Does an event horizon ever exist?

[photonkid]

I've been told that time slows down so much inside a black hole that an event horizon never actually comes into existence and that we don't know what happens inside a black hole.

Is it true that the event horizon never comes into existence - or at least, if time slows down like general relativity suggests, would an event horizon and a singularity never come into existence?

Have we observed any black holes where the density of matter is extremely high or can you never tell at what "stage of collapse" a black hole is at?

Thanks for any information.

 

[Dale]

That is merely an artifact of a particular choice of coordinates.

 

[Agerhell]

Let us first assume that there is a spherically symmetric non-rotating black hole. Then, according to general relativity, it will take an infinite amount of time for you to get to the event horizon and you are going to have to travel infinitely slow. That is as measured by an external clock. Your energy content will also be zero at the event-horizon, the way I understand it.

As you can never, in a finite amount of time, reach the event horizon you never get any singularity problems, the way I understand it. A singularity is basically a situation where your equations say "divide by zero". Now some would say that you can actually reach the event horizon and get inside it in a finite amount of your own time because your clock will tick infinitely slow, as measured by an external clock, and if your clock ticks infinitely slow it is possible for you to reach the event horizon even it it takes an infinite amount of time as measured by an external clock. Somehow, you make a coordinate transformation to get rid of this apparent problem.

That is, I guess, the standard view.

 

[pervect]

Somehow, you make a coordinate transformation to get rid of this apparent problem.

That is, I guess, the standard view.

The actual physical clocks that one might drop into a black hole reach the singularity in a finite amount of proper time.

As mentioned by Dale, and indirectly acknowledged by you, it's an artifiact of a particular coordinate choice that makes Schwarzschild coordinate clocks (which are mathematical abstractions, not the readings on any actual physical clock) infinite.

It's well known that Schwarzschild coordinates are ill-behaved at the event horizon. It's puzzling that people insist on using these particular coordinates in the regions where they behave poorly after they've been repeatedly warned about their ill behavior in that region.

 

[photonkid]

<quote> That is merely an artifact of a particular choice of coordinates. </>

I don't understand your answer. In what coordinates does an event horizon exist or not exist?

According to this web page
http://www.nasa.gov/audience/forstudents/k-4/stories/what-is-a-black-hole-k4.html

<quote> A black hole is a place in space where gravity pulls so much that even light can not get out. </>

Do we know for certain that black holes actually exist - i.e. do we know that there exists "a region of space where light can't escape"? How can I say this - if a star collapses into a black hole, the gravitational force "near" the center of the black hole gets stronger and stronger. To start with, the force isn't strong enough to prevent light escaping - so at some point, the mass density must reach the point where light can't escape. But from the point of view of an object that was orbiting the collapsing star, the total mass of the star hasn't changed - so how can you tell that the collapsing star has gone past the point at which there is a region within which light can't escape? i.e. how do you tell that there is actually a black hole there.

The NASA page says <quote> A black hole can not be seen because strong gravity pulls all of the light into the middle of the black hole. But scientists can see how the strong gravity affects the stars and gas around the black hole. </>

What is "strong gravity". Does an orbiting object feel an increasingly stronger gravitational field as the star collapses? If the Earth collapsed into a black hole would the moon notice any difference in the gravitational field? Some of the Earth's mass is now closer to the moon and an equal amount is now further away so the moon shouldn't notice any change.

And also, if the force of gravity is zero at the center of the earth, is the force of gravity zero at the center of a black hole?

 

[pervect]

Does Montgomery, Alabama "exist"? How do you know it exists?

I'm sure one could write buckets of philosophical prose about this question :-(

However, it's perfectly possible to go visit Montgomery Alabama in a finite amount of time. The major differences between Montomery Alabama and a black hole event horizon , according to current theory and experiment, are as follows:

1) The nearest event horizon, at the center of our galaxy, is a lot further away than Montgomery. So the "finite" amount of time is a lot longer, and the vehicles one would need to use aren't technologically feasible.

