The so-called "plunging region" is the area within the Innermost Stable Circular Orbit--that is, in order for an orbit to remain circular, the particle would have to orbit faster than the speed of...
The so-called "plunging region" is the area within the Innermost Stable Circular Orbit--that is, in order for an orbit to remain circular, the particle would have to orbit faster than the speed of light, which is impossible. Once it crosses the ISCO, the time until the particle reaches the event horizon is measured in milliseconds, and sometimes even microseconds (in its own frame of reference--remember that we're talking about general relativity with time dilation like in the movie Interstellar).
In actuality, what likely happens is that the particle never quite touches the event horizon because in their reference frame, the clocks in the rest of the universe sped up infinitely and either the universe died or the black hole dissolved in those microseconds...which seems to mean that nothing ever quite reaches the event horizon, which makes black holes even more confusing. How can they form if it takes an infinite amount of time (in our frame of reference) for matter to reach the event horizon? Shouldn't that mean that inside the event horizon is a neutron star of almost the mass needed to form a black hole and then there's a region of infinite density hovering just outside the event horizon? But if that's true, how can a black hole grow? Shouldn't it take infinite time for mass to accumulate to the point that it would get swallowed by the event horizon? š„“šµāš«
I don't think that's quite right. To an outside observer, the particles clock slows and slows till stopping just outside the event horizon. The outside observer doesn't ever see the particle...
what likely happens is that the particle never quite touches the event horizon because in their reference frame, the clocks in the rest of the universe sped up infinitely and either the universe died or the black hole dissolved in those microseconds...
I don't think that's quite right. To an outside observer, the particles clock slows and slows till stopping just outside the event horizon. The outside observer doesn't ever see the particle enter. It's as if the particle contributes to the black hole's mass by sitting there right at the horizon.
However from the particle's frame of reference, they just fall right in. The perceived time dilation of the exterior universe is not so extreme at the event horizon.
Your questions about extreme time dilation etc don't come up till the particle is much much closer to the singularity, but it doesn't really matter as far as growing the black hole. Once the thing crosses the event horizon, it's in there, contributing to the black hole's total mass.
My understanding is that it is true that time dilation reaches infinity at the event horizon when using Schwarzschild coordinates, though it is considered inaccurate to use those coordinates in...
My understanding is that it is true that time dilation reaches infinity at the event horizon when using Schwarzschild coordinates, though it is considered inaccurate to use those coordinates in that regime for that reason. The "frozen star" that I described is an outdated understanding of black holes. The problem js that I haven't been able to find an explanation for the actual truth that goes beyond "just trust me bro"while saying what we should trust. Like if you asked how we know that 1+1=2 and I said "well when you add 1 to 1, you get 2," and I didn't teach you that | = 1, | + | = ||, and || = 2, so 1+1=2.
So I accept that it's true that what I said is wrong, but my astrophysics professors taught us that we should not just trust the explanations that everyone else insists are true. That's how we discovered dark matter, after all.
Unfortunately, I was really shitty at the actual physics classes in my astrophysics degree, so I won't be able to pursue further formal education in that subject. Maybe GPT-6 will be good enough to teach me in a personalized way that helps where I was overwhelmed in my undergrad classes.
That the Schwarzschild coordinates blow up at the event horizon is an artifact of the coordinate system itself. You address it using EddingtonāFinkelstein coordinates, which introduces an opposite...
That the Schwarzschild coordinates blow up at the event horizon is an artifact of the coordinate system itself. You address it using EddingtonāFinkelstein coordinates, which introduces an opposite blow-up to negative infinity at the same rate of approach, cancelling out the behavior at the event horizon. That gives you a model to chart behavior through the event horizon while still showing that as time goes to infinity we only ever see light from outside of the event horizon.
Interesting, thanks. That's a pretty succinct explanation. Also interesting that I've never come across the name of that coordinate system before. My understanding before all this was that...
Interesting, thanks. That's a pretty succinct explanation. Also interesting that I've never come across the name of that coordinate system before.
My understanding before all this was that coordinate systems are always accurate but not always good at making sense of what's going on, similar to how radial and rectilinear coordinates make sense in different situations, but I guess they must all be approximations of some sort that simplify maybe the Einstein Field Equations? It's been several years since I last studied GR and that was only at the undergraduate level.
I took a run at your deeper question in your other reply to me. But to answer the question on coordinate systems, I think really what you are thinking of is the metrics we use to calculate...
I took a run at your deeper question in your other reply to me. But to answer the question on coordinate systems, I think really what you are thinking of is the metrics we use to calculate distances. Those different metrics reflect the spacetime we are measuring. They should always be accurate to be useful, but they are not necessarily "complete." In fact, the EddingtonāFinkelstein coordinates are still not complete; we need additional terms to make them complete, but that creates a few limitations in their use. But the big takeaway is that metrics are just different ways of measuring distances in different spaces.
An old and fun read is "One Two Three... Infinity" by George Gamow, who gives a very layperson motivation for the basic metrics of spacetime without all the mathematical wrapping. General Relativity from A to B by Robert Geroch is another good book that takes a much deeper look at GR.
Since the black hole is vanishing due to Hawking radiation, and the particles never enter the event horizon, what does the outside observer see as the black hole gets smaller and smaller? And when...
Since the black hole is vanishing due to Hawking radiation, and the particles never enter the event horizon, what does the outside observer see as the black hole gets smaller and smaller? And when the black hole goes poof, what does the outside observer see happen to the "stuck" particles?
Hawking radiation decreases the mass slowly, and particles that go past the event horizon do actually get pulled to the singularity, increasing the mass. So hawking radiation would only make black...
Hawking radiation decreases the mass slowly, and particles that go past the event horizon do actually get pulled to the singularity, increasing the mass. So hawking radiation would only make black holes smaller when there is little to no incoming particles.
When people say that it takes an infinite amount of time to reach the event horizon, they mean from the perspective of an observer some distance off. The particle itself continues to experience the normal progression of time as it passes the event horizon.
The discrepancy in observed vs experienced events is due to gravitational time dilation.
I get that you just explained how EddingtonāFinkelstein makes sense of the scenario, but is there a deeper, even graduate-level, if necessary, explanation that resolves the paradox of infinite...
I get that you just explained how EddingtonāFinkelstein makes sense of the scenario, but is there a deeper, even graduate-level, if necessary, explanation that resolves the paradox of infinite time in one reference frame and finite time in another and which doesn't involve needing to just do the calculus yourself? I just don't get how a time dilation equation can have infinity on one side and a finite number on the other...although, as I write this, I guess that in SR as v approaches c, Ī³ approaches infinity. But this feels different because it would be like saying that Bob sees Ī³ approach infinity when looking at Alice, but Alice sees Ī³ remain finite.
It's been a long time since I did any deep math in physics, and that was modeling fields of moving source charges, so it's not exactly in this space. That said, I think you are maybe grappling...
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It's been a long time since I did any deep math in physics, and that was modeling fields of moving source charges, so it's not exactly in this space. That said, I think you are maybe grappling with a conceptual issue upstream of the math of general relativity. Let's start by simplifying the math and see if that helps.
You have a good grasp, I think, on special relativity. Indeed, the time dilation factor pops out when applying the Pythagorean theorem and the classic example of bouncing light off moving mirrors. Here is one example that walks through the derivation, and there are also good videos out there on it.
Even more generally, I think we agree that nothing moves faster than causality, and it just so happens that photons move at the speed of causality. Things like time, signals, and the speed of light are emergent properties from the speed of causality. When we observe something going near the speed of causality, its coordinate time moves more slowly than ours from our frame of reference. Because the speed of causality is fixed in all frames, the only thing that is left to flex is spacetime itself.
