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Black Hole Puzzle

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Re: Black Hole Puzzle

#31

Post by codethief »

itishappy wrote: post #9

Fun! I think there's an interesting hidden puzzle in the first sentence: > 101 starship captains, bored with life in the Federation, decide to arrange their starships in a line, equally spaced, and let them fall straight into an enormous spherically symmetrical black hole—one right after the other. Does this problem have a globally consistent solution? In the curved spacetime around the blackhole, can everyone agree…

No, they can't. One could very well come up with some other coordinate system whose time & space coordinates are (non-linear) combinations of the usual Schwarzschild time & space coordinates. In that coordinate system, spatial slices of equal time would be different, so spatial distances would be measured differently.

TL;DR Just pretend the author wrote "[…] equally spaced with respect to some observer's frame of reference" (e.g. a stationary observer at infinity that uses the usual Schwarzschild coordinates).

Re: Black Hole Puzzle

#32

Post by raattgift »

cyberax wrote: post #12
kobalsky wrote: post #5

Earlier quoted context omitted.

this is my uninformed guess. why would bob see anything? I understood that the event horizon is a threshold, not a shell that you cross and suddenly can see inside. to see something photons have to bounce on something and reach our eyes, we stop seeing stuff inside the horizon because those photons don't bounce back and they are pulled into the singularity. my logic said that if light can't escape the horizon, then i…

The objects can emit photons by themselves. The problem is that (classically) when you cross the event horizon, the photons that you emit at just that moment will _stay_ _in_ _place_ forever.

> (classically) ... photons

Uhhh... one of those words should go.

Let's keep it fully classical and drop "photon": we're interested in gravitational effects rather than quantum ones (uncertainty, fluctuations, tunnelling, details about scattering and more). Really what we want is something to illuminate (pardon the pun) interesting null geodesics, so a thin collimated beam -- a pencil of light -- will do.

The relevant surface here is the apparent horizon, which can be measured by infalling apparatuses, and not the event horizon, the location of which is determined by the configuration of the entire spacetime. (See Visser PRD 2014 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.90.12...> or the corresponding arxiv version https://arxiv.org/abs/1407.7295>).

> stay in place forever

Note the region inside the shell and the downward-pointing wedge in Fig 1. of Visser 2014 is flat Minkowski spacetime. Everything in that region will work like Special Relativity, as one would expect from the shell theorem.

In particular, a pencil of light directed outwards through the apparent horizon in Fig. 1. will ride the AH down to the singularity, but a receiver intercepting the pencil of light just inside the shell would notice nothing unusual: spacetime is flat there.

Eventually the collapsing shell collides with observers floating weightlessly inside it, and they have a bad time. But they can direct a pencil of light inwards just before the shell hits them.

Re: Black Hole Puzzle

#33

Post by codethief »

jiggawatts wrote: post #21
while_true_ wrote: post #14

Earlier quoted context omitted.

It irks me so many physicists/cosmologists jump from the mathematical GR singularity at the center of a BH to "matter there has infinite density." That's highly unlikely, it's probably quark plasma.

My simple model of it is to just think about spatial surfaces and do "accounting" of the total flux through them. If you draw a sphere around a star collapsing into a black hole, you can treat it as a closed system. If the black hole evaporates, then all of the mass-energy of its progenitor original star needs to leave through these concentric surfaces. This is on the same order of magnitude as a supernova, as it is…

> If you draw a sphere around a star collapsing into a black hole, you can treat it as a closed system. If the black hole evaporates, then all of the mass-energy of its progenitor original star needs to leave through these concentric surfaces.

That would be great if energy were a conserved quantity in General Relativity, which it isn't. Heck, we don't even know how to write down the total energy/momentum of a given spacetime volume.

Re: Black Hole Puzzle

#34

Post by wiml »

jiggawatts wrote: post #13

Any such blog / article / video that features a Penrose diagram is just wrong, because it's using mathematics that doesn't apply to the physical universe. Penrose diagrams draw black holes as if they have existed forever, and will last forever -- that's what the "future infinity" line means . Obviously black holes form at some finite time, and Stephen Hawking showed that they evaporate in a finite time. This matters.…

https://arxiv.org/pdf/1907.04879

Re: Black Hole Puzzle

#35

Post by jiggawatts »

codethief wrote: post #33
jiggawatts wrote: post #21

Earlier quoted context omitted.

My simple model of it is to just think about spatial surfaces and do "accounting" of the total flux through them. If you draw a sphere around a star collapsing into a black hole, you can treat it as a closed system. If the black hole evaporates, then all of the mass-energy of its progenitor original star needs to leave through these concentric surfaces. This is on the same order of magnitude as a supernova, as it is…

> If you draw a sphere around a star collapsing into a black hole, you can treat it as a closed system. If the black hole evaporates, then all of the mass-energy of its progenitor original star needs to leave through these concentric surfaces. That would be great if energy were a conserved quantity in General Relativity, which it isn't. Heck, we don't even know how to write down the total energy/momentum of a given s…

> energy were a conserved quantity in General Relativity, which it isn't

It is conserved, except at cosmological scales. Locally GR conserves energy the same as any other self-consistent physical theory.