But the time needed to get there is still finite according to theory.

2) The more troubling question is that if you do reach the event horizon, you won't be able to report your findings back to the people on Earth. But you'll still reach there in a finite time - according to current theory.

 

[photonkid]

Does Montgomery, Alabama "exist"? How do you know it exists?

Are you answering my question? If so, I didn't understand any of your answer.

 

[Nugatory]

That is merely an artifact of a particular choice of coordinates.

I don't understand your answer. In what coordinates does an event horizon exist or not exist?

The event horizon exists regardless of which coordinates you use. However, some coordinate systems do not work at the event horizon (for about the same reasons that longitude doesn't work at the north pole) and if you try to use these to describe what is happening at the event horizon, you'll get very misleading results.

The time and distance coordinates that are natural for an observer far away from the black hole (they're called Schwarzschild coordinates, and you were using them even though you didn't know it) are good for calculating what that observer will SEE if he watches an object fall into hole (but remember, what he sees is not the object falling into the hole, it's the light from that object hitting his eyes), but they do not tell us anything about what really happens to the object as it moves towards and through the horizon.

 

[PeterDonis]

In what coordinates does an event horizon exist or not exist?

Whether or not the event horizon exists is not a matter of picking coordinates. That's the point. The event horizon is an invariant geometric feature of spacetime; the spacetime as a whole either has it, or it doesn't. Coordinates have nothing to do with it.

Do we know for certain that black holes actually exist - i.e. do we know that there exists "a region of space where light can't escape"?

We don't know "for certain", but very few things are known "for certain". We have a lot of strong indirect evidence that black holes do exist--that is, that the spacetime of our universe has event horizons in it.

how can you tell that the collapsing star has gone past the point at which there is a region within which light can't escape?

There was a fairly recent thread on this. Basically, you see objects falling into a region of spacetime from which nothing ever comes back out, and in which there is never any sign of the infalling objects hitting anything like a solid surface.

Technically, we have to interpret this evidence according to some theory; the interpretation according to which the objects are falling into a black hole is an interpretation using the general theory of relativity. It is in principle possible that there is some other theory that can explain the same observations without having to believe that there is an event horizon there; but nobody has come up with one, and general relativity has been well confirmed experimentally in other regimes, so physicists feel pretty confident about its predictions in this regime.

If the Earth collapsed into a black hole would the moon notice any difference in the gravitational field?

No. The field still gets weaker with distance from the center the same way it did before. The difference is that, if the Earth collapsed into a black hole, you could get a lot closer to the center without hitting any surface, so you could feel a much stronger field while still being "above" the hole than you can while remaining above the Earth's surface.

And also, if the force of gravity is zero at the center of the earth, is the force of gravity zero at the center of a black hole?

No. The "center" of a black hole is very, very different from the center of the Earth.

The "center" of the hole is not a "place in space" the way the center of the Earth is. It is really a moment of time, which is to the future of every other moment of time inside the horizon. That's why it's not really possible to define a "force of gravity" inside the hole's event horizon: everything inside the horizon does have to fall towards the "center", but that's because the "center" is in the future, and you can't avoid moving into the future.

If we look at "gravity" in the sense of spacetime curvature, then "gravity" goes to infinity at the center of the hole.

 

[Passionflower]

There is a lot of confusion on this, but the "it is because of the Schwarzschild coordinates" is not the answer.

An observer, far away from the black hole, does indeed measure that all objects that approach the event horizon come to a halt, their signals get red shifted and eventual fade away to approach zero. And he will never see them pass the event horizon . This has nothing to do with coordinates, it is a physical observation.

On the other hand an observer free falling radially starting from very far away does not notice anything unusual when he passes the event horizon, he might see curvature effects but that depends on the mass of the black hole, it is similar to a balloon, a small one has more curvature than a big one. But his days are counted as very quickly his future will simply stop.

