Event Horizon Conflicts: Understanding the Unknown

[_PJ_]

From another discussion, I realize my understanding of Event Horizons is quite lacking, but I am unable to find a definitive, reliable answer to fillbthe gaps.

My issue is essentially that of trying to resolve the apparent conflict between an observer, Alice who remains motionless wrt a BH at 'safe' distance, whilst Bob heads towards the Hole.

Now my current understanding is that using Schwarzschild coordinates, Bob will never reach the horizon, because the spacetime is distorted to singular extremes at that point, but this is a hint that that system is prrhaps insufficient/inadequate to describe the reality, so using a non-singular system, one can predict Bob accelerates towards and across the Horizon.
However, this entails that Alice will never be able to observe this event.
She might, if Bob flashes a gamma-ray torch towards her at regular intervals, detect somne flashesd at increasingly separated intervals, and ever-decreasing energy, but will not observe any event from the moment Bob reaches the Horizon.
That is how I am lead to believe, is the current concensus.

Almost all references to Bob's perspective suggest that from his perspective, the moment of crossing tyhe Horozon will be somewjat mundane and nothing noticably special will occur.
But this stems from an assumption no other forces or effects come into plau.

I am also under the impression, that the 'jury is still out' on precisely what occurs at the Horizon. If this is true, thern how can anyone be so absolutely certain that Bob actually crosses ther Horizon?

I still do not feel satisfied that there is any measuremernt that casn ber made to show Bob having crossed the EH. It was suggested that duer to therir own local time and acceleration, Bob must continue on, but fort anyoner other than Bob to experience this, must also be doomed - Alice can never see what's on Bob's wristwatch with the same interval.

Bob can never tell he has been within the horizon, Alice will never observe Bob crossing the Horizon, so what readon is there to really believe Bob ever does?

The only explanation is in non-singular coordinates in which Bob continuersd motion towards the Horizon and on through it.
Yet this makes grand assumption that there is a real event horizon.

If I am missing something, please explain it to me, because I cannot see how ideas such as Hawling's apparent horizon or the firewalls could even be put forth unless there was some unknowen quantity of what occurs-
If there is this unknown quantity, how can anyone trust that Bob's motion continues as 'predicted'?

Wouldnt't this be akin to assuming the predicting a ball thrown through a hoop will follow a parabolic path all the way even if there is something in the hoop?

 

[bcrowell]

I am also under the impression, that the 'jury is still out' on precisely what occurs at the Horizon.

I don't think the jury is out on this. What makes you think it is?

Bob can never tell he has been within the horizon,

Not true. For example, he can in principle measure the spacetime curvature in his neighborhood, and use it to infer the Schwarzschild r coordinate.

Alice will never observe Bob crossing the Horizon, so what readon is there to really believe Bob ever does?

The question of whether Bob crosses the horizon is not a question to which GR supplies a yes/no answer. This is because GR doesn't provide an unambiguous way of defining the simultaneity of events. This isn't evidence of a flaw or uncertainty in the theory, or of disagreement among the experts. It simply shows that there is a certain type of question that the theory tells us doesn't make sense. Similarly, I could ask whether our solar system is really at rest or really moving; we've known since Galileo that this is a question that doesn't make sense.

If you want a definite answer to the question about whether our solar system is at rest, you need to specify a frame of reference. Likewise, if you want a definite answer about whether Bob crosses the horizon, you have to describe what method of observation it is whose results you're trying to predict.

The only explanation is in non-singular coordinates in which Bob continuersd motion towards the Horizon and on through it.

Coordinates are irrelevant. You don't need to discuss coordinates in order to discuss any of these issues.

Yet this makes grand assumption that there is a real event horizon.

This is not an assumption. It is a theoretical prediction that has been empirically verified. As an example of observations that verify this prediction, we see that Sagittarius A* has a mass of about four million solar masses, confined within a sphere with a radius less than 2.2 × 10^7 km. The fact that we see this much mass in such a small space, but it doesn't emit enough light to be observable, is strong evidence that Sag A* is surrounded by an event horizon.

If I am missing something, please explain it to me, because I cannot see how ideas such as Hawling's apparent horizon or the firewalls could even be put forth unless there was some unknowen quantity of what occurs-
If there is this unknown quantity, how can anyone trust that Bob's motion continues as 'predicted'?

Your thoughts here seem very vague, too vague to make it possible to address your question.

 

[_PJ_]

I don't think the jury is out on this. What makes you think it is?