This gives rise to our notions of metrics, which is just a way of saying how we measure between two points in different geometries. To measure the distance between two points in spacetime separated by (dt, dx, dy, dz) we would use the following metric:
ds2=ādt2+dx2+dy2+dz2
Which should look pretty familiar as it is a basic extension of our distance equation to four dimensions. The left-hand side, ds, is the line element and invariant under all reference frames. Again, since all frames of reference will calculate ds the same, what is left to flex is spacetime itself (the RHS). The sign on the time unit is what gives rise to time dilation.
Quick recap. We agree that spacetime flexes, and we agree that this is because the rate of causality is fixed in all frames of reference.
Now, with general relativity, it isn't dilation caused by different velocities but by the warping of spacetime by mass. But we have the same basic simple concepts. We will have a metric that is used to measure a line element as the distance between two points separated by (dt, dx, dy, dz). All we do is a few simple translations to account for different spacetime curvatures by switching to polar coordinates and substituting different terms.
If you let the mass of the object warping spacetime go to 0, you can see that these are actually identical equations.
So, the math and the concepts of the different passages of time, even infinite vs 0 time, are qualitatively the same between special and general relativity. We have to use some fancier distance calculations to measure distances in general relativity with warped spacetime, just like we would measure distance differently along the wall of a curved flower vase compared to the table's flat surface.
At this point, you might object and say, but what does it mean for light to take an infinite time to leave the event horizon to reach a distant observer? You might accept the math's qualitative behaviors and geodesics but balk at what it represents.
So, let's get back to causality. Remember, the speed of light is bounded by the speed of causality. If events in spacetime are separated such that light cannot travel between the events in the time between them, then they can not be causally linked. Once a particle crosses the event horizon, it loses its ability to have a causal link to anything outside of the black hole. That must cause the time for any signal, such as light, to take an infinite time to reach an outside observer.
That's one of many ways to think about what happens when something crosses an event horizon. There are others, and I think depending on your own perspectives and thoughts, different explanations make more or less sense. I like the causality argument because it motivates a forcing behavior for why the light has to take infinite time, i.e., the speed of light is an emergent property of causality. Any event in spacetime involving the particle inside the event horizon is forever prevented from having a causal influence on anything outside, so any signal the particle can give off must take infinite time.
All the other metrics we introduce that model the behavior differently don't change the underlying behavior of the causal barrier that is an event horizon.
Anyway, I'm pretty low on sleep now and don't know if that helped. If you narrow down where you are skeptical, I'm happy to take another run at things.
I'm going to respond to this longer comment before looking at your other one. Thanks, this is a good refresher for sure, especially on exactly what metrics are. I knew I learned them in my...
I'm going to respond to this longer comment before looking at your other one.
Thanks, this is a good refresher for sure, especially on exactly what metrics are. I knew I learned them in my Cosmology & Relativity class, but I forgot that they were essentially the Pythagorean theorem in spacetime.
I also certainly understand and agree with everything you said about causality. It absolutely makes sense that something would need to take infinite time to pass through an event horizon due to causality, light cones, etc.
I think the problem I have is along the lines of Zeno's Paradox. If it take an infinite time for something you're observing to reach the event horizon, how could you reach the event horizon in a finite time?
If I hold a particle at arm's length while I'm falling toward a black hole, it would appear to take an infinite amount of time for that particle to reach the event horizon. Yet I can reach the event horizon in a finite time? So I guess it seems to logically follow that, from my perspective, the particle would reach the event horizon at the exact same time as me. Except that it also reaches the event horizon at t=ā? So it would seem that it would take me an infinite amount of time to reach the event horizon also--or at least until the black hole evaporates.
And now that I think of it, in the event horizon's reference frame, shouldn't time no longer exist similar to how a photon does not experience time because it moves at c? So shouldn't it be impossible to reach the event horizon in the same way that it's impossible to accelerate to c?
Maybe the explanation is the same as how infinite acceleration is impossible, yet accelerating from 0 to 0.000000...001 is both infinite and not? Although if spacetime is quantized, I suppose that could resolve that "paradox"...or with space and time both just being dimensions of spacetime, I guess that would render infinite acceleration moot because it's all just movement in spacetime. Fucking hell.
I think there are a few things going on. We've been a little loose with specifics, as is appropriate for a casual conversation. But I think we need to be careful with the specifics if we want to...
I think there are a few things going on. We've been a little loose with specifics, as is appropriate for a casual conversation. But I think we need to be careful with the specifics if we want to clarify further.
First of all, let's disclaim a few things. First, we just don't know some things yet. We have ideas and predictions, and areas of uncertainty and speculation. There will always be some physics grad student ready to wade into a conversation and say "well actually, black holes never form, those are collapsers..." At a some point there are some things we just don't know, and some distinctions that just don't help us model or understand.
That said, let's imagine a laser approaching the event horizon of a black hole, and a distant observer, with the laser emitting photons at the observer. That distant observer is maintaining, somehow, a relatively fixed position relative to the movement of the black hole through space.
From the perspective of the laser, let's say starting at 10r, it will take less than a second to cross the event horizon at 1r (which they don't experience) and then squish into the singularity.
To the outside observer, time will slow for the laser, and it will slow down as it approaches the event horizon. The light from the laser will become redshifted as the laser approaches the event horizon. Each photon will lose energy, not losing speed but reducing the frequency until it enters the radio spectrum.
The time between each photon will increase. From the lasers perspective, it is emitting just as many photons per second as normal. But as its time slows relative to the observers time, the observer will begin experiencing an increasing delay between photons.
Eventually, when the laser crosses the event horizon, there will be one last photon emitted that escapes. After that, the photons are trapped inside. But that last one will begin its long journey to the observer.
Now, in the lasers time, once it crosses the event horizon, the observer would be able to detect the increased mass of the black hole at the speed of causality, even if it appears that the laser hasn't entered it and is still emitting photons. Those photons have been crossing vast spaces to get to the observer long after the black hole has absorbed the laser in proper time, and the increased mass begun propagating through the gravitational field at the speed of causality.
This will stay that way for a long time. The observer will have to wait a finite but unknown amount of time to receive the last photon, tired and stretched from its journey. And that might happen to coincide with the final demise of the black hole through Hawking evaporation.
But there will be a last photon. That observer just won't see it until far into the future, likely as the black hole disappears, and the observer will never be able to know when the last one was received in that frame of reference.
It's all about the frame of reference, the warping of space and time, and the consequence of general relativity which is that multiple truths can exist, but some matter more than others. The laser can be in the black hole contributing to the mass of the singularity, and to the observer outside the event horizon, still be slowly firing off photons for billions of years.
People will equivocate over things like, did the laser cross the event horizon, or did the event horizon rise up to envelope the laser, etc... And maybe some of those distinctions matter some of the time. But I think what matters most is this:
The laser rapidly crosses the event horizon in proper time.
in proper time, the mass of the laser contributes to the singularity, increasing the mass, and thus modifying the gravitational field propagating through space, which is really the important thing about black holes.
any change in frame of reference approaching the event horizon will coverage to the frame where the laser crossed the event horizon and contributes to the mass of the black hole.
Everything outside of that is an artifact of warping space-time. What matters is causality. Once the laser crosses the event horizon, that's all she wrote. Any observer outside in any different frame of reference will see and experience different time dilations, etc. but none of them could travel to the laser they see and grab it before it goes in. There is only one laser, smeared across many perceptions of time, but as you change your frame of reference to approach it, it all collapses to the laser crossing the event horizon. Chasing the laser will put you right on through the event horizon, and you will experience in fast forward the lasers journey.