 

[Nugatory]

On the other hand an observer free falling radially starting from very far away does not notice anything unusual when he passes the event horizon, he might see curvature effects but that depends on the mass of the black hole, it is similar to a balloon, a small one has more curvature than a big one. But his days are counted as very quickly his future will simply stop.

And to be completely clear, his future stops at the central singularity, not as he crosses the event horizon. (Passionflower already knows this, but I've seen previous threads on the topic run off the rails when someone else, already confused by the "time slows as you get nearer the horizon" stuff, misunderstand and become even more confused).

 

[Passionflower]

And to be completely clear, his future stops at the central singularity, not as he crosses the event horizon. (Passionflower already knows this, but I've seen previous threads on the topic run off the rails when someone else, already confused by the "time slows as you get nearer the horizon" stuff, misunderstand and become even more confused).

Indeed, he will have a time of 4/3 times the mass of the black hole left once he passes the event horizon.

 

[pervect]

Are you answering my question? If so, I didn't understand any of your answer.

I'm attempting to get enough common ground to answer your question.

Whether or not something "exists" is a philoosphical question. I was offering the suggested defintiont that if you can visit a place, it "exists" as a starting point for discussion.

Given some agreement on what it means to "exist", your question can be answered. Without it, it can't.

At the moment, I still don't know if we have any sort of agreement on what you think it means to exist.

Some people like to debate what it means to "exist". I'm not one of them. But while I"m not particularly interested in debate, I try to be flexible in working with reasonable defintitions of "exist".

f you don't like my suggested definition of what "exist" means, it's really up to you to come up with one. If it's something I can work with, I can perhaps give you a better answer.

If you DO like my suggested definition, hopefully I have already answered your question, and you just neeed to read it and think it over a bit.

 

[Dale]

There is a lot of confusion on this, but the "it is because of the Schwarzschild coordinates" is not the answer.

That depends on the question. If the question is about observables like redshift then I agree, but if the question is about time slowing down then it is because of the coordinates.

 

[Passionflower]

There was a fairly recent thread on this. Basically, you see objects falling into a region of spacetime from which nothing ever comes back out, and in which there is never any sign of the infalling objects hitting anything like a solid surface.

Well that depends on the observer:

Consider an observer who hovers very closely above the event horizon. A free falling object zooms by at near light speed with an enormous momentum. Then the object's distance to the event horizon decreases exponentially with time and the momentum increases exponentially with time. The object appears to be squeezed to a pancake on top of the event horizon and basically stays there.

 

[PeterDonis]

Well that depends on the observer

Yes; I was talking about us, here on Earth, observing distant objects that are candidates for being black holes.

Consider an observer who hovers very closely above the event horizon. A free falling object zooms by at near light speed with an enormous momentum. Then the object's distance to the event horizon decreases exponentially with time and the moment increases exponentially with time. The object appears to be squeezed to a pancake on top of the event horizon and basically stays there.

Well, actually, the light from the object would be so strongly redshifted, even when it had just passed the hovering observer, that it probably wouldn't be visible. But I suppose we're idealizing that away.

What we can't idealize away, though, is this: suppose you're the hovering observer. You know you're close to the horizon. Something falls past you at almost the speed of light. Where could it go? If it hit something at any finite distance above the horizon, you would see light coming back from the impact. If it somehow stopped and turned around, you would see light from that event. If you don't see any such thing, what else could have happened? It doesn't help to say, well, the light gets more and more delayed as the object gets closer to the horizon, because that's the point: that only happens *if the object is free-falling towards the horizon.* If the object's trajectory changes, the light coming from it will change too. So if the light you see behaves the way that it's predicted to behave for an object that's falling to the horizon, wouldn't you conclude that it is, in fact, falling to the horizon? (And once it gets there, what else can it do but continue to fall inside?)