Because some physicists are debating the 'information loss paradox' and there are theories involing 'firewall' or 'apparent horizon's.
If the nature of what occurs at (or near) the EH was cut and dried, these theories would necessarily require to be congruent with that, surely?

This is not an assumption. It is a theoretical prediction that has been empirically verified.
As an example of observations that verify this prediction, we see that Sagittarius A* has a mass of about four million solar masses, confined within a sphere with a radius less than 2.2 × 10^7 km. The fact that we see this much mass in such a small space, but it doesn't

I think you misinterpret my words, or (more likely) I was not clear enough in explaining my meaning properly,
I know that the measured orbital paths of the stars around the heart of the gaslactic hub fit with a mass that, in such as small region is suggestive of a Black Hole and, excluding some hitherto unknown and mysterious phernomena, to our best understanding is extremely probably a Black Hole. I do not dispute this. Nor do I dispute that the nature of such by definition necessitates an escaper velocity exceeding the speed of causal celerity - by 'real horizon' I meant not an 'apparent horizon'.

Finally, by "Bob can never tell" I use 'tell' as into inform another, not that he is unable to discern his position

 

[PeterDonis]

I realize my understanding of Event Horizons is quite lacking, but I am unable to find a definitive, reliable answer to fillbthe gaps.

What mainstream sources (textbooks or peer-reviewed papers) have you read? Even at the pop science level, there are good books discussing this--for example, Kip Thorne's Black Holes and Time Warps.

my current understanding is that using Schwarzschild coordinates, Bob will never reach the horizon, because the spacetime is distorted to singular extremes at that point

This is not correct. The coordinates are distorted to singular extremes at the horizon, but that does not mean spacetime is. Spacetime is perfectly nonsingular and well-behaved at the horizon. Schwarzschild coordinates are simply the wrong coordinates to use to describe it.

It is a common error to think of coordinates as having some physical meaning. They don't. The only physical meaning is in invariants--quantities that are independent of any choice of coordinates. But your choice of coordinates can make a big difference in how easy it is to see which invariants are important, and to calculate them.

In the case of black holes, there are several coordinate charts which are better than Schwarzschild coordinates for understanding what goes on at and below the horizon: Painleve coordinates, Eddington-Finkelstein coordinates, and Kruskal coordinates. Andrew Hamilton has also put together some good diagrams showing how a black hole spacetime looks in these various charts, and showing how the transformations between the charts "morph" the diagrams:

http://casa.colorado.edu/~ajsh/schwp.html#geometry

I recommend taking some time to study these; it will help to give you a better feel for how Schwarzschild coordinates are distorted near the horizon, and how the other charts give better descriptions.

this entails that Alice will never be able to observe this event.

What entails this is not any choice of coordinates, but the physical fact that light emitted at or below the horizon cannot escape; it can never reach Alice's location, since that location is outside the horizon.

She might, if Bob flashes a gamma-ray torch towards her at regular intervals, detect somne flashesd at increasingly separated intervals, and ever-decreasing energy, but will not observe any event from the moment Bob reaches the Horizon.

Will not observe any event on Bob's worldline at or below the horizon, yes. That is indeed what GR says.

from his perspective, the moment of crossing tyhe Horozon will be somewjat mundane and nothing noticably special will occur.

Yes. More precisely, the spacetime geometry Bob observes at the horizon will be finite and well-behaved, and he will not be able to tell, purely from local measurements, that that region of spacetime works any differently from anywhere else.

this stems from an assumption no other forces or effects come into plau.

Yes. That's true any time we use the laws of physics to predict what will happen in a regime that has not (yet) been, or cannot be, observed directly.

I agree with bcrowell's responses to the rest of your post, except for the following:

The question of whether Bob crosses the horizon is not a question to which GR supplies a yes/no answer.

This is incorrect as you state it; Bob's worldline definitely does cross the horizon according to GR. What GR does not give a yes/no answer to is the question of what "time" he crosses according to some distant observer; this depends on what simultaneity convention you adopt, and simultaneity conventions are just that: conventions, like coordinate choices (actually they are part of what you choose when you make a coordinate choice).

(The time on Bob's own clock when he crosses, OTOH, is an invariant, and GR does give a definite answer as to what that time is.)

 

[bcrowell]

Because some physicists are debating the 'information loss paradox' and there are theories involing 'firewall' or 'apparent horizon's.
If the nature of what occurs at (or near) the EH was cut and dried, these theories would necessarily require to be congruent with that, surely?

