Comment by darkmighty | Hacker News Reader

Comment by darkmighty | Hacker News Reader

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> 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.

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.

> What matters in the end is what the observer sees, which, according to you, would be (for Bob, far away):

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.

What do you mean by at the same time? Those two photons reach Bob at exactly the same instant?

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.

> What do you mean by at the same time? Those two photons reach Bob at exactly the same instant?

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.

> I think you have a misconception about GR here.

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.

Well you've convinced me that, if Hawking's model is as you say, it's obviously incorrect :P

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.

> you've convinced me that, if Hawking's model is as you say, it's obviously incorrect

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?

I don't have time to explore this topic in depth right now (way too much on my plate already, and I'm not that fast or brilliant), but I suspect there's literature on this topic. Something I could find is this:

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 firewall hypothesis is one of the quantum gravity hypotheses that is an open area of research, yes. But even if the firewall hypothesis ends up being confirmed (which won't happen any time soon), that does not mean it's the only consistent hypothesis. Your claim was that the classical GR model, and Hawking's original model, were inconsistent. They're not. They might end up not being correct when quantum gravity effects are taken into account, but that doesn't make them inconsistent.

The Firewall as spelled out in the original paper is widely considered to be unlikely, not in the least because it violates the equivalence principle. There are weaker versions of the firewall based in M-Theory which exist because there is no singularity, and the event horizon is actually the surface of the fuzzball which takes its place, but that’s a different sack of weasels.

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