Black Holes: Event Horizon Causally Disconnected?

[Feynstein100]

I've heard quite frequently that events inside the event horizon of a black hole are causally disconnected from the rest of the universe.

I take it to mean that while outside events can interact with the events inside of the horizon, the reverse is not true i.e. inside events cannot interact with outside events.

However, a simple thought experiment caused me some confusion. What if we attach a stone to a rope and let it fall into the event horizon? Wouldn't the movement of the rope be the stone interacting with the outside universe even after it's fallen in?

The rope attached to a stone is just an example. Imagine a highly charged particle whose electric field spans quite some distance. We can measure the field from a safe distance while the particle falls in. Now if the event horizon really is causally disconnected, as soon as the particle falls in, its field would disappear instantly. However, we know from SR that causal influences cannot propagate instantly. It's kind of why time exists in the first place.

Anyway, there's an apparent contradiction. If the particle's field doesn't disappear instantly, then we can still follow its changes and kind of work out what's happening inside the horizon, which, if the horizon really is causally disconnected, shouldn't be possible.

So what actually happens? I guess the simple answer would be that events inside the horizon are, in fact, not causally disconnected and it's just a misconception prevalent in pop science. Or that my interpretation of causal disconnection is incorrect. But perhaps there's another possibility?

 

[Ibix]

What if we attach a stone to a rope and let it fall into the event horizon?

The rope's behaviour outside the horizon is independent of what happens inside. If you yank hard on it then it will snap somewhere outside the horizon. If you don't yank on it then it's going in anyway.

Now if the event horizon really is causally disconnected, as soon as the particle falls in, its field would disappear instantly.

No, you just get a charged black hole.

If the particle's field doesn't disappear instantly, then we can still follow its changes and kind of work out what's happening inside the horizon,

No you can't. You will continue to see some changes in the electric field outside the hole until it settles down into something like a Reissner-Nordstrom or Kerr-Newman black hole. However, if you backtrack the source of the changes in the field you will always back track them to the charged particle as it approaches the horizon. You will never see any effect once it crosses the horizon, because the definition of a horizon is (roughly speaking) the boundary between the region that can communicate with distant observers and the region that can't.

 

[Feynstein100]

The rope's behaviour outside the horizon is independent of what happens inside. If you yank hard on it then it will snap somewhere outside the horizon. If you don't yank on it then it's going in anyway.

Ah okay. I get it now. The rope would behave just the same as if it would've if there were no stone attached to it. Hence no information about the stone can be inferred. Perhaps it was not that good of a test subject. Good thing I also added the charged particle

No, you just get a charged black hole.

Ah I hadn't thought of that. However, wouldn't we be able to tell the difference? Because the particle's field would be localized whereas the black hole's field would be more......spread out across its entire volume? Wouldn't we be able to pinpoint exactly when the particle's field turned into the black hole's field?

However, if you backtrack the source of the changes in the field you will always back track them to the charged particle as it approaches the horizon. You will never see any effect once it crosses the horizon

That's kind of what I'm struggling to wrap my head around. How is that any different from the particle's field disappearing instantly?

 

[Ibix]

The rope would behave just the same as if it would've if there were no stone attached to it.

More precisely, the dynamics of the rope can only depend on the behaviour of the stone when it was in the past lightcone of the rope. The stone crossing the horizon is never in the past lightcone of the rope until it too falls through the horizon (if it ever does).

However, wouldn't we be able to tell the difference?

The difference between what?

Because the particle's field would be localized whereas the black hole's field would be more......spread out across its entire volume?

I don't think this makes any sense. Any electric field covers all of space.

Wouldn't we be able to pinpoint exactly when the particle's field turned into the black hole's field?

No. Again, if you backtrack why the field you are measuring looks like it does, and you do it with enough precision, it will always lead back to the infalling particle before it reaches the horizon. The "enough precision" will become unachievable in practice very rapidly, and the hole will be indistinguishable from an eternal charged black hole. But that merely tells you when your instruments are too insensitive, not anything about the hole itself. Again, you cannot get information out of an event horizon: by definition it is a region that cannot communicate with the outside world.

How is that any different from the particle's field disappearing instantly?

Because the field doesn't disappear.

 

[Feynstein100]

I don't think this makes any sense. Any electric field covers all of space.

I guess I wasn't clear about what I meant. So let's say we're measuring the electric field intensity around the particle, right? We can tell that the particle is moving farther and farther away because the field intensity gets smaller and smaller.