Remember also that, since you're hovering close to the horizon, you can test the fact that your proper time elapses much more slowly than a static observer at a much higher altitude, by exchanging light signals with such observers. So you can verify all the predictions about how Schwarzschild coordinates get more and more distorted as you get closer and closer to the horizon. (Kip Thorne talks about such a thought experiment in Black Holes and Time Warps, including dropping a probe towards the horizon from a ship hovering near it.)

Of course, we can't run such tests here on Earth, since we have no black hole candidates within range of our spaceships. But the evidence that physicists use to judge, for example, that there is a million solar mass black hole at the center of the Milky Way galaxy, is the same kind of evidence I described: we see things falling into a certain region and never coming out, and what we see matches what we expect to see if they are falling into a black hole, and *not* what we would expect to see if something else was there.

 

[Passionflower]

If it hit something at any finite distance above the horizon, you would see light coming back from the impact. If it somehow stopped and turned around, you would see light from that event. If you don't see any such thing, what else could have happened?

Well, one could ask the question 'How hot does the hovering observer measure the temperature near the event horizon"?

 

[Omega0]

Have we observed any black holes where the density of matter is extremely high or can you never tell at what "stage of collapse" a black hole is at?

I am not sure why this question wasn't answered but just as a link:
http://en.wikipedia.org/wiki/Sagittarius_A*

 

[Jonathan Scott]

I don't think the argument that calculations show that a free falling observer passes the event horizon in finite time proves anything about whether this "actually" happens.

Suppose for example as a thought experiment I create a clock such that when $n$ units have elapsed on a normal clock, it shows a time of $1 - 2^{-n}$ units, and I connect up a (science fiction) "stasis unit" box with someone in it so that the time they experience matches the clock. It is clear that subjectively they have no reason to expect time to end at 1 unit, yet according to anyone outside the box they effectively slow down to a complete halt before reaching 1 unit and remain frozen for unlimited time.

As far as I can see, this is very similar to what appears to happen to the free falling observer in any static coordinates.

 

[PeterDonis]

Suppose for example as a thought experiment I create a clock such that when $n$ units have elapsed on a normal clock, it shows a time of $1 - 2^{-n}$ units, and I connect up a (science fiction) "stasis unit" box with someone in it so that the time they experience matches the clock.

You're assuming that these things are consistent with the laws of GR. Are they? I'm particularly curious about the stasis box: how do I build one assuming that the laws of GR hold? At the very least, I think you would need a very special kind of stress-energy tensor for the walls of the box; certainly you can't just do it in vacuum.

As far as I can see, this is very similar to what appears to happen to the free falling observer in any static coordinates.

No, they're not, because in the standard Schwarzschild solution the spacetime is vacuum; there are no stasis boxes. Obviously if you change the conditions, you change the predictions; but that doesn't mean anything if you're trying to interpret the predictions that are made when the conditions are *not* changed. Your "stasis box" scenario describes a different spacetime from Schwarzschild spacetime.

 

[Dale]

Suppose for example as a thought experiment I create a clock such that when $n$ units have elapsed on a normal clock, it shows a time of $1 - 2^{-n}$ units, and I connect up a (science fiction) "stasis unit" box with someone in it so that the time they experience matches the clock.

I don't think that such a stasis box is possible, even allowing negative energy density (i.e. allowing violations of the weak energy condition).

 

[PeterDonis]

Well, one could ask the question 'How hot does the hovering observer measure the temperature near the event horizon"?

Classically, he measures zero temperature.

If we include quantum mechanics, he measures a temperature proportional to the hole's surface gravity, at least if we believe the Hawking calculation is basically correct. Close to the horizon, the constant of proportionality would be increased by the inverse "redshift factor" at the observer's radius, relative to the temperature measured at infinity; so an observer hovering close enough to the horizon could see a significant temperature.

However, the question we really should ask is, does the temperature, or some other characteristic of the Hawking radiation, *change* when an object free-falls past the hovering observer? The answer to that depends on which candidate theory of quantum gravity you believe.