Re: Black Hole Puzzle

#36

Post by jiggawatts »

daxfohl wrote: post #28
af3d wrote: post #27

Earlier quoted context omitted.

Somewhat tangentially, what really perplexes me about Hawking radiation (HR) is this: What happens to the individual particles within the black hole as it evaporates? Like say we start with X particles. The black hole emits HR and shrinks a bit. But how exactly does it "give up" the energy from the black hole without destroying something in return? Does one particle just disappear and now we are left with X-1 particl…

At steady state, a classical black hole is fully described just mass, charge, and angular momentum. So there are no individual particles. Which itself was disconcerting to physicists because in the quantum world, information is supposed to be conserved. But they were okay-ish with it being "trapped in there somewhere". Hawking radiation is what blew that up because now the black hole evaporates. So now, nobody really…

> At steady state, a classical black hole is fully described just mass, charge, and angular momentum.

That's just wrong, we know this not to be the case from QM information theory and from thermodynamic arguments! This is the main point Hawking was making. While we don't yet have a good microscopic theory of what's going on, macroscopically we know that the information (entropy) doesn't just vanish into three numbers.

Re: Black Hole Puzzle

#37

Post by 20k »

What this thread is really missing is a simulation. I can't promise its the enterprise (as the performance constraints are crippling), but here's a bunch of cubes instead:

https://www.youtube.com/watch?v=iTw0pJvTkGw

It seems that what you see is the object flattened on the shadow in front of you, and it remains flattened. Apparently past me didn't implement redshift on objects, but its likely extremely redshifted

Edit:

Here's a second better clip, showing this more clearly

https://www.youtube.com/watch?v=npC6lCwYUN0

Re: Black Hole Puzzle

#38

Post by jiggawatts »

daxfohl wrote: post #17
jiggawatts wrote: post #13

Any such blog / article / video that features a Penrose diagram is just wrong, because it's using mathematics that doesn't apply to the physical universe. Penrose diagrams draw black holes as if they have existed forever, and will last forever -- that's what the "future infinity" line means . Obviously black holes form at some finite time, and Stephen Hawking showed that they evaporate in a finite time. This matters.…

This is inaccurate. The object can fall in. Where the argument fails is that it relies on the idea that an observer will see the object redshift forever. But that applies in the classical GR realm only. However, when combined with QFT (which is required for BH evaporation) it no longer holds. In the classical approach, the light that the object emits a second before crossing the horizon will take years to reach the o…

> When this happens, that last bit of light the object emitted >>before(>>highlightYou're not contradicting my argument: I'm saying that there is only a "before", and never an "after". Saying that light emitted before crossing a horizon is visible in a finite time is not incompatible with what I'm saying.

Keep in mind that Hawking's model is known to be oversimplified as well! In his simple evaporation model, the information encoded in the infalling matter is lost, violating QM information conservation.

If you simply assume that no infalling matter ever crosses any horizon, that it all just "blows up" very slowly from the perspective of an outside observer, then there is no QM information paradox, no inconsistent observations, etc...

If you disagree, please cite a recent paper.

Here's a nice thought experiment for you: What happens at the last moment of an evaporating black hole's life? How does the horizon "disappear"? Whatever you imagine happens, now update your mental model for a relativistic observer. What do they see? I.e.: Does the increased apparent mass delay the observed disappearance of the horizon!? If so, how can this be? How can two observers disagree on the presence or absence of this horizon? Now consider what would occur at this juncture if there was only smooth curvature, no horizon, and no singularity. Would this enable the last moments of a BH's life to be consistently modelled for all observers?

Re: Black Hole Puzzle

#39

Post by daxfohl »

jiggawatts wrote: post #36
daxfohl wrote: post #28

Earlier quoted context omitted.

At steady state, a classical black hole is fully described just mass, charge, and angular momentum. So there are no individual particles. Which itself was disconcerting to physicists because in the quantum world, information is supposed to be conserved. But they were okay-ish with it being "trapped in there somewhere". Hawking radiation is what blew that up because now the black hole evaporates. So now, nobody really…

> At steady state, a classical black hole is fully described just mass, charge, and angular momentum. That's just wrong , we know this not to be the case from QM information theory and from thermodynamic arguments! This is the main point Hawking was making. While we don't yet have a good microscopic theory of what's going on, macroscopically we know that the information (entropy) doesn't just vanish into three number…

Correct, that's why I explicitly said "classical" in that sentence. Classical relativity means our understanding from Einstein's field equations, prior to the information-theoretic approaches.

Re: Black Hole Puzzle

#40

Post by raattgift »

wiml wrote: post #34
jiggawatts wrote: post #13

Any such blog / article / video that features a Penrose diagram is just wrong, because it's using mathematics that doesn't apply to the physical universe. Penrose diagrams draw black holes as if they have existed forever, and will last forever -- that's what the "future infinity" line means . Obviously black holes form at some finite time, and Stephen Hawking showed that they evaporate in a finite time. This matters.…

https://arxiv.org/pdf/1907.04879

Thanks, this looks like it will be an interesting read!
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