Does matter accumulate just outside the event horizon of a black hole?

Question

My understanding is that time slows and approaches stopping when approaching the event horizon of a black hole. I have seen this explained several places, including a brief explanation in the last paragraph under: http://en.wikipedia.org/wiki/Black_hole#General_relativity, quoted below:

Oppenheimer and his co-authors interpreted the singularity at the boundary of the Schwarzschild radius as indicating that this was the boundary of a bubble in which time stopped. This is a valid point of view for external observers, but not for infalling observers. Because of this property, the collapsed stars were called "frozen stars",[17] because an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius.

Does this mean then that no matter actually falls into a black hole (except possibly what was there at its formation)? Would this also mean matter is accumulating just outside its event horizon? As I understand it, this would be the perspective from outside the black hole. If this is the case, I wonder if we would observe a tremendous amount of matter surrounding the event horizon, but it would be extremely red shifted?

Edit:

I noticed an answer to a different question, especially the end portion, provides some insight here as well: https://astronomy.stackexchange.com/a/1009/1386

Edit:

These YouTube videos someone put together explain the concept very well, and seem to indicate this idea is gaining traction!

https://www.youtube.com/watch?v=yZvgeAbrjgc&list=PL57CC037B74307650&index=118 https://www.youtube.com/watch?v=b1s7omTe1HI

Edit:

This new YouTube video describes this idea very well, and describes it as the way black holes work!

https://youtu.be/mquEWFutlbs

Answer 1

What you're describing is basically the "collapsed star" (Eng) or "frozen star" (Rus) interpretation of black holes that was common prior to the late mid-1960s. It was a mistake.

Suppose you are distant and stationary relative to the black hole. You will observe infalling matter asymptotically approaching the horizon, growing ever fainter as it redshifts. Does it mean that matter "clumps" around the horizon? To find out, suppose you throw yourself towards the black hole to try to catch the matter that you see. What you will find is that it fell into the black hole long ago.

In other words, the most sensible way to answer whether or not infalling matter clumps on the horizon is to look at the situation from the frame of that infalling matter. And there, it is clear: no, it does not clump, as it crosses the horizon in finite proper time. (As an aside, for a Schwarzschild black hole, falling from rest is exactly Newtonian in Schwarzschild radial coordinate and proper time.)

The "comoving viewpoint" was recognized by Oppenheimer and Snyder in 1939, but it was not until the 1960s, with the work of Zel'dovich, Novikov, et al., that it was generally recognized as truly significant in the community. In 1965, Penrose introduced conformal diagrams based on the Eddington-Finkelstein coordinates (1924/1958) that showed quite clearly that the stellar collapse is not slowed, but instead continues to a singularity. For an overview of the history of this change of viewpoint, cf. Kip Thorne, et al., The Memberane Paradigm (1986). These topics are commonly covered in many relativity textbooks.

Ok, but since it still takes an infinite amount time in the frame adapted to a stationary distant observer, does that mean that the horizon never forms in that frame? It does form: the underlying assumption in the argument that it does not would be either that the infalling matter needs to reach the center for the horizon to form or cross a pre-existing horizon to make it expand. But that assumption is simply not true.

An event horizon is defined in terms of future lightlike infinity, roughly speaking in terms of whether or not light rays escape if one waits an infinite amount of time. That means the location of the horizon at any time depends on not just what has happened, but also what will happen in the future. In the frame of the distant stationary observer, as matter falls towards the event horizon, it does slow down to asymptotically approach... but the horizon also expands to meet it. Similarly, the initial collapsing matter does not need to collapse all the way to the center for the event horizon to form.

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How can the finite life-time of the Black hole due to Hawking radiation be made consistant with the infinite amount of time (future) needed for the expansion of the event horizon (in the outer time-frame)?

There's no need to: [edit]that a particular time coordinate doesn't cover the full manifold is a fault of the coordinate chart, not of spacetime[/edit]. From every event, send out an omnidirectional locus of idealized light rays. The event horizon is the boundary of the spacetime region from which none of these light rays escape to infinity. This question has an objective answer--for any given light ray, either it will escape or it won't.

An external observer would need to wait infinitely long to know for sure where the event horizon is exactly, but that's a completely different issue. With Hawking radiation, the black hole shrinks, but it doesn't change the fact that light rays from some events will fail to escape, and thus that an event horizon will exist.

