black hole forms a shell at the EH or a singularity at the centre. We are trying to decide this theoretically, but I wonder whether the question is determinable by observation. Clearly our present technology is insufficient, but is it theoretically possible to tell by observation?

By Newtonian mechanics, the gravitational field outside the black hole would be the same in either case. But what if we consider frame-dragging? Would the effect be any different for the shell (which would be rotating at the EH with a finite angular velocity) than for the singularity (which, in order to conserve angular momentum, would, I presume, be spinning with infinite angular velocity at the centre, well away from the EH).

My knowledge of GR is nowhere near sufficient to know if there would be a difference observable to someone outside the EH, but someone reading this might know the answer to that question.

 

[Grinkle]

To me, the question is whether the matter/energy in a black hole forms a shell at the EH or a singularity at the centre.

Post 57 is a laudably clear response to this.

 

[anorlunda]

To me, the question is whether the matter/energy in a black hole forms a shell at the EH or a singularity at the centre.

That was your question, and I see that you are most interested in the first part, but my follow-up regarded the second part of the question. The existence of a singularity is speculation.

Once the matter falls inside the EH, we lose our abiliy to observe it from outside the EH. One could also speculate that the matter gets stuck in a shell 1 millimeter inside the EH. That is probably ridiculous but the point is that we are unable to prove or refute that by observation from outside the EH. Even frame dragging might not reveal whether the interior is a singularity or a hollow shell or any intermediate case. That is quite a bit to chew on.

 

[Bernie G]

With all we know about physics and math, few physicists believe in the 'infinitely dense' singularity thing anymore. Nature abhors a vacuum, and infinities,

If the singularity isn't infinitely dense there is a support mechanism that isn't taken into account by the curvature model.

 

[rootone]

If the singularity isn't infinitely dense there is a support mechanism that isn't taken into account by the curvature model.

Indeed, and I don't think there are many who think that a infinitely dense dimensionless object which the present model leads to could be a physical reality.
Many suspect that the support mechanism could be found within a theory of gravity at quantum scale, and proposals of such so exist, but afaik, nobody is close to pinning that down yet.

 

[Nvitinaros]

Forgive me if I misunderstand the scenario but my understanding of static (non rotating) black hole dynamics goes something like this.
1. The event horizon is merely the point at which light cannot escape to the outside universe, the consequence being that matter reaching this point releases its energy (as xrays due to compression from spagetification or gama rays.. energy released during the rest of the trip stays inside the EH).
2. The time dilation occurs as a function of gravity and speed in the object frame, not the observers. the object frame slows to a near stop,, imagine a million light years per tic.
3. To the observer the object simply accelerates into the EH with a bright flash and a slight enlargement of the EH (no time dilation or slowing of time).
The redsift to black would be there, but tough to observe given the other high energy activity..
Once inside the EH the theories multiply, my favorite is that time is reversed and the black hole is its own universe.

 

[Nugatory]

Forgive me if I misunderstand the scenario but my understanding of static (non rotating) black hole dynamics goes something like this.
1. The event horizon is merely the point at which light cannot escape to the outside universe, the consequence being that matter reaching this point releases its energy (as xrays due to compression from spagetification or gama rays.. energy released during the rest of the trip stays inside the EH).
2. The time dilation occurs as a function of gravity and speed in the object frame, not the observers. the object frame slows to a near stop,, imagine a million light years per tic.
3. To the observer the object simply accelerates into the EH with a bright flash and a slight enlargement of the EH (no time dilation or slowing of time).

None of that is right. There are many threads here and in the relativity forum in which this is discussed.

Once inside the EH the theories multiply, my favorite is that time is reversed and the black hole is its own universe.

There is only one generally accepted theory about what happens inside the black hole but away from the singularity, it is General Relativity, and it says neither that time is reversed (what does that mean?) nor that the black hole is its own universe.

 

[Gerhard Mueller]

If a sun collapses to a black hole, the matter does not cross the event horizon. Instead as soon as the even horizon exists, the matter stays inside. But it seems that during the collapse gravitational forces have been so intense, that even protons and neutrons became squeezed to something we do not understand. May be these squeezed particles together with electromagnetic radiation still exist inside the black hole.

 

[Grinkle]

If a sun collapses to a black hole, the matter does not cross the event horizon. Instead as soon as the even horizon exists, the matter stays inside. But it seems that during the collapse gravitational forces have been so intense, that even protons and neutrons became squeezed to something we do not understand. May be these squeezed particles together with electromagnetic radiation still exist inside the black hole.

Does an event horizon form at "full size" instantaneously? For some reason I thought it would start at the very center of the object (singularity or whatever one calls it) and propagate out at the speed of gravity, c, and stop at the diameter determined by the mass of the singularity plus, I suppose, whatever other matter ended up inside it as it expanded. If it forms at full size all at once, how does it "know" about the matter it will have swallowed once it exists? Space time curvature changes at the speed of gravity, doesn't it?

 

[phinds]

If a sun collapses to a black hole, the matter does not cross the event horizon. Instead as soon as the even horizon exists, the matter stays inside. But it seems that during the collapse gravitational forces have been so intense, that even protons and neutrons became squeezed to something we do not understand. May be these squeezed particles together with electromagnetic radiation still exist inside the black hole.

Maybe, maybe not but there is no evidence for it or theory that suggests it so this is personal speculation which is not allowed here.