> You can fall into a black hole in finite time. It just looks like it takes forever.
This one is really interesting! I've definitely never seen anyone emphasize this before.
This one is really interesting! I've definitely never seen anyone emphasize this before.
1) It looks like it takes forever, to an outside observer, for anything to reach the event horizon. So if no matter appears to reach event horizons, how can they (event horizons) form in the first place (i.e. exist in our universe)?
2) While it takes forever for matter to fall in (again to outside observers), it takes finite time for black holes to evaporate via Hawking radiation. So not only do black holes would take forever to form, they seem to have to extinguish before being able to exist (again in the sense of event horizons).
I'm not a physicist, but my speculation is that Black Holes don't really exist, they're just a limit of a process that approaches but doesn't converge to a singularity, which I think is unphysical.
1. Because if you don't have a black hole yet then there is no event horizon to prevent you from falling in and creating one. I think the event horizon wouldn't form at exactly the same point whose crossing would finally increase density enough to create it, so this shouldn't be a problem. (Although, again, since the event horizon doesn't exist yet, I think it might still not be a problem even in that case?) I would also expect that quantum fluctuations can also inject matter into a black hole, just as they can remove matter from it.
2. Again, they wouldn't take forever to form -- see above.
I'm pretty sure black holes have been observed indirectly, so the idea that they actually don't exist would require a pretty rock solid alternative explanation!
What we have observed indirectly are compact objects that emit no light, but contain a large enough mass in a small enough volume that they can't be anything else but a black hole, if we only take classical GR into account.
As I responded in another post just now, it is possible that black holes, in the sense of objects with actual event horizons (boundaries of regions from which light will never escape, even in the infinite future), cannot exist when quantum gravity effects are taken into account. If that is the case (and it is not clear whether it is--as I said, this is an open area of research), then the objects we call black holes based on our current observations won't have actual event horizons--eventually, in the very far future, light will escape from those compact regions. But they will still have apparent horizons, i.e., surfaces from which outgoing light is not escaping now (or for a very long time in the future). And that, in itself, is sufficient to show that the issues raised by darkmighty are not valid.
Then you haven't spent much time looking at actual textbooks on GR, since all of these issues are addressed there. (Not to mention in many peer-reviewed papers in the field.)
> if no matter appears to reach event horizons, how can they (event horizons) form in the first place (i.e. exist in our universe)?
This is the same fallacy as the fallacy that nothing can actually fall into a black hole because it looks like it takes forever from the outside. Oppenheimer and Snyder published a mathematical model way back in 1939 that shows how a black hole can form in a finite time from the gravitational collapse of a massive object, as seen by an observer falling inward on the surface of the object. The collapse appears to take forever as seen by a distant observer, but this is an optical illusion caused by the effect of spacetime curvature on the paths of light rays. This has been studied for decades and is thoroughly understood.
> While it takes forever for matter to fall in (again to outside observers), it takes finite time for black holes to evaporate via Hawking radiation.
Wrong. First, if matter is falling in, the hole is gaining mass, not losing it, so it will never evaporate even though, in principle, it is emitting Hawking radiation (in practice this radiation is many, many orders of magnitude too faint to detect for any black hole we can observe).
Second, if you include quantum effects, and therefore Hawking radiation in your model, you've changed the model, and it is no longer true that a distant observer will never see anyone falling into the hole. Instead, the distant observer will see light signals emitted by objects falling through the hole's horizon at the same time the distant observer sees the hole evaporate. (At least, that is the case in the simplest model, the one Hawking used when he first published his prediction of Hawking radiation. More complicated models have been developed since, and we won't know which, if any, of them is really correct until we have an experimentally confirmed theory of quantum gravity.)
> I'm not a physicist, but my speculation is that Black Holes don't really exist, they're just a limit of a process that approaches but doesn't converge to a singularity, which I think is unphysical.
Your speculation is uninformed and wrong. It is possible that an actual black hole, with an actual event horizon, is impossible when all of the laws of physics, including the laws of quantum gravity, are taken into account. This is an open area of research. But if it turns out that actual black holes cannot exist, it won't be for any of the reasons you give.
But isn't equating the two observers incorrect? That is, when speaking of 'formation time', we are speaking of the formation time by observers at infinity, free from the effects of local curvature. What I understand is that all observers must agree on reality, thus on whether the BH forms at all: if the infalling observer makes it through an EH and into a singularity, then those exist (by definition) as unique reality. But evaporation seems to complicate this classical GR view understood for a while: since now outside observers see finite-time quasi-evaporation, infalling observers must observe this phenomenom while infalling, and actually before reaching the EH.
There's no way I can see that:
1) EHs and singularities (i.e. Black Holes as a steady-state phenomenon) exist;
2) All observers agree on reality of their formation and evaporation.
I defiantly conclude they don't exist (or I'm missing something major) :)
That is, black holes in nature would be something akin to a extremely time-dilated "Object trap" without singularties (although perhaps it must gain an apparent horizon?).
There is no "equating the two observers".
