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

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!

Edit:

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

https://youtu.be/mquEWFutlbs

• You should quote where you read it. However, I guess you are talking about relativistic effects (delay) observed from a distant observer. Is it correct? – Py-ser May 15 '14 at 3:09
• My personal opinion: That's the reason (together with Hawking radiation making the BH vanishing over finite time, as seen from outside), why an event horizon never can form. But that's not (yet?) the main-stream opinion. – Gerald May 15 '14 at 9:31
• @Py-ser - Yes, this is correct, I am talking about the relativistic effects. – Jonathan May 15 '14 at 14:57

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.

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.

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.

The path through the event horizon does lead to a singularity in each case, but it is indefinitely far in the future in all cases. If we are in this universe, no singularity has yet been formed. If it has not been formed yet, where is the mass?  The mass is exerting pull on this universe, correct?  Then it must be IN this universe.  From our point of view it must be just this side of the event horizon.

ASTONISHINGLY IT MAY BE POSSIBLE TO PROVE THIS. The recent announcement of gravitational waves detected on the merger of 2 black holes was accompanied by an unverified but potentially matching gamma ray burst from the same area of the sky. This is inexplicable from the conventional viewpoint which holds that all the matter would be compressed into a singularity and would be incapable of coming out again.

If 2 black holes merge and emit gamma rays… the above is certainly an explanation which is also consistent with General Relativity. The mass never quite made it through the event horizon (from our viewpoint) and was perturbed by the huge violence of the merger, some escaping. It may be a deep gravitational well, but a very powerful gamma ray should just be able to escape given the right kick (attraction by an even larger black hole approaching).

Further more refined observations of similar events, which are likely to be reasonably frequent, may provide more evidence. There is not likely to be any other credible explanation.

• Thank you for your answer, I would like to see if this generates further discussion! – Jonathan Mar 19 '16 at 16:07
• One more comment on your original question. The black hole would start like a tiny vapour bubble in the middle of the imploding star which had reached a sufficiently strong gravitational "pressure". It would then expand as surrounding matter and energy fell in and reached its critical circumference, therefore I do not think any matter from the viewpoint of an external observer would be "inside" the critical circumference. – ctrebor Mar 19 '16 at 16:40
• FYI, I am looking for proof / references to award the bounty. – Jonathan Mar 23 '16 at 15:32
• Proof/references for what? There was a considerable reference to Oppenheimer & Snyder. Do you want more? – ctrebor Mar 24 '16 at 16:02
• Your gravitational waves comments seem to have trouble understanding the difference between the mass and the gravitational field. Nothing about the GW detection said that mass was expelled or otherwise converted from (within) the black holes into various forms of radiation. The energy was already present in the gravitational fields, which exists within the universe and outside the event horizon. It was that energy that was converted to radiation. What's "actually" in the hole is irrelevant: what matters is the fields (gravitational and EM, namely). – zibadawa timmy Mar 18 '17 at 2:03

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.

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: 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.

• So is this correct? From a reference point outside the black hole, matter does indeed accumulate (or clump together) approaching the event horizon, but eventually the event horizon expands to engulf it when more matter is accumulating? – Jonathan May 15 '14 at 15:43
• If you insist on defining 'clumping' that way, yes, though I wouldn't. As for the latter question, actually, no: as the horizon expands, it carries the frozen, redshifted images of the stuff that has fallen in the past outward with it. That's one reason I wouldn't call the former case 'clumping'; rather, the Schwarzschild time coordinate (or appropriate generalization for distant stationary observers) is badly behaved at the horizon at so simply shouldn't be used there. – Stan Liou May 15 '14 at 15:52
• I don't agree that the external time reference should not be used, as that is what we would "see" if we look at a black hole. It is an interesting point you made that the "image" of all the matter that has fallen in before moves outward when the event horizon expands. Thank you for taking the time to provide a detailed answer too, very thought provoking! – Jonathan May 15 '14 at 15:59
• @StanLiou 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)? – Gerald May 15 '14 at 16:25
• "... but the horizon also expands to meet it." How long does that take from the point of view of distant stationary observer? – Kamil Szot May 17 '16 at 15:21

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.
• How then can the observer see a black hole at all, if from his position, never enough mass falls into it for it to take shape and exist to begin with? – LocalFluff Nov 27 '15 at 8:07
• @LocalFluff What does "see a black hole" mean? If by that you mean observe its gravitational effects, I don't see the problem. – Rob Jeffries Nov 27 '15 at 19:30
• Your first section is mistaken. It takes a finite amount proper time to fall in, i.e. time experiences by the object, such as you. As a cute coincidence illustrating this, for radial freefall from rest into a Schwarzschild black hole, the time it takes to reach the horizon (or any particular Schwarzschild radial coordinate) happens to exactly match the prediction of Newtonian gravity. – Stan Liou Nov 28 '15 at 19:52
• @RobJeffries But then it would remain a neutron star for all outside observers. Black holes would never form for outside observers regardless of how they are observed. One can potentially see a black hole transiting background objects. A non-accreting SMBH doesn't shine at all, while a neutron star with millions of Solar masses very near its surface would be pretty wild. – LocalFluff Dec 2 '15 at 8:06
• @LocalFluff A neutron star and a black hole are completely different. No neutron star can exist with a radius anywhere near the Schwarzschild radius. That's why you can see a neutron star. – Rob Jeffries Dec 2 '15 at 8:18

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.