Here's a Penrose diagram of a spherically collapsing star forming a black hole that subsequently evaporates:

Light rays run diagonally at ±45° on the diagram. Note that there is a region from which outgoing light rays (running diagonally lower-left to upper-right) don't escape and instead meet the $r = 0$ singularity (the bolded, undashed horizontal line). The horizon itself is the the $r = 2m$ line marked on the diagram and its extension into the star: it should actually go from the (dashed, vertical) $r = 0$ line on the left, rather than extending from the star's collapsing surface. That's because some of the (idealized, noninteracting) light rays from inside the star will also fail to escape to infinity.

Now suppose that on this diagram you draw timelike curves that stubbornly stay away from the horizon, and you insist on using a parameter along them as a time coordinate. Does the fact that you've chosen coordinates that exclude the horizon needs to be made consistent with whether or not the event horizon actually exist? The resolution is simple: if you want to talk about the horizon, stop using coordinates that exclude it.

Answer 2

Yes, you are absolutely right, from OUR VIEWPOINT it does.

From Kip Thorne's book "Black Holes and Time Warps: Einstein's Outrageous Legacy."

Like a rock dropped from a rooftop, the star’s surface falls downward (shrinks inward) slowly at first, then more and more rapidly. Had Newton’s laws of gravity been correct, this acceleration of the implosion would continue inexorably until the star, lacking any internal pressure, is crushed to a point at high speed. Not so according to Oppenheimer and Snyder’s relativistic formulas. Instead, as the star nears its critical circumference, its shrinkage slows to a crawl. The smaller the star gets, the more slowly it implodes, until it becomes frozen precisely at the critical circumference. No matter how long a time one waits, if one is at rest outside the star (that is, at rest in the static external reference frame) one will never be able to see the star implode through the critical circumference. That is the unequivocal message of Oppenheimer and Snyder’s formulas.

Is this freezing of the implosion caused by some unexpected, general relativistic force inside the star? No, not at all, Oppenheimer and Snyder realized. Rather, it is caused by gravitational time dilation (the slowing of the flow of time) near the critical circumference. Time on the imploding star’s surface, as seen by static external observers, must flow more and more slowly, when the star approaches the critical circumference, and correspondingly everything occurring on or inside the star including its implosion must appear to go into slow motion and then gradually freeze.

As peculiar as this might seem, even more peculiar was another prediction made by Oppenheimer and Snyder’s formulas: Although, as seen by static external observers, the implosion freezes at the critical circumference, it does not freeze at all as viewed by observers riding inward on the star’s surface. If the star weighs a few solar masses and begins about the size of the sun, then as observed from its own surface, it implodes to the critical circumference in about an hour’s time, and then keeps right on imploding past criticality and on in to smaller circumferences.

By looking at Oppenheimer and Snyder’s formulas from the viewpoint of an observer on the star’s surface, one can deduce the details of the implosion, even after the star sinks within its critical circumference; that is one can discover that the star gets crunched to infinite density and zero volume, and one can deduce the details of the spacetime curvature at the crunch. (P217-218)

OK, so from our perspective all the matter will be clustered around the critical circumference and no further. That's fine, this shell in theory can exert all the forces required on the external universe such as gravitational attraction, magnetic field etc. The point like singularity which is in the indefinite future of the black hole, (from our point of view) indeed in the indefinite future of the universe itself could not exert such forces on this universe. This singularity is only "reached" as an observer rides in past the critical circumference and, through the process of time dilation, reaches the end of the universe.

This is obviously an area of active research and thinking. Some of the greatest minds on the planet are approaching this issue in different ways but so far have not reached a consensus but intriguingly a consensus appears to be beginning to emerge.

http://www.sciencealert.com/stephen-hawking-explains-how-our-existence-can-escape-a-black-hole

Stephen Hawking said at a conference in August 2015 that he believes that "information is stored not in the interior of the black hole as one might expect, but on its boundary, the event horizon." His comment refers to the resolution of the "information paradox," a long-running physics debate in which Hawking eventually concedes that the material that falls into a black hole isn't destroyed, but rather becomes part of the black hole.

Read more at: http://phys.org/news/2015-06-surface-black-hole-firewalland-nature.html#jCp

In the mid-90s, American and Dutch physicists Leonard Susskind and Gerard 't Hooft also addressed the information paradox by proposing that when something gets sucked into a black hole, its information leaves behind a kind of two-dimensional holographic imprint on the event horizon, which is a sort of ‘bubble’ that contains a black hole through which everything must pass.

What occurs at the event horizon of a black hole is very hard to understand. What is clear, and what proceeds from General Relativity, is that from the viewpoint of an external observer in this universe, any infalling matter cannot proceed past the critical circumference. Most scientists then change the viewpoint to explain how, from the viewpoint of an infalling observer, they will proceed in a very short period of time to meet the singularity at the centre of the black hole. This has given rise to the notion that there is a singularity at the centre of every black hole.