> when speaking of 'formation time', we are speaking of the formation time by observers at infinity
No, we aren't. The hole isn't formed at infinity. The time that is being talked about for observers at infinity (or more correctly, very far away) is the time it takes light rays, coming outward from the object that is collapsing into a black hole, to reach those observers. The curvature of spacetime near the horizon is such that it takes longer and longer for those light rays to get out to the observer far away, the closer to the horizon they are emitted. At the horizon, outgoing light rays do not move outward at all, due to the curvature of spacetime there, so they never reach the observer far away--hence that observer never sees the horizon form. But, as I said, that is an optical illusion caused by the curvature of spacetime.
> What I understand is that all observers must agree on reality, thus on whether the BH forms at all
All observers agree on observable events and measurement results that they can all observe, yes. But if an observer cannot observe a particular event (such as the horizon forming) because spacetime curvature prevents light rays from that event from ever reaching him, then he can say nothing at all about whether that event happens or not.
> evaporation seems to complicate this classical GR view understood for a while
It complicates it in the sense I said before: that observers far away, instead of never seeing infalling objects cross the horizon, now see those objects cross the horizon (more precisely: see light rays emitted outward by those objects when they crossed the horizon) at the same time they see the hole evaporate (more precisely: see light rays from the hole's final evaporation). It does not mean what you claim, that infalling observers will see the hole evaporate before they fall in. The spacetime geometry of an evaporating black hole (i.e., including quantum effects) is different from the spacetime geometry of a classical black hole that never evaporates. The statement that a distant observer never sees an object cross the horizon is only true of the latter, not the former.
> I defiantly conclude they don't exist (or I'm missing something major) :)
The second is the correct choice. You need to stop being defiant and start learning what the models of black holes in physics actually say.
> black holes in nature would be something akin to a extremely time-dilated "Object trap" without singularties (although perhaps it must gain an apparent horizon?)
To us far away, an apparent horizon looks the same as an event horizon, and works the same--all the things I said above would still be true (at least for the time we have been observing--see below for how long it would take for differences to become observable) if the objects we observe and call black holes actually have only apparent horizons (because of hypothetical quantum gravity effects that, as I've already said, are an open topic of research), not event horizons. And all of your criticisms would still be wrong. (In at least some of the hypothesized quantum gravity models, there is no singularity and no event horizon, only an apparent horizon; but to us far away, the object looks and works the same into the very far future; it takes something like 10^70 years for the difference to be observable.)
I think you have a misconception about GR here. In GR, spacetime isn't just an "optical device" that delays rays cast in an absolute reference. In relativity, the behavior of light rays is actually closely related to interpretation of time and space. You can't separate the two. In fact, the definition of (relative) local time is given exactly by the rate a "light clock" ticks when communicating periodically to a "light clock" located elsewhere. Approaching the event horizon, the rate of clock ticking goes to 0 relative to an outside observer (to the the limited extent that coordinate frames can be defined in GR). So classically you can't say that to the outside observer the BH forms in finite time, I don't think. What matters in the end is what the observer sees, which, according to you, would be (for Bob, far away):
Alice falls into BH -> Alice approaches EH -> Alice's BH evaporates -> Alice finishes falling into the BH
That's not possible! The light rays from evaporation, which happens, in Alice's own frame, after she falls into the BH, cannot precede the light rays from her fall. So she cannot truly go past the EH.
Not what you said. What Bob sees is:
Alice falls into BH -> Alice approaches EH -> Alice reaches EH/Alice's BH evaporates
In other words, as I said, Bob sees Alice crossing the EH at the same time he sees the BH evaporate. Bob still never sees any light signals from Alice that were emitted below the EH; those signals are trapped inside the hole and never escape. In Hawking's original model, those signals, along with Alice herself, hit the singularity and are destroyed; they cease to exist, so they never come out again even when the hole evaporates away. An open question is what the correct model will end up being when we have a full understanding of quantum gravity; but whatever that model ends up being, it won't validate the particular issues you are raising.
We had already agreed that General Relativity should imply Bob never sees Alice reach EH, regardless of quantum effects (at least not in finite time). We also agreed that Bob does see the BH evaporate (in finite time to any desired fraction), as seemingly dictated by QM. Thus it cannot be that the two are observed simultaneously!
Moreover, there cannot be a chain of events whereby Alice evaporates into photons (emanating from EH), and those photons (originating from Alice's mass-energy) hit Bob before the photons of Alice when she was near, but did not reach the EH yet (again because Alice cannot be observed to reach EH). It would violate causality.
It can't be that both Alice falls into the EH and we receive Alice's energy from evaporation: either the BH does not evaporate or Alice doesn't cross the EH (even in her own observation). Assuming Hawking radiation really does exist, then some kind of evaporation would need to occur as objects approach the EH, it cannot come directly from the EH boundary.
Could it be that Alice herself is seen to evaporate -- the evaporation might stem directly from Alice, before reaching the EH? My claim that the EH/singularity never forms would be valid.
I could be terribly mistaken of course, but your arguments did not convince me unfortunately (quite the contrary).
I wonder if what I'm missing could be related to the expansion of the EH as a body approximates.