From what you're telling me, it seems that once the particle crosses the horizon, we can no longer tell where it is. It effectively becomes part of the black hole and the particle's charge now becomes the hole's charge. This is what I meant by delocalization.

Once the particle crosses the horizon, instead of electric field lines coming out from a small point outside the horizon, we now see them coming from the entire horizon. The charge is the same. It's just that instead of being localized inside a small particle, it now expands to cover the volume of the entire event horizon. This should definitely have a measurable effect on the field intensity measured by the distant observer. That's what I meant.

For a more visual analogy, let's assume that just as mass/energy makes a dent on spacetime, electric charge makes a similar dent on some hypothetical continuum. In the experiment, we're observing the particle's dent, which is very deep. As soon as the particle crosses the horizon, this dent disappears completely, and a new dent appears around the entire horizon, which previously didn't have one. However, this dent is very shallow. This is the picture I have in my mind from your description. Is this what you're saying happens or did I get it wrong?

 

[DrGreg]

Changes to an electric field propagate at the speed of light (via electromagnetic radiation), so the electric field you detect depends on what happened some time in the past, not what is happening now. You'll never actually see (with your eyes, or detect via other radiation) the particle cross the horizon; you'll see it slow down as it approaches the horizon but never see it get there. So the field you detect will be consistent with where the particle was as you see it.

 

[Feynstein100]

Changes to an electric field propagate at the speed of light (via electromagnetic radiation), so the electric field you detect depends on what happened some time in the past, not what is happening now. You'll never actually see (with your eyes, or detect via other radiation) the particle cross the horizon; you'll see it slow down as it approaches the horizon but never see it get there. So the field you detect will be consistent with where the particle was as you see it.

That's an interesting possibility I hadn't thought of. And you are right that any change is limited by the speed of causality. What we're doing with the particle is associating its change in position with a change in the electric field. But once the particle is inside the horizon, the change is no longer able to propagate outside. So just like with light, we get kind of stuck with a phantom field from just before the particle crossed the horizon.

I find this answer to be satisfactory. However, doesn't this violate charge conservation? Because we now see the charge as hovering just above the horizon but also being inside it?

Although, I suppose the same could be said with mass conservation in the normal scenario of a spaceship entering the horizon. We'd see the mass of the spaceship both outside and inside the horizon. How is this resolved?

I guess the scenario is analogous to Einstein's thought experiment of whether the Earth would continue orbiting the sun if it suddenly disappeared? The answer being yes because the change in the gravitational field wouldn't reach earth for 8 minutes. So for these 8 minutes, the earth would be orbiting a phantom, something that isn't there.

It seems that once we introduce SR, we get the notion of these "phantoms" that seemingly violate conservation laws.

Damn, I just realized that we can relate this thought experiment to Einstein's. Instead of simply disappearing, the sun goes inside the horizon. The question is, would the earth continue orbiting the sun's final position? I wanna say yes. However, unlike the original thought experiment, the sun's final position will always be there, unchanging. So will the earth continue to orbit it indefinitely? (Or at least until it too falls into the horizon?)

In reality the black hole's gravity would most likely mess the orbit up and the earth would just end up orbiting the black hole instead of the sun. However, instead of the earth and sun, imagine a macro proton and electron, if you will, which are electrically bound and thus (relatively) unperturbed by the black hole's gravity.

 

[Nugatory]

Although, I suppose the same could be said with mass conservation in the normal scenario of a spaceship entering the horizon. We'd see the mass of the spaceship both outside and inside the horizon. How is this resolved?

There’s nothing to resolve if the mass of spaceship is zero, and that’s what you’re seeing in most of the popular treatments - the zero mass is implied when the size and mass of the black hole doesn’t change. This is a really good approximation when considering a stellar mass black hole and it simplifies the math no end (which is why we use it).

But if we are going to consider the non-zero mass of the spaceship…. It’s easier to see what what happens with that mass if we surround a black hole of mass $M$ and Schwarzschild radius $R_M$ with a spherical shell of dust of mass $m$ and allow that to fall into the black hole. The gravitational field outside the shell is always going to be that of a point mass $M+m$, so nothing changes as the shell falls in - we just end up with a slightly larger black hole.

The situation with the charged particle is analogous, although way harder to visualize because the field of a point charge very near the event horizon doesn’t behave anything like what we’d expect from our experience with charged particles in flat spacetime.

 

[Feynstein100]

we just end up with a slightly larger black hole.