However this is is an illusion, as the time it will take to reach the singularity is essentially infinite to us in the external universe.

The fact that the matter cannot proceed past the critical circumference is perhaps not an “illusion” but very real. The matter must from OUR VIEWPOINT become a “shell” surrounding the critical circumference. It will never fall through the circumference while we remain in this universe. So to talk of a singularity inside a black hole is incorrect. It has not happened yet.

Answer 3

We need to think about just where the time dilation effect occurs. By then thinking about the observations from each point of view, that is the free falling object and the external observer, we can come to terms with just what is happening as opposed to what appears to be happening.

The experience of time

We must remember that an object moving at a certain speed will travel through time (or the 4th dimension) at a slower rate. This does not mean that it moves slower, otherwise it would obviously not be travelling "at a certain speed".

Where time slows is in the ticking of the physical processes of the object itself. In other words, my clock would tick twice as slow according to you as I flew past you at 87% the speed of light. I would be waving my arms normally, but according to you, I would appear to be waving my arms twice as slow and would also appear to be squeezed in size (not really relevant to this).

The falling object's point of view

If you were the object falling into the black hole, you would accelerate as you approached the event horizon, but you would take longer and longer to react to the approach, to the point where you would fall into the black hole in no time at all. From your perspective, your approach to the event horizon would become exponentially faster.

In other words, you would fall incredibly fast into the black hole, but you would have barely registered it in your mind because there just wasn't enough time for you due to relativity.

The stationary observer's point of view

Now, the stationary observer outside the black hole's influence would observe something very different. The light (or rather, information) about your descent would become more and more redshifted, but also take longer and longer to actually reach their eyes.

This means that according to the observer, the falling object would slow down to a halt at the event horizon and have disappeared.

So what really "happened"?

• The falling object fell in very quickly, but hardly realised it happening
• The stationary observer would think that the object disappeared and never reached the event horizon.
• Cooper taps on some gravity books and saves the human race.

Answer 4

The logical consequence is, that an event horizon cannot form, since the first particle slows down asymptotically to zero, just before the event horizon forms (Fermat's infinite descent).

The emergence of the event horizon therefore takes infinite time seen from outside. But due to Hawking radiation a black hole exists only a finite time. Hence an event horizon doesn't form.

The frustrating thing about this is, that you need to be at least Stephen Hawking, to not be called a geek.

The current mainstream way to circumvent this paradoxon is to switch to a purely general relativistic geometry of infalling space-time, which doesn't experience the event horizon. That way you avoid the event horizon as a pole, but you get the singularity at the center of the black hole, governed by yet to investigate physical laws of quantum gravity.

Answer 5

Several wonderful yet technical answers have been given, and I cannot add anything to those very nice answers that explain why it is not useful to think black holes get "frozen" at their event horizons. But I can give an answer with a more essentially useful philosophical perspective, which is that the central lesson of relativity is that reality involves a bunch of things happening at various places and times, so reality is something local. As such, if you want to know what happened at some place and time (regardless of how you decide to give numbers to that place and time, that's like choosing how to coordinatize the surface of the Earth), then you should ask someone who was at that place and time!

According to this simple rule, we should imagine asking someone falling past an event horizon if a black hole has formed yet or not. They will say it has, and they will say they get to that central black hole in a finite time. Whether or not you get to receive that message is a more difficult issue, but they will say it all the same because reality happens somewhere, and we can always imagine someone there to experience it-- and ask them. Or at least, imagine what they would say in cases where communication gets difficult or impossible.

If you follow that one simple rule, then all these apparent coordinate paradoxes disappear immediately. Coordinates are a useful language for making calculations, but they are not a useful language for making assertions about "what is." That is an issue for observation, and all observations are local-- no one ever observes a coordinate, and way too much is made out of arbitrary coordinate choices.

Answer 6

Thought provoking cosmologists!

I'm uber-late to this discussion as I see it has been ongoing for literally years and don't know if there is still anyone monitoring this thread, but here goes.

I studied astrophysics at UC Berkeley in the late 80's, so perhaps my info is a little dated, upfront apologies if so. I spent a lot of time thinking about this problem for the past 30 years and have postulated a couple of ideas.

First, these conjectures are based on the presumptions:

• Time stops at the event horizon.
• An in-falling observer into the EH looking backward would watch the universe rapidly age to heat death.
• Non-charged, non-rotating, solar-mass black hole.
• A star of 2-3 solar masses is sufficient to overcome neutron degeneracy pressure and form a black hole (call it 2 for the discussion).