As I understand the current mainstream model (which is basically the one Susskind describes in The Black Hole War), information about the quantum state of the infalling object would indeed be encoded in the Hawking radiation seen by the hovering observer, after a sufficient time had elapsed since the infalling object passed him; but that wouldn't stop the infalling object from falling through the horizon. In other words, to the best of my understanding, the Susskind model does not say the horizon doesn't form; it just says that the existence of the horizon and the region inside it does not violate quantum unitarity.

There are other candidate quantum gravity models that appear to claim that quantum corrections prevent the horizon from forming in the first place, but AFAIK none of them have wide acceptance.

 

[Jonathan Scott]

I don't think that such a stasis box is possible, even allowing negative energy density (i.e. allowing violations of the weak energy condition).

That's why I referred to it as "science fiction". The point is however to illustrate that one can have different time rates that appear to be related in a continuous way but where one of them cannot exceed a fixed maximum value.

 

[Dale]

That's why I referred to it as "science fiction". The point is however to illustrate that one can have different time rates that appear to be related in a continuous way but where one of them cannot exceed a fixed maximum value.

I don't think that a fictional example illustrates anything about reality. The question isn't what some author, unconstrained by physical laws, could fantasize. The question is what is consistent with the laws of nature as we currently understand them.

As we currently understand the laws of physics, worldlines do not simply end with no physical cause. This is related to the concept of "geodesically complete manifolds". What you are describing would be a geodesically incomplete manifold.

 

[Jonathan Scott]

I don't think that a fictional example illustrates anything about reality. The question isn't what some author, unconstrained by physical laws, could fantasize. The question is what is consistent with the laws of nature as we currently understand them.

As we currently understand the laws of physics, worldlines do not simply end with no physical cause. This is related to the concept of "geodesically complete manifolds". What you are describing would be a geodesically incomplete manifold.

I'm not saying this DISPROVES the idea. I'm just saying that the fact that the falling observer time apparently continues beyond the event horizon does NOT in itself prove that the situation can be reached in reality.

 

[Dale]

Sure, but it is consistent with known laws of physics, and the alternative is not.

 

[PeterDonis]

The point is however to illustrate that one can have different time rates that appear to be related in a continuous way but where one of them cannot exceed a fixed maximum value.

"Illustrate" without qualification is not the same as "illustrate using a valid solution of the Einstein Field Equation". The question is not what is possible with math without any constraints whatsoever; the question is what is possible within the mathematical constraints of GR.

the fact that the falling observer time apparently continues beyond the event horizon does NOT in itself prove that the situation can be reached in reality.

Well, it does prove that the situation can be reached in reality if the laws of GR continue to be valid. If the laws of GR turn out not to be valid in this regime (if, for example, one of the more exotic quantum alternatives proves to be correct), then we'll end up having to make predictions using the laws that *are* valid.

But all that shows is that the predictions you make depend on the laws of physics you believe. It still doesn't show that you can make up a mathematical scenario unconstrained by any physical laws and have it mean something.

 

[Jonathan Scott]

Well, it does prove that the situation can be reached in reality if the laws of GR continue to be valid. If the laws of GR turn out not to be valid in this regime (if, for example, one of the more exotic quantum alternatives proves to be correct), then we'll end up having to make predictions using the laws that *are* valid.

But all that shows is that the predictions you make depend on the laws of physics you believe. It still doesn't show that you can make up a mathematical scenario unconstrained by any physical laws and have it mean something.

I'm sorry, but I don't agree that the fact that the maths continues means that something "actually happens" which according to any static coordinate system occurs after an infinite time.

I think I'm correct in saying (after doing a quick integral to check) that even light takes an infinite time to pass the event horizon in static coordinates. If so, a conveniently placed static mirror could reflect the light beam back from any point arbitrarily close to the event horizon, and we could unambiguously assign a time to that reflection event in static coordinates by assuming it to occur at the half-way point of the symmetrical round trip, as usual for clock synchronization. There is no theoretical limit on how far in the future the round trip could be set to complete.