Your thoughts here seem pretty vague. For example, there is no connection between the black hold information paradox and the kind of question you're asking about an observer falling through the horizon. In general, the existence of doubt and confusion about quantum gravity has zero impact on the predictions of classical GR.

Nor do I dispute that the nature of such by definition necessitates an escaper velocity exceeding the speed of causal celerity - by 'real horizon' I meant not an 'apparent horizon'.

You seem to be confused about what an apparent horizon is and what its significance is in this context.

 

[bcrowell]

This is incorrect as you state it; Bob's worldline definitely does cross the horizon according to GR. What GR does not give a yes/no answer to is the question of what "time" he crosses according to some distant observer; this depends on what simultaneity convention you adopt, and simultaneity conventions are just that: conventions, like coordinate choices (actually they are part of what you choose when you make a coordinate choice).

(The time on Bob's own clock when he crosses, OTOH, is an invariant, and GR does give a definite answer as to what that time is.)

I think we're just running into the ambiguities inherent in stating such things in English. I think both your statement and mine are correct. There is never any time on Alice's watch at which Alice can say with certainty that Bob has already passed the event horizon. So in this sense the statement "Bob passes the event horizon" is not one that has a true/false value for Alice.

 

[PeterDonis]

some physicists are debating the 'information loss paradox' and there are theories involing 'firewall' or 'apparent horizon's.

These all involve quantum gravity, and are speculations about how a correct theory of quantum gravity, if and when we discover it, would affect what happens at the classical level that GR describes. Those speculations fall, basically, into two categories:

(1) Event horizons still form--i.e., quantum gravity does not change things enough to prevent them from forming--but quantum gravity changes what happens deep inside them so that singularities don't form.

(2) Quantum gravity changes things at the classical level enough that event horizons never form in the first place.

Your misunderstandings about Alice and Bob are still misunderstandings regardless of which of the two possibilities above turns out to be true. If #1 is true, event horizons work just as GR predicts they do, which is what bcrowell and I have been describing. If #2 is true, the Alice and Bob scenario you describe can never take place because there are no event horizons anywhere, so your questions are meaningless.

 

[PeterDonis]

I think we're just running into the ambiguities inherent in stating such things in English.

Yes, but IMO the very existence of this thread (and all the other threads where people have expressed the same confusion) shows that how we state such things in English matters--not to the physics, but to how likely it is that people will misunderstand the physics based on our ordinary language descriptions. I prefer to emphasize that Bob's crossing the horizon is an objective fact about his worldline in relationship to the spacetime geometry, and that fact is not affected at all by the lack of a unique simultaneity convention for Alice with respect to events on Bob's worldline.

 

[_PJ_]

http://arxiv.org/abs/1401.5761

Thank you both andf you have clarified a lot and thanks especially for being able to navigate my very poor descriptions and attempts!

Your thoughts here seem pretty vague. For example, there is no connection between the black hold information paradox and the kind of question you're asking about an observer falling through the horizon. In general, the existence of doubt and confusion about quantum gravity has zero impact on the predictions of classical GR.You seem to be confused about what an apparent horizon is and what its significance is in this context.

I refer to the theories in which objects never actually cross an Event Boundary.

Yes, but IMO the very existence of this thread (and all the other threads where people have expressed the same confusion) shows that how we state such things in English matters--not to the physics, but to how likely it is that people will misunderstand the physics based on our ordinary language descriptions. I prefer to emphasize that Bob's crossing the horizon is an objective fact about his worldline in relationship to the spacetime geometry, and that fact is not affected at all by the lack of a unique simultaneity convention for Alice with respect to events on Bob's worldline.

Perhaps overall, you need need only GR prediction to satisfy your fact, but I still cannot see this as a complete enough picture. Thank you so much forbyour herlp, though :)

 

[PeterDonis]

I refer to the theories in which objects never actually cross an Event Boundary.

What theories are these? If you are referring to quantum gravity possibility #2 from my previous post, i.e., to theories in which quantum gravity effects prevent event horizons from ever forming, then, as I said, your whole Alice and Bob scenario is meaningless. But if you are referring to possibility #1, where quantum gravity effects do not prevent event horizons from forming, then there are no theories in which objects never cross event horizons.

 

[pervect]

Given that the topic is event horizons, and not black holes, it is useful to study the existence and behavior of event horizons in special relativity, without the complications caused by the curvature of space-time that are required to study them in black holes.

"Einstein's elevator", an accelerating platform, has often been used to motivate a discussion of "gravity". The relevant point with regards to this discussion is that an observer riding on Einstein's elevator experiences an event horizon, and evaluating this event horizon sheds much light on what can and cannot be said about event horizons.