If true, then conjecture:

• Start with star of say 3 solar masses.
• We must consider an even horizon's existence and parameters from its "birth".
• Minimum Schwarzschild radius is only 12 miles (2 solar masses).
• Original main sequence star radius appx 100,000Km (100M+ Km for red giant).
• Observer is orbiting star initially.
• Star burns through last percentages of helium and cascade collapses directly to black hole.
• As star collapses, some amount of matter contracts to within 12 miles of star centroid (call it 2 solar masses).
• Event horizon now mathematically is formed and time STOPS for all matter at that radius.
• Matter outside that radius continues to fall in since time has not yet stopped creating a compression sphere around the EH.
• Matter already INSIDE the EH continues to fall (it has momentum that must be conserved). OR, does time STOP WITHIN the EH as well throughout the entire Schwarzschild sphere causing all that matter to FREEZE in position (relative to the outside observer? (Unknown.) (Perhaps time REVERSES?!)
• The outside observer would watch the matter at the EH STOP falling and radiating.
• The in-falling matter looking back at the universe would now watch the universe rapidly age, perhaps even to its death?
• If so, this means that all in-falling EH matter, after the EH has formed, is trapped at the EH until the black hole evaporates.
• Which also leads to a huge COMPRESSION of the in-falling matter in successively faster time frames falling in from behind.
• In the given example, this is an entire solar mass of matter all rapidly compressing and increasing in pressure. (At the EH time has stopped so no interaction is going on from the perspective of our orbiting solar observer, but successively less time dilated layers further away from the EH compress into the equivalent of a whole new star burning its fuel in fempto-seconds to many seconds. I.E. SUPERNOVA)
• AND there is the gravitational attraction imbalance that has now been caused between the solar mass of matter at the EH and the 2 solar masses inside the SW.
• In fact, all black holes formed by stellar collapse should begin life as a 12 mile wide Schwarzschild radius of 2 solar masses.
• Growth of blackhole sizes of this type (excluding primordial black holes) should ONLY be due to EH matter accretion or merging of black hole's EH's.
• No matter should ever fall into (or through) the EH in our lifetimes, or even the lifetime of the universe as long as we maintain that an observer falling into a blackhole sees the universe rapidly age behind him/her (the future).
• Therefore, all detection of radiation from black holes is due to interactions of matter very near the EH.
• Which begs the question, does GRAVITY transcend the EH?
• If not, a black hole should lose "2" solar masses at is creation (can only test if we can measure the mass before an after its creation in perhaps a visible binary pair supernova).
• But if gravity DOES transcend the EH as accepted, then the gravity of the solar masses at the EH should be exerting an opposing force on the matter inside, DECELERATING the collapse inside the EH!
• Also, there should be a "ringing" effect "heard" by our new gravity wave detectors as the matter inside doesn't just collapse infinitely into a singularity but "bounces" and reverberates from gravity and different layers of time dilation.
• As a thought, this COULD even result in a "torus" of sorts with dimensionalities being swapped or reversed (time/distance), rather than a singularity.
• Add to this the Planck density with these opposing internal forces and we possibly end up with some bizarre space-time topologies.
• PURE speculation: The environment INSIDE the black hole starts to look a whole lot like our own universe's history from the big bang (white hole?) if you simply change time's arrow. (The universe isn't expanding as we perceive but compressing into a torus with different distances from our viewpoint having different levels of time dilation.)
• As an undergrad I wrote a paper that our universe is the inside of a black hole and I have seen many theories gravitating (sorry) to this solution over the past 30 years.
• Including the most recent ideas that our universe is a compressed (3D) hologram on a 4 dimensional "sphere" that represents an event horizon equal to the entropy of our entire known universe. Elegant.

Apologies for the terribly longwinded comments here. I'm sure the idea has more holes than Swiss cheese. Which is what the universe starts to look like with all these little pocket universes forming that we can't interact with!

The question and the answer that could take use to the next level of understanding of these concepts is this:

Can an event horizon change shape?

If the matter is time-dilation-locked to the event horizon, it cannot move (relative to the EH). If in-falling matter can witness the end of the universe, or even just a very long time, then the matter is time-dilation-locked by definition. If it is NOT TD-locked, an in-falling observer SHOULD NOT BE ABLE TO SEE THE UNIVERSE RAPIDLY AGE BEHIND THEM.