In the original idealized model of Hawking, yes. That is what the spacetime geometry says. One way of thinking about it is that, with this spacetime geometry, the path of any light ray emitted outward at the event horizon travels along that horizon into the future, but the area of the horizon decreases as the hole evaporates. At the instant of the hole's final evaporation, all of the light rays emitted anywhere along the horizon are at the same point as the final evaporation of the hole, and they all go outward from there together. This is a highly idealized model; but that's what the model says.
> We had already agreed that General Relativity should imply Bob never sees Alice reach EH, regardless of quantum effects
No, we haven't. You claimed that, and I pointed out that you were wrong. Bob never sees Alice reach the EH in the classical GR model, with no quantum effects. Quantum effects change the model. In the model including quantum effects, Bob does see Alice reach the EH. See above and my previous posts.
> there cannot be a chain of events whereby Alice evaporates into photons (emanating from EH), and those photons (originating from Alice's mass-energy) hit Bob before the photons of Alice when she was near
This is correct. And it is also what the model of a hole evaporating by Hawking radiation says. All of the light signals emitted by Alice before she reaches the EH will reach Bob before he sees the hole's final evaporation (and the light signal emitted by Alice when she crossed the EH).
> I could be terribly mistaken of course, but your arguments did not convince me
You are terribly mistaken, and you didn't read my arguments carefully enough. See above.
> the expansion of the EH as a body approximates
I don't know what you're talking about here. As a black hole evaporates by Hawking radiation, the area of its horizon decreases. It doesn't increase.
No, you do. Everything I am saying is taken straight from GR textbooks--mainly Misner, Thorne, & Wheeler (1973) and Wald (1984)--and peer-reviewed papers, such as Hawking's original paper on black hole evaporation. You need to go read them.
> In GR, spacetime isn't just an "optical device" that delays rays cast in an absolute reference.
I never said it was. The paths of light rays in GR are determined by the geometry of spacetime. "Optical illusion" is one way of trying to describe the effect of that in the case under discussion. But the effect is there regardless of what you call it.
> In relativity, the behavior of light rays is actually closely related to interpretation of time and space. You can't separate the two.
This is just another way of saying that the paths of light rays in GR are determined by the geometry of spacetime. Which is true, but to figure out what that means in a specific scenario, you need to properly understand the spacetime geometry in that scenario. You evidently do not.
> In fact, the definition of (relative) local time is given exactly by the rate a "light clock" ticks when communicating periodically to a "light clock" located elsewhere.
There is a limited set of scenarios in which this works, but that limited set does not include the case under discussion (Alice falls into a black hole while Bob remains far away). In general in GR, there is no well-defined way of comparing "times" for spatially separated observers. The only well-defined time is local--proper time along a particular observer's worldline.
> Alice falls into BH -> Alice approaches EH -> Alice's BH evaporates -> Alice finishes falling into the BH
I never said that was the sequence of events. It isn't. The correct sequence of events is (note: this is what happens to Alice, Bob does not see all of these events--see my other post in response)
Alice falls into BH -> Alice approaches EH -> Alice finishes falling into BH -> Alice's BH evaporates
If you don't understand how that happens, you need to go study GR textbooks. The model that gives the sequence of events I just described has been well understood for several decades now--Hawking published the first paper using it in the 1970s.
I don't know if this is just a mathematical simplification that doesn't impact conclusions about existence of EHs and singularties, but it all looks fishy.
Why? Note that I'm not claiming (and Hawking never claimed) that his model is experimentally verified--that's obviously impossible since Hawking radiation from any black hole we can observe is many orders of magnitude too faint to observe, if it exists and has the intensity predicted by the model. But the model is perfectly self-consistent.
> it all looks fishy
Why?
https://en.wikipedia.org/wiki/Firewall_(physics)
Basically, my intuition is more or less in line with this firewall phenomenon and that no particle crosses a true event horizon, even in their own frame, and no certainly no singularity.
The point (and this is the main point behind SR, see my comment elsewhere in this thread) is that in your rest-frame, you are, well, at rest. In some ways, it's sort of like an extension of the classical mechanical view that the easiest frame to do physics in is an inertial frame, while in moving frames, you have to add a velocity or a non-inertial frame, you have pseudo-forces. Newton still contented that there was some universal rest frame, somewhere, out there. Einstein essentially made the "inertial frame" a general thing: the best place to do physics is the rest frame for a system, but there is no "universal rest frame" and every observer lives in their own rest frame.
Technically, in GR, space time is also flat where you are, you only notice curvature when you look across distances, so, if you're dilly-dallying in your own rest frame as you fall into a black hole, well, you notice nothing because you're in your rest frame. You already experience this in free fall (which was Einstein's insight), you're just at rest. It's just other observers accelerating with respect to you (say, people on the ground, or the ground itself) measure you as accelerating with respect to them. When you hit the ground is when you are essentially violently accelerated into the ground's frame.
Of course, it's complicated in real life, because people aren't points, and if the scale of curvature is smaller than you're body's height, well, different parts will accelerate differently from each other (say, your eyes observing your feet), so you'll be torn apart.