The technical name for the event horizon experienced by an observer riding Einstein's elevator would see is "The Rindler Horizon". There is a fair amount of literature of differing degrees of sophistication on this topic on the WWW.

We can imagine an observer on the elevator - I have mixed my metaphors a bit, and occasionally call the elevator a rocket, or a spaceship - watching an object in free fall at the point of departure, and exchanging signals with it. We can compute the signals departure and arrival times in various coordinate systems, or utilize the coordinate-independent concepts of proper time. We can construct a viewpoint for the observer riding the elevator/rocket, and find that they never see signals after a certain time. To avoid these general statements and make more specific ones, if our elevator/rocket accelerates at a rate of 1 light year / year^2 (which is roughly 1g of proper acceleraton) there will be an event horizon 1 light year behind them from their point of view. Objects behind the event horizon can never send a signal to the elevator observer.

But it's reasonably clear that in this situation that nothing dramatic happens to the observer left behind. If you are on Earth, and a spaceship takes off in the year 3000ad, you celebrate New Years day on 3001ad as if nothing has happened, it doesn't matter to you that there is a spaceship out there. It's true that the space-ship never sees you having your party, or receives any broadcast signals from it, but that doesn't mean it "never happens".

If you want to do any of the math, the following two concepts may be useful. The concept of rapidiity makes it easy to describe acclerated motion. https://en.wikipedia.org/w/index.php?title=Rapidity&oldid=702157913

$$\varphi = tanh \frac{v}{c} \quad v = c \, \tanh^{-1} \, \varphi$$

In terms of rapidity we can write $\varphi = a \tau / c$. This will eventually lead us to the relativistic rocket equations, http://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html

We can plot the trajectory of the rocket, which turns out to be described by a hyperbola, and we can show that a light signal emitted at t = c/a will never be received by an observer on the rocket. But we can also clearly see that nothing unusual happens from the viewpoint of the observer who "stays behind".

It makes no difference to the stay-behind observer at their New Years day party whether a rocket was launched or not, or what year the rocket may have been launched. The stay-behind observer still enjoy the party. The rocket observer never gets to see the party, or listen to the New Years day broadcasts - but that doesn't mean the party "didn't happen".

 

[PeterDonis]

The technical name for the event horizon experienced by an observer riding Einstein's elevator would see is "The Rindler Horizon".

It's a technical point, but a Rindler horizon is not an event horizon by the standard definition of that term. An event horizon is the boundary of a region of spacetime that cannot send light signals to future null infinity. Events behind a Rindler horizon can send light signals to future null infinity (because every event in Minkowski spacetime can do so).

There is a different general property that Rindler horizons and event horizons do share: they are both Killing horizons, i.e., surfaces on which a Killing vector field is null, and which divide spacetime into two other regions, a region "above" the horizon where the KVF is timelike, and a region "below" the horizon where the KVF is spacelike. This means a Killing horizon is a more general type of "causal boundary" between regions of spacetime, of which event horizons and Rindler horizons are different subtypes.

 

[pervect]

It's a technical point, but a Rindler horizon is not an event horizon by the standard definition of that term. An event horizon is the boundary of a region of spacetime that cannot send light signals to future null infinity. Events behind a Rindler horizon can send light signals to future null infinity (because every event in Minkowski spacetime can do so).

There is a different general property that Rindler horizons and event horizons do share: they are both Killing horizons, i.e., surfaces on which a Killing vector field is null, and which divide spacetime into two other regions, a region "above" the horizon where the KVF is timelike, and a region "below" the horizon where the KVF is spacelike. This means a Killing horizon is a more general type of "causal boundary" between regions of spacetime, of which event horizons and Rindler horizons are different subtypes.

Would you go for "Causal horizon?" I'm not sure I've seen the term "Causal Horizon" actually used, but I think it expresses the intent of what I was trying to say better than "Killing Horizon". I also think the meaning is fairly clear from context (perhaps I'm mistaken on that, but it seems to me that a technically oriented reader would know what I meant by the term). And it fits better with the intent of what I was saying.

One way of interpreting what I was pointing out is that the rocket is outside the light cone of the even emitted 1 year after it's departure - so it's causally disconnected, as cause and effect are limited to light speed.

 

[PeterDonis]

Would you go for "Causal horizon?"

That would work. The only potential issue is that eventually someone will notice that any null surface whatsoever is a causal horizon for somebody.