If nothing else, the fact that black holes have a lifespan through evaporation means that nothing can truly be held at the boundary forever, or take truly infinite time to approach, barring some fundamental change in our understanding of them.
One last caveat: at one point in my career I got into quite a heated argument with an editor from nature over sensationalist claims about black holes. So my explanation is one of multiple explanations you might hear. What I would say in defense of mine, is that it furthers a conceptual understanding at the expense of hypothetical nuances that may or may not be true, and may or may not matter. But the people pushing the truly infinite approach time argument, are, in my opinion, doing it to promote the mystic of general relativity to the general population rather than to help them develop a real qualitative understanding of what is going on.
Edit: I think I cleaned up a few inconsistencies and ambiguities, but let me know if I missed something. I'm on my phone, so it's a little hard to proof for consistency across multiple paragraphs.
I appreciate the patient, in-depth responses, and especially the last but talking about how the "infinite time" claim is just sensationalizing GR. I still just don't get how the laser actually...
I appreciate the patient, in-depth responses, and especially the last but talking about how the "infinite time" claim is just sensationalizing GR.
I still just don't get how the laser actually reaches the event horizon though. Am I wrong in seeing the event horizon as the point of infinite time dilation, similar to how c is the speed of infinite time dilation in Special Relativity?
You are bringing the point right down to the razor of what is known vs what is predicted. That said, I believe you are incorrect in that the event horizon is a point of infinite dilation. The...
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You are bringing the point right down to the razor of what is known vs what is predicted.
That said, I believe you are incorrect in that the event horizon is a point of infinite dilation. The event horizon is only a coordinate singularity. The physical singularity is the actual singularity inside the event horizon. That said, the event horizon is very, very close relatively speaking to the physical singularity. It would be like picking a point very close to an asymptote. It might be a small difference but it is the difference between arbitrarily large and truly infinite.
I can already feel someone ready to disagree with my assertion above, so let me further defend it. The usual models that show a blow up at the event horizon are modeling a simplified static black hole, not a growing one. When you model a growing one, either the object "passes" the event horizon, or the horizon "envelops" the object. What is the functional difference? Mostly thousands of hours of people arguing in physics forums.
Whether proper time really extends past the event horizon, whether event horizons ever even really form, black holes vs collapsors, etc. is more of a semantic debate than a practical one.
At the end of the day the observed phenomena we call a black hole exists, new mass is incorporated into the phenomena in proper time with the one quibble of passing the horizon versus enveloped at t=o, and the phenomena has a finite lifespan in the form of evaporation. Those core facts pretty definitively rule out "infinity" with the one exception of information reaching the distant observer in their original frame of reference.
Also, the above is the exact argument I had with the editor from nature. š
Okay, so you would say the singularity is equivalent to reaching the speed of causality and the event horizon is like reaching...nothing, because it's an imperfect analogy, which sounds fine to...
Okay, so you would say the singularity is equivalent to reaching the speed of causality and the event horizon is like reaching...nothing, because it's an imperfect analogy, which sounds fine to me.
And yes, of course the practical difference between everything falling through the event horizon and everything chilling just outside the event horizon is essentially non-existent because the forces experienced by everything outside of that point will be identical.
That said, there would of course be important differences for quantum gravity, using wormholes to travel the Universe, etc., but until we can figure out how to harness the power of quantum gravity...there's no practical difference.
I'm also glad to finally find someone who agrees that infinity is silly when black holes are expected to have finite lifespans. Especially because in the rest of physics, we use perfect, theoretical objects all the time, so it would be silly to ignore that we could just discuss a theoretical laser that emits nearly infinite photons at a nearly infinite energy with an infinitesimal time gap between photons so that even the idea of "photons keep coming less and less frequently so you never know quite when you've seen the last one" is pointless within a theoretical, educational framework.
So I'd say that while the exact question of "how does something ever actually cross the event horizon?" isn't exactly answered, it's at least resolved by "that's where physics kind of starts to break down and it doesn't really make a difference anyway."
I think that's a good way to look at it. We have some observational support for things like Hawking radiation, which seems to put a lifespan on black holes, and that is in tension with any model...
I think that's a good way to look at it. We have some observational support for things like Hawking radiation, which seems to put a lifespan on black holes, and that is in tension with any model choices that require an infinite blow up without some new process or model that resolves things at the end of the black holes existence.
One of the most important topics I took in college years ago was the philosophy of empiricism, which I think is an important thing to balance with theoretical models. We don't want to dismiss sound modeling, but we also don't want to be dogmatic in the face of obvious tensions with observed phenomena.
Folks that insist on infinity without at least acknowledging the unknowns and the tensions are, in my mind, still trying to grapple with the concept themselves, or probably not engaged in the observational side of things at all.
Sounds like that would be a great class for all STEM majors to take. It seems like far too many people blindly trust in "science" for science's sake, without knowing what they are actually putting...
Sounds like that would be a great class for all STEM majors to take. It seems like far too many people blindly trust in "science" for science's sake, without knowing what they are actually putting their faith in and without understanding that it is just a philosophical system in the end and it has its limits just like everything else, especially when it comes to poorly conducted research.
Cheers! I'm specifically curious about, from the perspective of an immortal observer studying the black hole that watches it for trillions of years, what does the process of the black hole...
Cheers! I'm specifically curious about, from the perspective of an immortal observer studying the black hole that watches it for trillions of years, what does the process of the black hole vanishing due to Hawking radiation look like, when no particle has ever crossed? I definitely understand that for the particle itself, there's no contradiction. But for an outside observer, mass that has never fallen into the singularity is being shed away, and I'm wondering if that's ever resolved.
It would probably look pretty boring for most of the time. Once the black hole finished pulling new matter towards it, its accretion disk would shrink and disappear, which is the source of the...
It would probably look pretty boring for most of the time. Once the black hole finished pulling new matter towards it, its accretion disk would shrink and disappear, which is the source of the light black holes give off.
You would be able to detect changes in the black hole by observing changes in the region of space it occupies and its shrinking sphere of gravitational influence.
We don't have good models for what happens at the very end though, when the black hole gets small. Maybe it just fizzles, or maybe something more exciting happens. We just don't understand gravity at small scales very well.
I think what might be confusing is that we talk about a particle taking forever to reach the event horizon. However, that isn't really the case, so it's not as if particles are hanging out forever emitting light and other signals.
What really happens is that light that passes the event horizon takes an infinite to reach any fixed observer outside of the event horizon. The light emitted outside the event horizon travels off into space like normal, although locally it follows the distortion lines created by the black hole.
So to an observer fixed relative to the black hole, it would be a boring show once the accretion disk was finished being absorbed.
My understanding, and I'm absolutely not a scientist, is that there's no preferred frame of reference, right? From the point of view of the observer, it's not that there's an illusion that the...
My understanding, and I'm absolutely not a scientist, is that there's no preferred frame of reference, right? From the point of view of the observer, it's not that there's an illusion that the light didn't cross; the light doesn't cross, from the observer's point of view. Am I misunderstanding the concept?
I just think that it's an interesting contradiction that from the point of view of the observer, nothing ever crosses the event horizon, but the black hole still shrinks.
There's no contradiction from the point of view of the falling observer. You fall through, die in some awful way, and reach whatever the hell thing exists in the centre. But from outside, the observer never falls in, but the black hole is still losing mass that the observer swears never made it to the centre.