This seems to make it very clear that the time at which the light actually crosses the event horizon is after an infinite time in our universe, as defined in a normal physically measurable way.

 

[Dale]

I'm sorry, but I don't agree that the fact that the maths continues means that something "actually happens" which according to any static coordinate system occurs after an infinite time.

Your disagreement notwithstanding, PeterDonis is correct. "The maths" you refer to are how GR makes its predictions, so "the fact that the maths continue" unambiguiously means that GR predicts that it "actually happens".

There is currently no viable mainstream alternative to GR which predicts anything different. We cannot just base our statements here on wishes and hopes, they must be based on mainstream physics theories and laws.

Also, whether or not light can bounce back from an event to another observer is irrelevant as to whether or not that event occurs in a finite amount of proper time, even in flat spacetime. It is well-known that radar coordinates do not always cover the entire manifold.

 

[Jonathan Scott]

Your disagreement notwithstanding, PeterDonis is correct. "The maths" you refer to are how GR makes its predictions, so "the fact that the maths continue" unambiguiously means that GR predicts that it "actually happens".

There is currently no viable mainstream alternative to GR which predicts anything different. We cannot just base our statements here on wishes and hopes, they must be based on mainstream physics theories and laws.

Also, whether or not light can bounce back from an event to another observer is irrelevant as to whether or not that event occurs in a finite amount of proper time, even in flat spacetime. It is well-known that radar coordinates do not always cover the entire manifold.

Now I think you're overstating the case.

My last example shows that crossing the event horizon does not occur until after an infinite time has elapsed in a static coordinate system, in a physically measurable sense. The light path and the mirror are all outside the event horizon and the light path is symmetrical in time. I cannot see any way this could be ambiguous.

This means that even though there appears to be a time at which something can fall through the event horizon from the falling point of view, the event at which the event horizon is reached, in a standard coordinate system as seen by a static observer, is infinitely into the future, in a physically measurable sense (in that we can at least measure that any event before that point can be arbitrarily far into the future). That means that BEFORE the falling object can do whatever GR says it does after crossing the event horizon, it first remains above the event horizon for an infinite time into the future.

As far as I can see, this matches up with my original model of a "stasis box", in that something falling towards the horizon effectively ends up slowed down to zero relative to our universe. What happens AFTER an infinite time doesn't seem like meaningful physics to me.

 

[Dale]

My last example shows that crossing the event horizon does not occur until after an infinite time has elapsed in a static coordinate system, in a physically measurable sense. The light path and the mirror are all outside the event horizon and the light path is symmetrical in time. I cannot see any way this could be ambiguous.

This means that even though there appears to be a time at which something can fall through the event horizon from the falling point of view, the event at which the event horizon is reached, in a standard coordinate system as seen by a static observer, is infinitely into the future, in a physically measurable sense (in that we can at least measure that any event before that point can be arbitrarily far into the future). That means that BEFORE the falling object can do whatever GR says it does after crossing the event horizon, it first remains above the event horizon for an infinite time into the future.

As far as I can see, this matches up with my original model of a "stasis box", in that something falling towards the horizon effectively ends up slowed down to zero relative to our universe. What happens AFTER an infinite time doesn't seem like meaningful physics to me.

Your logic applies equally well to a uniformly acclerating observer in flat spacetime. For such an observer the same radar coordinates that you use here leads to an event horizon in flat spacetime (Rindler horizon). So, by your logic, what happens after an infinite amount of Rindler time isn't meaningful physics either. And since a Rindler horizon can be anywhere then no physics is meaningful since any physics is after some Rindler horizon.

This highlights a problem that you have with assigning some sort of existential importance to radar coordinates. They are known to be observer-dependent not merely in terms of the exact coordinates given to specific events, but also which portions of spacetime they cover. If it isn't physically meaningful to speak of something which is not covered by some observer's radar coordinates then who determines which observer's coordinates are right? How does that observer become so privileged that his or her radar coordinates determines what is meaningful and what is not?