• That is an interesting point, and very thought provoking. It will be interesting to see what further discoveries are made about black holes. I wonder still about the matter that was "inside" the black hole when it formed (e.g. I would think this matter is indeed inside the black hole / event horizon). Although, if it is correct that the "image" of the matter expands with the event horizon, even that matter could be on the edge of the event horizon from an external view point. – Jonathan May 15 '14 at 16:03
• @Jonathan If you assume e.g. the Schwarzschild solution, the simplest form of a black hole, from an outside observer you need to distinguish three zones: the space-like, the light-like, and the time-like zone. The light-like zone corresponds to the event horizon. If you transform properties of matter between these zones they change their physical properties so much, that the term "the matter is" doesn't make much sense, neither "matter" nor "is". One space dimension changes roles with time. – Gerald May 15 '14 at 16:18
• @Jonathan One way of thinking may be, that the information of the matter is stored at the event horizon, some fluid-simulations indicate a fractal structure of the event horizon due to infalling matter; this might be a way to overcome the information paradox. That's neither the Schwarzschild nor the Kerr solution. – Gerald May 15 '14 at 16:48
• I wonder if we could actually "peek under the skirts" of a black hole if there'd be any 'there' at all. We can't of course, and anyone that asserts a singularity exists inside a black hole is simply saying that the mathematical model they're using says there is one. If all of the mass/energy that makes up a black hole was compressed into a two dimensional surface at the event horizon, is there any way to observationally tell the difference? Swiss cheese has holes in it, but no one asserts that the holes are Swiss cheese. – Howard Miller Mar 22 '16 at 3:19
• @Gerald FYI, I am looking for proof / references to award the bounty. – Jonathan Mar 23 '16 at 15:33

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 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:

• 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 (reletive 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 blackholes 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 though, 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. (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 long winded 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 theanswer 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!

• 1) Put your text between two stars, so: *this text*, so it will be italic. 2) 3 Sun masses is far not enough to produce a black hole. 3) Time stops on the EH only for the far observers, objects falling in the EH experience nothing while they pass it. 4) All capital texts don't look very good, I suggest to use the italic formatting (or, double stars make your text bold). – peterh Jan 23 '18 at 21:21
• And do something about your wall of text. If you want people to read your contribution make sure it is easy to read. – Jan Doggen Jan 24 '18 at 8:33
• Very interesting feedback, and definitely thought provoking! Would be interesting to see if future observations (especially LIGO observations of merging black holes) "shine more light" on if time is indeed frozen at the event horizon. It is an interesting thought that the event horizon should not be able to change shape if time is frozen there! Definitely thought provoking. – Jonathan Jan 25 '18 at 22:54

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.

• "all observations are local" - this simple statement packs a punch! Copenhagen Interpretation ... entanglement ... there is no such thing as an independent reality? – Chappo Feb 6 at 21:51
• Not accessible to science, anyway. Science must be empirical, so it must be observer based, so it can only describe local events. That may limit its scope. It's how we keep invisible faeries out of science, but we don't know what else we lose. Still, if someone somewhere is saying the black hole has formed, and that they are crossing an event horizon, then we must allow the black hole does exist-- even if we know we can never receive the message and therefore cannot generate a global concept from our own observations. – Ken G Feb 6 at 21:58
• Einstein was deeply troubled by the realisation that reality is relative, which is why he wrote to Schrödinger in 1950, "You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality, if only one is honest. Most of them [other physicists] simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established." – Chappo Feb 6 at 22:07
• I am always surprised by that attitude, because it seems clear to me that we will always be limited by our ability to perceive. There was never any guarantees that we would be able to perceive reality in some kind of pure form-- it was always going to be what passes our filters. Even the choice to do science presents additional filters, where was the guarantee nothing would ever be lost? – Ken G Feb 6 at 22:20

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.

• And by the way, physicists everywhere seem to be confused about what happens when you add infinity. Ignore black hole evaporation. The claim is that physics holds similarly true in all frames of reference. Except there is no frame of reference for a far away observer, because after an infinite amount of time, the infalling subject still never falls past the horizon. So there is no obvious reason to say the infalling observer will have a normal experience at time=infinity. You don't get to add infinity or divide by infinity. You have lost touch with physical concepts when you try to do it. – Smart guy Sep 9 '17 at 1:19
• The whole issue arises from an invalid analytical extension. It's like trying to describe the universe as a photon would see it unfold. The universe would exist only with two states: t=0 and t=1. The two states would share no discoverable relationship and would be truly arbitrary, because the photon experience requires dividing time by infinity, and is therefore meaningless to talk about. – Smart guy Sep 9 '17 at 1:40
• I don't see what is wrong with this answer, assuming black holes actually do evaporate due to hawking radiation, and time dilation is such that the observer falling into the black hole observes the future of the universe. Might be nice if the answer elaborated on this a bit. Definitely an intriguing thought! In this case, I don't believe infinite time is involved, because a finite amount of time would pass before the black hole evaporates. Also see: astronomy.stackexchange.com/questions/2524/… – Jonathan Sep 9 '17 at 13:00
• It's wrong because the infaller reaches the center in a short time, on their own clock. They just don't care about the time coordinate being used by some person at infinity, and we should not use a nonlocal time coordinate to say 'what is going on' somewhere else. This is one of the central lessons of relativity-- reality is local, so ask the person on the scene. All else is just coordinates, and way too much is made of coordinates. – Ken G Feb 6 at 17:35
• Indeed, this is similar to the issue that arises in cosmology-- the "observable universe." Beyond the edge of that, there be dragons, that we assume away with a swipe of the cosmological principle-- yet all we know is that we will never know the full, global, universe, and whatever else it might contain that some observer is experiencing but we never will. – Ken G Feb 6 at 22:06