You are correct, I think, with maybe one clarification. Like you say, to the object falling in, there is no magic line. It goes in and squish. But any signal it emits inside the event horizon...
You are correct, I think, with maybe one clarification. Like you say, to the object falling in, there is no magic line. It goes in and squish. But any signal it emits inside the event horizon never leaves.
To the outside observer, the object approaches the event horizon and then disappears. There isn't some perpetual ghost emission of the object emanating forever. That is why we can't directly observe many of the black holes we've identified. All of the matter in their accretion disk has been absorbed and no more light is being emitted.
Now, an object might appear to be really slowly disappearing into the event horizon depending on dilation effects, but that is different than the object never disappearing. You would see the object redden, dim, and eventually vanish.
Does that make sense?
Edit: @Raistlin I forgot to address your main point. The reason the black holes shrink is because they emit radiation through a quantum action. You can look into Hawking radiation for the details, but that is why they shrink. That is also part of the issue in understanding them better: we don't have a unified model for gravity and quantum effects. So light never leaves, but quantum effects create particles just outside of the event horizon that in some cases are able to leave, reducing the energy of the black hole.
Could I ask a hypothetical? Say you're an immortal observer watching the collapse of a star. You also have unbelievably advanced technology that allows you to detect the most minute signals, down...
Could I ask a hypothetical? Say you're an immortal observer watching the collapse of a star. You also have unbelievably advanced technology that allows you to detect the most minute signals, down to the Planck length. You observe the star collapse on itself. Most of the matter gets blasted away in the supernova, which you of course survive.
You never see any matter cross the event horizon, right? From your point of view, nothing crosses it, and it's all smeared across the surface of the event horizon. Yet there's still a singularity, and the black hole is still losing mass due to quantum effects. Where did the singularity come from, just taking the point of view of the observer? Where is that lost mass coming from? If I'm understanding this right (and I'm likely not), you never observe the lost mass cross the event horizon, and some random other mass is being emitted as heat due to quantum effects, and eventually the black hole dissipates and you never once saw anything cross the horizon.
What you're saying makes sense practically. If the light is red shifted into invisibility, then as far as a normal human is concerned, it might as well have crossed the event horizon. But mathematically, from your pov, it can't have. It has to be smeared across the event horizon.
So I think I understand a possible point of confusion. As the observer, you would see things cross the event horizon and disappear. It would be a gradual dimming, and then it would disappear....
So I think I understand a possible point of confusion. As the observer, you would see things cross the event horizon and disappear. It would be a gradual dimming, and then it would disappear.
Things can cross the event horizon, just only inwards. The models that blow up at the event horizon, showing an asymptotic approach are doing that due to a limitation of the model. We can fix it, and show the path something would take inwards, while still showing that nothing from the inside will ever reach an outside observer. In one of the other comment chains in this thread, I discussed those coordinate schemes.
It's a dense read, but you can get a sense of them by skimming the Wikipedia page.
Stars can become a black by either collapsing directly into one, which takes less than a second, by collapsing into a neutron star and accreting enough matter to collapse into one, or by going Nova while leaving behind a core too dense to stabilize as a neutron star. That is the case you describe.
In that case, the black hole would form and quickly form an accretion disk from the ejected matter. The matter would be pulled in, redden, dim, and then disappear through the event horizon and contribute to the mass of the singularity. As the observer, you wouldn't see the singularity, but you would see the explosion of the Nova, the formation of the spinning accretion disk, the matter disappearing, and the lensing of light from behind the disk. Eventually, you would run out of matter to sustain the accretion disk, and all light around the black hole would dim to nothing. Then the only detectable energy would be very low levels of hawking radiation. That, coupled with the changing observation of the effects of gravity on the region coupled with any lensing of light from behind the black hole would be all you would see.
Something to remember is that (gravitationally) a solid sphere, a hollow sphere, and a point mass all behave the same from the outside. If the outside observer determined all infalling matter to...
Something to remember is that (gravitationally) a solid sphere, a hollow sphere, and a point mass all behave the same from the outside. If the outside observer determined all infalling matter to be smeared on the horizon (hollow sphere) they'd make the same predictions as if they considered only the singularity (point mass) or considered the volume of the event horizon itself (solid sphere).
Solid and hollow spheres do not (gravitationally) behave the same on the inside, though, so there is a discrepancy on the predictions there that I am frankly unqualified to speculate about.
In some way it doesn't matter though, because both models agree that the interior is casually disconnected from the outside, and they agree on the exterior behavior.
IIRC they do disagree on what happens to the event horizon while an object passes through it. I think this is what @krellor was getting at, referring to active research on how black holes actually form.
This is going to start of strangely, but bear with me here: Imagine the path of a plane drawn on a flat map, and it flies over the north pole. As the path gets drawn over time, assuming the plane...
How can they form if it takes an infinite amount of time (in our frame of reference) for matter to reach the event horizon?
This is going to start of strangely, but bear with me here:
Imagine the path of a plane drawn on a flat map, and it flies over the north pole. As the path gets drawn over time, assuming the plane has roughly a constant velocity, at first the line will start slow. Then go slightly more faster as it gets closer to the north pole. And faster, and faster... and then, when it reaches the northern most point of the map, its speed reaches infinity as it crosses the north pole, and appears at some other point in the northern edge of the map. It will then go slightly slower and slower as it moves away from the north pole.
This is of course, complete bullshit. The plane doesn't just pop in and out of existence, nor does it reach infinite speed. What happened here is that because you're trying to project a 3D sphere with a 2D flat rectangle, there are weird points where your math just breaks down.
The event horizon of the black hole is like that, because general relativity describes gravity as a curvature of space-time, not a force. Here, the later part is especially important: time also gets 'bend' the more energy is packed in a single region.
Because you're looking it at is an outside observer, from your frame of reference, the same thing sort of happens as with the plane analogy. The paths look weird for you, but anything that falls into the black hole won't experience that sort of weirdness.
Another way to think about this is that, because gravity here is bending of space-time, the closer something is to the event horizon, the longer it will take to go outside of the black hole. If a light bulb is far away from the black hole, there's little difference. But if it's close enough, the light needs to travel more space-time as it's effectively stretched near the event horizon.
So if a light bulb emitting light falls into the black hole, at first, you'll see the light just fine. But when it gets closer, it will take just slightly more time, then longer, and longer... in a way, the 'signal' of light gets spread out over time. This is also why the light gets red-shifted by the way, the photons get smeared out over space-time, increasing it's wavelength. But in the mean time, the light bulb will cross the event horizon, no problem.
Now, there's one problem with this, which relates to another point in your comment:
Shouldn't that mean that inside the event horizon is a neutron star of almost the mass needed to form a black hole and then there's a region of infinite density hovering just outside the event horizon?
The idea what I've just said about reference frames doesn't quite work at the core of a black hole. If you do the math, the time it takes for something to fall towards to very centre of the black hole is finite. Meaning that everything that falls in the black hole does reach that point in space-time. At that point, the math of general relativity breaks down. Which is commonly perceived as a breakdown in the theory.
Gravitational waves emitted by merging black holes have been studied to look on whether there are 'echoes' of potential inner structures but so far, nothing has turned up. There are of course all kind of exotic theories on what goes on in a black hole but really, no one knows.
Thank you for the great simplification. I had a decent length response that just vanished, so I'll just say I'm confused because your example seems to be like saying that Bob's speed appears to...
Thank you for the great simplification. I had a decent length response that just vanished, so I'll just say I'm confused because your example seems to be like saying that Bob's speed appears to approach infinity as he nears the North Pole, but on a map centered on Bob, Alice's speed doesn't appear to approach infinity as her location relative to Bob approaches the "North Pole."