Then for if the EH can change shape, either:

• matter needs to move with the EH (acceleration? momentum? free energy?)
• OR the EH, being a mathematical definition, can move irrespective of the location of the matter, thereby changing the amount of time-dilation on the matter, slowing/speeding/stopping matter outside the EH, or UNKNOWN effects if it was already inside the EH. (Presumably an EH will always INCREASE in size, but what about shape?)
• Back to shape: Can an EH be ellipsoid? Pancake? If it can change from sphere to pancake, does this not mean that matter that was already inside the EH near the spherical radius has now EMERGED FROM THE BLACK HOLE as it were if that radius suddenly shrinks? (Unless, again, it is somehow dragged with the EH.)
• If this is the case, would not black hole mergers allow for matter from within the EH to escape there by constituting a whole new form of black hole emission other than Hawking radiation? How would we detect this? How would we know?

I think the answer lies squarely with LIGO and more powerful versions of this instrument to be brought online in the future. Observing changes, arrival times, spectrum comparisons, and eventually direction, of gravity waves and their associated gamma ray bursts from merging black holes will help us pin down exactly what happens when event horizons collide!

Thanks for taking the time to review these ideas!

Answer 7

As I understand it, the presence of an event horizon (EH) from gravitational collapse is a case in which GR violates local causality in the outer (w.r.t. EH) universe. By Birkhoff theorem the EH can only be caused by the inner T, not by whatever is outside the EH. The (collapse) EH yields a causal disconnection: the outside is not affected by what is on or inside the EH. This notwithstanding, the EH's presence (in the scenario suggested by continuation across the EH) "affects" the local outer metric, thus violating the local causality notion that whatever is determined at one event can only be determined by what can causally affect that event.

In theoretical principle, this is not an inconsistency: we can derive SR from causality and other assumed properties, then GR from SR and other properties. This derivation concludes that GR is a property of causality together with the other axioms, but it is not necessarily invertible: there might be solution of GR that violate causality. The question is then if GR is a property of some fundamental physics, maybe including causality, so that the solutions of GR that violate the foundations won't be physical, or if GR is itself fundamental, and then causality is, sometimes, false. The information loss problem can be traced back to the causality violation in the outer universe, if an EH is present.

On the other hand, GR seems to fix the issue elegantly. In no event perspective (intended as the causal perspective of what affects the event itself, which conveniently is what observers placed in that event would "see", note that their different velocities do not affect the considerations that we are making), where the event is in the outer universe, the EH has already formed. Only proto-black holes, i.e. black holes (mass undergoing gravitational collapse) before the formation of the EH, are present in, i.e. causally affects, the outer universe. This causation is complete and consistent, there is no "input" from the causally disconnected interior of an EH. In particular, the EH outer metric is not "presented" to the outer universe, excluding the derivation of the inconsistency with causality that opened this post. This would also imply that the entire history of the physics of a (proto-)BH, as described from an outer perspective, will be causally consistent and entirely determined within the outer universe. In this scenario the information loss problem is prevented by not posing it. This "fix" is effected by the delay "ad infinitum" of the EH formation, which is valid in all outer perspectives.

Respect to the OP question, this would mean that it is not so much that "stuff" accumulates "just outside" the EH, it is rather that the EH is always "just about" to form, and this little change fixes everything.

Answer 8

An observer falling into a black hole does not see himself fall into the singularity unimpeded. The black hole will always evaporate before infinity, therefore the infalling observer will fall to the center of an evaporated black hole and find nothing special other than universal heat death.

Answer 9

Zeno's Paradox of Motion

(Full disclosure: I'm not a physicist.)

I am reminded of this claim, attributed to Zeno. In its classical form, Zeno argued that the hero Achilles, pitted in a race against a tortoise, could not win the race if the tortoise was given a head start. His reasoning was that in the time it took Achilles to reach the point where the tortoise began, the tortoise would have advanced some distance, and that during the time that Achilles took in covering this distance, the tortoise would again advance by some amount. Zeno concluded that it was impossible for Achilles to catch up to the tortoise, let alone pass it, and therefore any observation we make to the contrary must be an illusion, and thus all motion is illusory.

Zeno's error lies in supposing that the intervals of time, being infinite in number, must necessarily add up to an infinite sum. His argument takes the interval of time leading up to the point of passing and stretches it by an ever-increasing factor so that the event never takes place.

This is actually what happens if we were to observe something falling into a black hole; our perception of the passing of time local to the event is distorted by gravity, and the closer the falling object gets to the event horizon, the greater the distortion, leading to the appearance (from our viewpoint) that the object never reaches this point. In fact, it is as if we were watching a film of the object falling in, but the film runs ever more slowly as the time of reaching the event horizon gets closer.