 

[Mordred]

I often post this link on Blackhole accretion disk as questions such as ths often arise. I found this article useful as its a good collection of formulas etc on accretion disk/jets as well as some of its maths involving event horizons. There is also a section covering a possible manner of determining if a BH candidate has a solid core (neutron star) or classic singularity by measuring its jets in a specific manner.

http://arxiv.org/abs/1104.5499

its a lengthy 91 technical pages I'm still studying it myself as its so broad in scope that study is taking a while.

I should also note the article is continually updated since I first came across it I've seen 4 updates on it

 

[ZVdP]

Now I think you're overstating the case.
As far as I can see, this matches up with my original model of a "stasis box", in that something falling towards the horizon effectively ends up slowed down to zero relative to our universe. What happens AFTER an infinite time doesn't seem like meaningful physics to me.

There is a significant difference between your box and someone falling into a black hole. If an observer in the box were to look outside, he would see the rest of the universe age at an ever increasing rate as his time approaches 1 (and see the infinite future of the rest of the universe).

An observer in free fall towards a black hole doesn't see that. He won't be able to see all future events happening in the universe. He will see the universe age a limited amount of time before he hits the singularity.
A distant observer can for example send light pulses to someone falling towards a black hole. The falling observer can send a response back when he receives the signal. For the distant observer the responses will take longer and longer to arrive, but there exists a time on his watch after which he never receives a response at all when he sends a pulse towards the black hole.

 

[Passionflower]

An observer in free fall towards a black hole doesn't see that. He won't be able to see all future events happening in the universe. He will see the universe age a limited amount of time before he hits the singularity.

Do you agree that most (or perhaps all) black holes rotate?
Do you agree that what you write is not true for rotating black holes?

 

[PeterDonis]

I'm sorry, but I don't agree that the fact that the maths continues means that something "actually happens" which according to any static coordinate system occurs after an infinite time.

But the whole point is that GR does not make predictions based on coordinates; it makes predictions based on invariants. GR predicts that something does "actually happen" when an object falls through a BH horizon. You are basically saying you don't agree that this case is within GR's domain of validity: but classically, there is no good reason to make such a claim. Classically, the rule is that GR makes predictions based on proper time along worldlines, not coordinate time (whether it's in the Schwarzschild chart or any other chart). You are basically claiming you can arbitrarily change that rule for no good reason at the event horizon.

If you want to say that the classical rule is correct, but that what "actually happens" is not governed by classical GR but by some quantum gravity theory, that's a different discussion. But you appear to be talking about the classical prediction.

I think I'm correct in saying (after doing a quick integral to check) that even light takes an infinite time to pass the event horizon in static coordinates.

Infinite coordinate time, yes. So what?

If so, a conveniently placed static mirror could reflect the light beam back from any point arbitrarily close to the event horizon, and we could unambiguously assign a time to that reflection event in static coordinates by assuming it to occur at the half-way point of the symmetrical round trip, as usual for clock synchronization. There is no theoretical limit on how far in the future the round trip could be set to complete.

Yes. Again, so what?

This seems to make it very clear that the time at which the light actually crosses the event horizon is after an infinite time in our universe, as defined in a normal physically measurable way.

This is fine, as long as you recognize that there can be a whole region of spacetime "after an infinite time in our universe". You are implicitly assuming that this can't be the case, but that assumption is not valid. At least, it's not valid unless you are also willing to claim that you can arbitrarily change the rules by which GR assigns physical interpretations to the math, for no good reason, at the event horizon. (The only difference with a light beam is that you can't use proper time as an affine parameter; but you can still assign an affine parameter along an ingoing null geodesic and show that it has a finite value at the horizon, indicating that the geodesic must continue further.)

[Edit: Another way of seeing this is to note that, as DaleSpam pointed out, your argument proves too much: it proves that the region behind a Rindler horizon in Minkowski spacetime "can't exist", because it is "after an infinite time" according to Rindler observers. I doubt you are willing to defend that claim.]