Well, the thing is, the moment that Bob crosses north pole, it doesn't really make sense to talk about the flat map projection as a frame of reference. If you fall into a black hole, you don't see...
Well, the thing is, the moment that Bob crosses north pole, it doesn't really make sense to talk about the flat map projection as a frame of reference.
If you fall into a black hole, you don't see anything out of the ordinary either. An outside observer would see a person never quite falling in, only vanishing over time as light gets red shifted, but the the person falling inside the black hole will just see the Universe go on (although it will get blue shifted).
The problem is that as Bob reaches the north pole, on a flattened map, his frame of reference breaks mathematically because the north pole, despite being a single point, is stretched out. You literally get a divide by zero problem.
This also happens in the Schwarzschild metric! Except that, just like how the north and south pole on a flat map are points where math breaks, the Schwarzschild metric has the event horizon and the center of the black hole as places where you can get a divide by zero error.
If you do a coordinate transformation you can get rid of the problem with the event horizon in a Schwarzschild metric. The same way you can get rid of the problem if you do a coordinate transformation of a flat map to a spherical map.
I do think that the infalling observed will experience their universe "fast-forward" as they approach the event horizon; each infalling second increasing in non-infalling duration, soon to be...
I do think that the infalling observed will experience their universe "fast-forward" as they approach the event horizon; each infalling second increasing in non-infalling duration, soon to be second to decades if not more, but another effect occurs. The two observers (infalling vs not) will no longer agree on what dimension is temporal.
The singularity becomes temporal for an observer that travels beyond the event horizon. So what's a point in space for those outside the event horizon is an event in the future for those that do cross.
Likewise, for the infalling observer the event horizon becomes temporal, it becomes an event in the past, no longer accessible. And funnily enough, a point in spacetime where matter is ejected by forces so strong there's no way to approach it; a repellant force similar to the opposite of gravity (the opposite of a black hole) is the definition of a white hole.
Keeping in mind that to an observer within the black hole this white hole will always be temporal, not spatial - an event in the past where all known matter and energy was ejected with no way to travel backwards in time to approach it - I think a better name for the "Big Bang" might be our "White Hole Event".
This hypothesis could also describe why we don't see white holes as they're predicted - because all white holes can only be perceived as an event in the past.
The so-called "plunging region" is the area within the Innermost Stable Circular Orbit--that is, in order for an orbit to remain circular, the particle would have to orbit faster than the speed of light, which is impossible. Once it crosses the ISCO, the time until the particle reaches the event horizon is measured in milliseconds, and sometimes even microseconds (in its own frame of reference--remember that we're talking about general relativity with time dilation like in the movie Interstellar).
In actuality, what likely happens is that the particle never quite touches the event horizon because in their reference frame, the clocks in the rest of the universe sped up infinitely and either the universe died or the black hole dissolved in those microseconds...which seems to mean that nothing ever quite reaches the event horizon, which makes black holes even more confusing. How can they form if it takes an infinite amount of time (in our frame of reference) for matter to reach the event horizon? Shouldn't that mean that inside the event horizon is a neutron star of almost the mass needed to form a black hole and then there's a region of infinite density hovering just outside the event horizon? But if that's true, how can a black hole grow? Shouldn't it take infinite time for mass to accumulate to the point that it would get swallowed by the event horizon? š„“šµāš«
I don't think that's quite right. To an outside observer, the particles clock slows and slows till stopping just outside the event horizon. The outside observer doesn't ever see the particle enter. It's as if the particle contributes to the black hole's mass by sitting there right at the horizon.
However from the particle's frame of reference, they just fall right in. The perceived time dilation of the exterior universe is not so extreme at the event horizon.
Your questions about extreme time dilation etc don't come up till the particle is much much closer to the singularity, but it doesn't really matter as far as growing the black hole. Once the thing crosses the event horizon, it's in there, contributing to the black hole's total mass.
My understanding is that it is true that time dilation reaches infinity at the event horizon when using Schwarzschild coordinates, though it is considered inaccurate to use those coordinates in that regime for that reason. The "frozen star" that I described is an outdated understanding of black holes. The problem js that I haven't been able to find an explanation for the actual truth that goes beyond "just trust me bro"while saying what we should trust. Like if you asked how we know that 1+1=2 and I said "well when you add 1 to 1, you get 2," and I didn't teach you that | = 1, | + | = ||, and || = 2, so 1+1=2.
So I accept that it's true that what I said is wrong, but my astrophysics professors taught us that we should not just trust the explanations that everyone else insists are true. That's how we discovered dark matter, after all.
Unfortunately, I was really shitty at the actual physics classes in my astrophysics degree, so I won't be able to pursue further formal education in that subject. Maybe GPT-6 will be good enough to teach me in a personalized way that helps where I was overwhelmed in my undergrad classes.
That the Schwarzschild coordinates blow up at the event horizon is an artifact of the coordinate system itself. You address it using EddingtonāFinkelstein coordinates, which introduces an opposite blow-up to negative infinity at the same rate of approach, cancelling out the behavior at the event horizon. That gives you a model to chart behavior through the event horizon while still showing that as time goes to infinity we only ever see light from outside of the event horizon.
Interesting, thanks. That's a pretty succinct explanation. Also interesting that I've never come across the name of that coordinate system before.
My understanding before all this was that coordinate systems are always accurate but not always good at making sense of what's going on, similar to how radial and rectilinear coordinates make sense in different situations, but I guess they must all be approximations of some sort that simplify maybe the Einstein Field Equations? It's been several years since I last studied GR and that was only at the undergraduate level.
I took a run at your deeper question in your other reply to me. But to answer the question on coordinate systems, I think really what you are thinking of is the metrics we use to calculate distances. Those different metrics reflect the spacetime we are measuring. They should always be accurate to be useful, but they are not necessarily "complete." In fact, the EddingtonāFinkelstein coordinates are still not complete; we need additional terms to make them complete, but that creates a few limitations in their use. But the big takeaway is that metrics are just different ways of measuring distances in different spaces.
An old and fun read is "One Two Three... Infinity" by George Gamow, who gives a very layperson motivation for the basic metrics of spacetime without all the mathematical wrapping. General Relativity from A to B by Robert Geroch is another good book that takes a much deeper look at GR.
Since the black hole is vanishing due to Hawking radiation, and the particles never enter the event horizon, what does the outside observer see as the black hole gets smaller and smaller? And when the black hole goes poof, what does the outside observer see happen to the "stuck" particles?
Hawking radiation decreases the mass slowly, and particles that go past the event horizon do actually get pulled to the singularity, increasing the mass. So hawking radiation would only make black holes smaller when there is little to no incoming particles.
When people say that it takes an infinite amount of time to reach the event horizon, they mean from the perspective of an observer some distance off. The particle itself continues to experience the normal progression of time as it passes the event horizon.
The discrepancy in observed vs experienced events is due to gravitational time dilation.
I get that you just explained how EddingtonāFinkelstein makes sense of the scenario, but is there a deeper, even graduate-level, if necessary, explanation that resolves the paradox of infinite time in one reference frame and finite time in another and which doesn't involve needing to just do the calculus yourself? I just don't get how a time dilation equation can have infinity on one side and a finite number on the other...although, as I write this, I guess that in SR as v approaches c, Ī³ approaches infinity. But this feels different because it would be like saying that Bob sees Ī³ approach infinity when looking at Alice, but Alice sees Ī³ remain finite.