I've been wondering about that too. It's said that we'll never see the spaceship cross the event horizon. However, at the time of the crossing, won't the black hole expand and engulf the phantom spaceship, thus allowing us to infer that the event horizon has actually been crossed?

The situation with the charged particle is analogous, although way harder to visualize because the field of a point charge very near the event horizon doesn’t behave anything like what we’d expect from our experience with charged particles in flat spacetime.

That sounds interesting. Would you mind telling me more?

 

[Nugatory]

I've been wondering about that too. It's said that we'll never see the spaceship cross the event horizon. However, at the time of the crossing, won't the black hole expand and engulf the phantom spaceship, thus allowing us to infer that the event horizon has actually been crossed?

Both statements are true.
We can and do observe the presence of a black hole of mass $M+m$.
Light from the ship crossing the horizon never reaches us so we never see that.

 

[Nugatory]

That sounds interesting. Would you mind telling me more?

@Ibix gave the qualitative explanation in #4 above : the external field very quickly settles down to something that looks like an eternal charged black hole.

However you may find it easier to visualize what's going on if we push the analogy with gravity: surround the black hole with a uniform spherically symmetric shell of massless electrically charged dust with total charge $Q$. Outside of that shell the electric field is that of a point charge $Q$ and it stays that way as the charge falls through the event horizon.

 

[PeterDonis]

I've heard quite frequently

Where? Please give a specific reference.

 

[vanhees71]

Changes to an electric field propagate at the speed of light (via electromagnetic radiation), so the electric field you detect depends on what happened some time in the past, not what is happening now. You'll never actually see (with your eyes, or detect via other radiation) the particle cross the horizon; you'll see it slow down as it approaches the horizon but never see it get there. So the field you detect will be consistent with where the particle was as you see it.

Of course there's also the part of the em. field which is "carried with the particle", i.e., what's a Coulomb field in the particle's rest frame.

 

[Dale]

However, doesn't this violate charge conservation? Because we now see the charge as hovering just above the horizon but also being inside it?

...

It seems that once we introduce SR, we get the notion of these "phantoms" that seemingly violate conservation laws.

There are no phantoms violating conservation laws. However, a lot of the conservation laws become local, with a global definition no longer being covariant or well defined. For charge, the local conservation law is $$\nabla_\mu J^\mu = 0$$ which holds locally everywhere

I suppose the same could be said with mass conservation in the normal scenario of a spaceship entering the horizon. We'd see the mass of the spaceship both outside and inside the horizon. How is this resolved?

It is resolved by correcting the “I suppose” part. That supposition is incorrect.

 

[Ibix]

I guess the scenario is analogous to Einstein's thought experiment of whether the Earth would continue orbiting the sun if it suddenly disappeared? The answer being yes because the change in the gravitational field wouldn't reach earth for 8 minutes. So for these 8 minutes, the earth would be orbiting a phantom, something that isn't there.

I rather doubt Einstein posited that scenario, since it's not consistent with general relativity. It violates local conservation of stress-energy.

 

[PeterDonis]

Einstein's thought experiment of whether the Earth would continue orbiting the sun if it suddenly disappeared?

Where did EInstein pose this thought experiment? Please give a reference.

 

[Feynstein100]

Where? Please give a specific reference.

Well, today it was Arvin Ash but I think I've also heard it on PBS Space Time and Fermilab. I can't remember a specific instance though.

 

[Feynstein100]

I rather doubt Einstein posited that scenario, since it's not consistent with general relativity. It violates local conservation of stress-energy.

It does? Wait, then what would actually happen in that scenario?

 

[Feynstein100]

Where did EInstein pose this thought experiment? Please give a reference.

Something I watched on Nat Geo back in 2012. Oh wait. It was from a Nat Geo show but I watched it on youtube. I'll see if I can find it.

I can't find it. Man, I miss the old youtube

 

[Dale]

It does? Wait, then what would actually happen in that scenario?

The scenario itself is inconsistent with GR. Mass cannot disappear.

 

[Ibix]

It does? Wait, then what would actually happen in that scenario?

GR won't let you describe it. It's not even theoretically possible.

 

[PeterDonis]

today it was Arvin Ash but I think I've also heard it on PBS Space Time and Fermilab

These are not valid references. You want to be looking at textbooks or peer-reviewed papers.

Something I watched on Nat Geo back in 2012. Oh wait. It was from a Nat Geo show but I watched it on youtube. I'll see if I can find it.

I can't find it. Man, I miss the old youtube

These aren't valid references either.