It's been a long time since I did any deep math in physics, and that was modeling fields of moving source charges, so it's not exactly in this space. That said, I think you are maybe grappling with a conceptual issue upstream of the math of general relativity. Let's start by simplifying the math and see if that helps.
You have a good grasp, I think, on special relativity. Indeed, the time dilation factor pops out when applying the Pythagorean theorem and the classic example of bouncing light off moving mirrors. Here is one example that walks through the derivation, and there are also good videos out there on it.
Even more generally, I think we agree that nothing moves faster than causality, and it just so happens that photons move at the speed of causality. Things like time, signals, and the speed of light are emergent properties from the speed of causality. When we observe something going near the speed of causality, its coordinate time moves more slowly than ours from our frame of reference. Because the speed of causality is fixed in all frames, the only thing that is left to flex is spacetime itself.
This gives rise to our notions of metrics, which is just a way of saying how we measure between two points in different geometries. To measure the distance between two points in spacetime separated by (dt, dx, dy, dz) we would use the following metric:
ds2=ādt2+dx2+dy2+dz2
Which should look pretty familiar as it is a basic extension of our distance equation to four dimensions. The left-hand side, ds, is the line element and invariant under all reference frames. Again, since all frames of reference will calculate ds the same, what is left to flex is spacetime itself (the RHS). The sign on the time unit is what gives rise to time dilation.
Quick recap. We agree that spacetime flexes, and we agree that this is because the rate of causality is fixed in all frames of reference.
Now, with general relativity, it isn't dilation caused by different velocities but by the warping of spacetime by mass. But we have the same basic simple concepts. We will have a metric that is used to measure a line element as the distance between two points separated by (dt, dx, dy, dz). All we do is a few simple translations to account for different spacetime curvatures by switching to polar coordinates and substituting different terms.
ds2=ā(1ā2M/r)dt2+dr2/(1ā2M/r)+r2(dĪø2+sin2Īø dĻ2)
If you let the mass of the object warping spacetime go to 0, you can see that these are actually identical equations.
So, the math and the concepts of the different passages of time, even infinite vs 0 time, are qualitatively the same between special and general relativity. We have to use some fancier distance calculations to measure distances in general relativity with warped spacetime, just like we would measure distance differently along the wall of a curved flower vase compared to the table's flat surface.
At this point, you might object and say, but what does it mean for light to take an infinite time to leave the event horizon to reach a distant observer? You might accept the math's qualitative behaviors and geodesics but balk at what it represents.
So, let's get back to causality. Remember, the speed of light is bounded by the speed of causality. If events in spacetime are separated such that light cannot travel between the events in the time between them, then they can not be causally linked. Once a particle crosses the event horizon, it loses its ability to have a causal link to anything outside of the black hole. That must cause the time for any signal, such as light, to take an infinite time to reach an outside observer.
That's one of many ways to think about what happens when something crosses an event horizon. There are others, and I think depending on your own perspectives and thoughts, different explanations make more or less sense. I like the causality argument because it motivates a forcing behavior for why the light has to take infinite time, i.e., the speed of light is an emergent property of causality. Any event in spacetime involving the particle inside the event horizon is forever prevented from having a causal influence on anything outside, so any signal the particle can give off must take infinite time.
All the other metrics we introduce that model the behavior differently don't change the underlying behavior of the causal barrier that is an event horizon.
Anyway, I'm pretty low on sleep now and don't know if that helped. If you narrow down where you are skeptical, I'm happy to take another run at things.
I'm going to respond to this longer comment before looking at your other one.
Thanks, this is a good refresher for sure, especially on exactly what metrics are. I knew I learned them in my Cosmology & Relativity class, but I forgot that they were essentially the Pythagorean theorem in spacetime.
I also certainly understand and agree with everything you said about causality. It absolutely makes sense that something would need to take infinite time to pass through an event horizon due to causality, light cones, etc.
I think the problem I have is along the lines of Zeno's Paradox. If it take an infinite time for something you're observing to reach the event horizon, how could you reach the event horizon in a finite time?
If I hold a particle at arm's length while I'm falling toward a black hole, it would appear to take an infinite amount of time for that particle to reach the event horizon. Yet I can reach the event horizon in a finite time? So I guess it seems to logically follow that, from my perspective, the particle would reach the event horizon at the exact same time as me. Except that it also reaches the event horizon at t=ā? So it would seem that it would take me an infinite amount of time to reach the event horizon also--or at least until the black hole evaporates.
And now that I think of it, in the event horizon's reference frame, shouldn't time no longer exist similar to how a photon does not experience time because it moves at c? So shouldn't it be impossible to reach the event horizon in the same way that it's impossible to accelerate to c?
Maybe the explanation is the same as how infinite acceleration is impossible, yet accelerating from 0 to 0.000000...001 is both infinite and not? Although if spacetime is quantized, I suppose that could resolve that "paradox"...or with space and time both just being dimensions of spacetime, I guess that would render infinite acceleration moot because it's all just movement in spacetime. Fucking hell.
I think there are a few things going on. We've been a little loose with specifics, as is appropriate for a casual conversation. But I think we need to be careful with the specifics if we want to clarify further.
First of all, let's disclaim a few things. First, we just don't know some things yet. We have ideas and predictions, and areas of uncertainty and speculation. There will always be some physics grad student ready to wade into a conversation and say "well actually, black holes never form, those are collapsers..." At a some point there are some things we just don't know, and some distinctions that just don't help us model or understand.
That said, let's imagine a laser approaching the event horizon of a black hole, and a distant observer, with the laser emitting photons at the observer. That distant observer is maintaining, somehow, a relatively fixed position relative to the movement of the black hole through space.
From the perspective of the laser, let's say starting at 10r, it will take less than a second to cross the event horizon at 1r (which they don't experience) and then squish into the singularity.
To the outside observer, time will slow for the laser, and it will slow down as it approaches the event horizon. The light from the laser will become redshifted as the laser approaches the event horizon. Each photon will lose energy, not losing speed but reducing the frequency until it enters the radio spectrum.
The time between each photon will increase. From the lasers perspective, it is emitting just as many photons per second as normal. But as its time slows relative to the observers time, the observer will begin experiencing an increasing delay between photons.
Eventually, when the laser crosses the event horizon, there will be one last photon emitted that escapes. After that, the photons are trapped inside. But that last one will begin its long journey to the observer.
Now, in the lasers time, once it crosses the event horizon, the observer would be able to detect the increased mass of the black hole at the speed of causality, even if it appears that the laser hasn't entered it and is still emitting photons. Those photons have been crossing vast spaces to get to the observer long after the black hole has absorbed the laser in proper time, and the increased mass begun propagating through the gravitational field at the speed of causality.
This will stay that way for a long time. The observer will have to wait a finite but unknown amount of time to receive the last photon, tired and stretched from its journey. And that might happen to coincide with the final demise of the black hole through Hawking evaporation.
But there will be a last photon. That observer just won't see it until far into the future, likely as the black hole disappears, and the observer will never be able to know when the last one was received in that frame of reference.
It's all about the frame of reference, the warping of space and time, and the consequence of general relativity which is that multiple truths can exist, but some matter more than others. The laser can be in the black hole contributing to the mass of the singularity, and to the observer outside the event horizon, still be slowly firing off photons for billions of years.
People will equivocate over things like, did the laser cross the event horizon, or did the event horizon rise up to envelope the laser, etc... And maybe some of those distinctions matter some of the time. But I think what matters most is this:
Everything outside of that is an artifact of warping space-time. What matters is causality. Once the laser crosses the event horizon, that's all she wrote. Any observer outside in any different frame of reference will see and experience different time dilations, etc. but none of them could travel to the laser they see and grab it before it goes in. There is only one laser, smeared across many perceptions of time, but as you change your frame of reference to approach it, it all collapses to the laser crossing the event horizon. Chasing the laser will put you right on through the event horizon, and you will experience in fast forward the lasers journey.
If nothing else, the fact that black holes have a lifespan through evaporation means that nothing can truly be held at the boundary forever, or take truly infinite time to approach, barring some fundamental change in our understanding of them.
One last caveat: at one point in my career I got into quite a heated argument with an editor from nature over sensationalist claims about black holes. So my explanation is one of multiple explanations you might hear. What I would say in defense of mine, is that it furthers a conceptual understanding at the expense of hypothetical nuances that may or may not be true, and may or may not matter. But the people pushing the truly infinite approach time argument, are, in my opinion, doing it to promote the mystic of general relativity to the general population rather than to help them develop a real qualitative understanding of what is going on.
Edit: I think I cleaned up a few inconsistencies and ambiguities, but let me know if I missed something. I'm on my phone, so it's a little hard to proof for consistency across multiple paragraphs.
I appreciate the patient, in-depth responses, and especially the last but talking about how the "infinite time" claim is just sensationalizing GR.
I still just don't get how the laser actually reaches the event horizon though. Am I wrong in seeing the event horizon as the point of infinite time dilation, similar to how c is the speed of infinite time dilation in Special Relativity?
You are bringing the point right down to the razor of what is known vs what is predicted.
That said, I believe you are incorrect in that the event horizon is a point of infinite dilation. The event horizon is only a coordinate singularity. The physical singularity is the actual singularity inside the event horizon. That said, the event horizon is very, very close relatively speaking to the physical singularity. It would be like picking a point very close to an asymptote. It might be a small difference but it is the difference between arbitrarily large and truly infinite.
I can already feel someone ready to disagree with my assertion above, so let me further defend it. The usual models that show a blow up at the event horizon are modeling a simplified static black hole, not a growing one. When you model a growing one, either the object "passes" the event horizon, or the horizon "envelops" the object. What is the functional difference? Mostly thousands of hours of people arguing in physics forums.
Whether proper time really extends past the event horizon, whether event horizons ever even really form, black holes vs collapsors, etc. is more of a semantic debate than a practical one.
At the end of the day the observed phenomena we call a black hole exists, new mass is incorporated into the phenomena in proper time with the one quibble of passing the horizon versus enveloped at t=o, and the phenomena has a finite lifespan in the form of evaporation. Those core facts pretty definitively rule out "infinity" with the one exception of information reaching the distant observer in their original frame of reference.
Also, the above is the exact argument I had with the editor from nature. š
Okay, so you would say the singularity is equivalent to reaching the speed of causality and the event horizon is like reaching...nothing, because it's an imperfect analogy, which sounds fine to me.
And yes, of course the practical difference between everything falling through the event horizon and everything chilling just outside the event horizon is essentially non-existent because the forces experienced by everything outside of that point will be identical.
That said, there would of course be important differences for quantum gravity, using wormholes to travel the Universe, etc., but until we can figure out how to harness the power of quantum gravity...there's no practical difference.
I'm also glad to finally find someone who agrees that infinity is silly when black holes are expected to have finite lifespans. Especially because in the rest of physics, we use perfect, theoretical objects all the time, so it would be silly to ignore that we could just discuss a theoretical laser that emits nearly infinite photons at a nearly infinite energy with an infinitesimal time gap between photons so that even the idea of "photons keep coming less and less frequently so you never know quite when you've seen the last one" is pointless within a theoretical, educational framework.
So I'd say that while the exact question of "how does something ever actually cross the event horizon?" isn't exactly answered, it's at least resolved by "that's where physics kind of starts to break down and it doesn't really make a difference anyway."
...for now ;)
I think that's a good way to look at it. We have some observational support for things like Hawking radiation, which seems to put a lifespan on black holes, and that is in tension with any model choices that require an infinite blow up without some new process or model that resolves things at the end of the black holes existence.
One of the most important topics I took in college years ago was the philosophy of empiricism, which I think is an important thing to balance with theoretical models. We don't want to dismiss sound modeling, but we also don't want to be dogmatic in the face of obvious tensions with observed phenomena.
Folks that insist on infinity without at least acknowledging the unknowns and the tensions are, in my mind, still trying to grapple with the concept themselves, or probably not engaged in the observational side of things at all.
Cheers!
Sounds like that would be a great class for all STEM majors to take. It seems like far too many people blindly trust in "science" for science's sake, without knowing what they are actually putting their faith in and without understanding that it is just a philosophical system in the end and it has its limits just like everything else, especially when it comes to poorly conducted research.
Thanks again!
Cheers! I'm specifically curious about, from the perspective of an immortal observer studying the black hole that watches it for trillions of years, what does the process of the black hole vanishing due to Hawking radiation look like, when no particle has ever crossed? I definitely understand that for the particle itself, there's no contradiction. But for an outside observer, mass that has never fallen into the singularity is being shed away, and I'm wondering if that's ever resolved.
It would probably look pretty boring for most of the time. Once the black hole finished pulling new matter towards it, its accretion disk would shrink and disappear, which is the source of the light black holes give off.
You would be able to detect changes in the black hole by observing changes in the region of space it occupies and its shrinking sphere of gravitational influence.
We don't have good models for what happens at the very end though, when the black hole gets small. Maybe it just fizzles, or maybe something more exciting happens. We just don't understand gravity at small scales very well.
I think what might be confusing is that we talk about a particle taking forever to reach the event horizon. However, that isn't really the case, so it's not as if particles are hanging out forever emitting light and other signals.
What really happens is that light that passes the event horizon takes an infinite to reach any fixed observer outside of the event horizon. The light emitted outside the event horizon travels off into space like normal, although locally it follows the distortion lines created by the black hole.
So to an observer fixed relative to the black hole, it would be a boring show once the accretion disk was finished being absorbed.
My understanding, and I'm absolutely not a scientist, is that there's no preferred frame of reference, right? From the point of view of the observer, it's not that there's an illusion that the light didn't cross; the light doesn't cross, from the observer's point of view. Am I misunderstanding the concept?
I just think that it's an interesting contradiction that from the point of view of the observer, nothing ever crosses the event horizon, but the black hole still shrinks.
There's no contradiction from the point of view of the falling observer. You fall through, die in some awful way, and reach whatever the hell thing exists in the centre. But from outside, the observer never falls in, but the black hole is still losing mass that the observer swears never made it to the centre.
You are correct, I think, with maybe one clarification. Like you say, to the object falling in, there is no magic line. It goes in and squish. But any signal it emits inside the event horizon never leaves.
To the outside observer, the object approaches the event horizon and then disappears. There isn't some perpetual ghost emission of the object emanating forever. That is why we can't directly observe many of the black holes we've identified. All of the matter in their accretion disk has been absorbed and no more light is being emitted.
Now, an object might appear to be really slowly disappearing into the event horizon depending on dilation effects, but that is different than the object never disappearing. You would see the object redden, dim, and eventually vanish.
Does that make sense?
Edit: @Raistlin I forgot to address your main point. The reason the black holes shrink is because they emit radiation through a quantum action. You can look into Hawking radiation for the details, but that is why they shrink. That is also part of the issue in understanding them better: we don't have a unified model for gravity and quantum effects. So light never leaves, but quantum effects create particles just outside of the event horizon that in some cases are able to leave, reducing the energy of the black hole.
Could I ask a hypothetical? Say you're an immortal observer watching the collapse of a star. You also have unbelievably advanced technology that allows you to detect the most minute signals, down to the Planck length. You observe the star collapse on itself. Most of the matter gets blasted away in the supernova, which you of course survive.
You never see any matter cross the event horizon, right? From your point of view, nothing crosses it, and it's all smeared across the surface of the event horizon. Yet there's still a singularity, and the black hole is still losing mass due to quantum effects. Where did the singularity come from, just taking the point of view of the observer? Where is that lost mass coming from? If I'm understanding this right (and I'm likely not), you never observe the lost mass cross the event horizon, and some random other mass is being emitted as heat due to quantum effects, and eventually the black hole dissipates and you never once saw anything cross the horizon.
What you're saying makes sense practically. If the light is red shifted into invisibility, then as far as a normal human is concerned, it might as well have crossed the event horizon. But mathematically, from your pov, it can't have. It has to be smeared across the event horizon.
So I think I understand a possible point of confusion. As the observer, you would see things cross the event horizon and disappear. It would be a gradual dimming, and then it would disappear.
Things can cross the event horizon, just only inwards. The models that blow up at the event horizon, showing an asymptotic approach are doing that due to a limitation of the model. We can fix it, and show the path something would take inwards, while still showing that nothing from the inside will ever reach an outside observer. In one of the other comment chains in this thread, I discussed those coordinate schemes.
It's a dense read, but you can get a sense of them by skimming the Wikipedia page.
Stars can become a black by either collapsing directly into one, which takes less than a second, by collapsing into a neutron star and accreting enough matter to collapse into one, or by going Nova while leaving behind a core too dense to stabilize as a neutron star. That is the case you describe.
In that case, the black hole would form and quickly form an accretion disk from the ejected matter. The matter would be pulled in, redden, dim, and then disappear through the event horizon and contribute to the mass of the singularity. As the observer, you wouldn't see the singularity, but you would see the explosion of the Nova, the formation of the spinning accretion disk, the matter disappearing, and the lensing of light from behind the disk. Eventually, you would run out of matter to sustain the accretion disk, and all light around the black hole would dim to nothing. Then the only detectable energy would be very low levels of hawking radiation. That, coupled with the changing observation of the effects of gravity on the region coupled with any lensing of light from behind the black hole would be all you would see.
Does that help?
Something to remember is that (gravitationally) a solid sphere, a hollow sphere, and a point mass all behave the same from the outside. If the outside observer determined all infalling matter to be smeared on the horizon (hollow sphere) they'd make the same predictions as if they considered only the singularity (point mass) or considered the volume of the event horizon itself (solid sphere).
Solid and hollow spheres do not (gravitationally) behave the same on the inside, though, so there is a discrepancy on the predictions there that I am frankly unqualified to speculate about.
In some way it doesn't matter though, because both models agree that the interior is casually disconnected from the outside, and they agree on the exterior behavior.
IIRC they do disagree on what happens to the event horizon while an object passes through it. I think this is what @krellor was getting at, referring to active research on how black holes actually form.
This is going to start of strangely, but bear with me here:
Imagine the path of a plane drawn on a flat map, and it flies over the north pole. As the path gets drawn over time, assuming the plane has roughly a constant velocity, at first the line will start slow. Then go slightly more faster as it gets closer to the north pole. And faster, and faster... and then, when it reaches the northern most point of the map, its speed reaches infinity as it crosses the north pole, and appears at some other point in the northern edge of the map. It will then go slightly slower and slower as it moves away from the north pole.
This is of course, complete bullshit. The plane doesn't just pop in and out of existence, nor does it reach infinite speed. What happened here is that because you're trying to project a 3D sphere with a 2D flat rectangle, there are weird points where your math just breaks down.
The event horizon of the black hole is like that, because general relativity describes gravity as a curvature of space-time, not a force. Here, the later part is especially important: time also gets 'bend' the more energy is packed in a single region.
Because you're looking it at is an outside observer, from your frame of reference, the same thing sort of happens as with the plane analogy. The paths look weird for you, but anything that falls into the black hole won't experience that sort of weirdness.
Another way to think about this is that, because gravity here is bending of space-time, the closer something is to the event horizon, the longer it will take to go outside of the black hole. If a light bulb is far away from the black hole, there's little difference. But if it's close enough, the light needs to travel more space-time as it's effectively stretched near the event horizon.
So if a light bulb emitting light falls into the black hole, at first, you'll see the light just fine. But when it gets closer, it will take just slightly more time, then longer, and longer... in a way, the 'signal' of light gets spread out over time. This is also why the light gets red-shifted by the way, the photons get smeared out over space-time, increasing it's wavelength. But in the mean time, the light bulb will cross the event horizon, no problem.
Now, there's one problem with this, which relates to another point in your comment:
The idea what I've just said about reference frames doesn't quite work at the core of a black hole. If you do the math, the time it takes for something to fall towards to very centre of the black hole is finite. Meaning that everything that falls in the black hole does reach that point in space-time. At that point, the math of general relativity breaks down. Which is commonly perceived as a breakdown in the theory.
Gravitational waves emitted by merging black holes have been studied to look on whether there are 'echoes' of potential inner structures but so far, nothing has turned up. There are of course all kind of exotic theories on what goes on in a black hole but really, no one knows.
Thank you for the great simplification. I had a decent length response that just vanished, so I'll just say I'm confused because your example seems to be like saying that Bob's speed appears to approach infinity as he nears the North Pole, but on a map centered on Bob, Alice's speed doesn't appear to approach infinity as her location relative to Bob approaches the "North Pole."
Well, the thing is, the moment that Bob crosses north pole, it doesn't really make sense to talk about the flat map projection as a frame of reference.
If you fall into a black hole, you don't see anything out of the ordinary either. An outside observer would see a person never quite falling in, only vanishing over time as light gets red shifted, but the the person falling inside the black hole will just see the Universe go on (although it will get blue shifted).
The problem is that as Bob reaches the north pole, on a flattened map, his frame of reference breaks mathematically because the north pole, despite being a single point, is stretched out. You literally get a divide by zero problem.
This also happens in the Schwarzschild metric! Except that, just like how the north and south pole on a flat map are points where math breaks, the Schwarzschild metric has the event horizon and the center of the black hole as places where you can get a divide by zero error.
If you do a coordinate transformation you can get rid of the problem with the event horizon in a Schwarzschild metric. The same way you can get rid of the problem if you do a coordinate transformation of a flat map to a spherical map.
I do think that the infalling observed will experience their universe "fast-forward" as they approach the event horizon; each infalling second increasing in non-infalling duration, soon to be second to decades if not more, but another effect occurs. The two observers (infalling vs not) will no longer agree on what dimension is temporal.
The singularity becomes temporal for an observer that travels beyond the event horizon. So what's a point in space for those outside the event horizon is an event in the future for those that do cross.
Likewise, for the infalling observer the event horizon becomes temporal, it becomes an event in the past, no longer accessible. And funnily enough, a point in spacetime where matter is ejected by forces so strong there's no way to approach it; a repellant force similar to the opposite of gravity (the opposite of a black hole) is the definition of a white hole.
Keeping in mind that to an observer within the black hole this white hole will always be temporal, not spatial - an event in the past where all known matter and energy was ejected with no way to travel backwards in time to approach it - I think a better name for the "Big Bang" might be our "White Hole Event".
This hypothesis could also describe why we don't see white holes as they're predicted - because all white holes can only be perceived as an event in the past.
As someone who was never in a science major, I am in genuine awe of the comments in this post. Please keep this going.