How does the String Theory Propeller behave as you approach the event horizon?

[dubsed]

Yeah ... It looks like he thinks that the metric just "jumps" to flatness when it hits infinity being curved all the way before that :) Oh, well ...

Do we really need to argue semantics? You don't like that he says its flat at infinity. I don't like that you say it actually hits infinity. Saying that it is flat at infinity is the same as saying that (1/9) + (8/9) = 1

 

[Dale]

Yeah ... It looks like he thinks that the metric just "jumps" to flatness when it hits infinity being curved all the way before that :) Oh, well ...

Do you somehow think it is flat at some finite distance? If so, where?

See here https://www.physicsforums.com/showpost.php?p=2712746&postcount=38 where I calculated the proper acceleration of a stationary observer in the Schwarzschild metric. It is non-zero for any finite r meaning that such an observer is non-inertial. And here http://www.gregegan.net/SCIENCE/Rindler/RindlerHorizon.html is a page I like on Rindler coordinates and event horizons in flat spacetime.

 

[weaselman]

Do we really need to argue semantics? You don't like that he says its flat at infinity.
I don't like that you say it actually hits infinity.

I was being sarcastic :)
If it is flat at infinity (and it, of course, is), and you don't like saying that it hits infinity (and you should not), then you realize that you can make the curvature as small as you want by moving farther away. In other words, you can make a reference frame as close to inertial as you need by increasing the distance from the black hole. Insisting that such observer is not inertial is even less reasonable than saying that Alice's propeller is non-inertial, because it rotates, and the Alice herself is non-inertial, because her propeller somehow affects her acceleration.
All three statements are actually true, but the effects are so totally and completely insignificant, that it is obvious that arguing them cannot possible have any constructive goal.


And this is not semantics. Dale thinks that the difference between Bob and Alice is inertiality, which is incorrect. The real difference is the curvature of space-time that decreases with distance to the black whole. Bob spacetime is (ok, almost) flat, Alice's isn't.
At the event-horizon it becomes so curved, that the horizon itself is time-like. That is the real reason Bob cannot see anyone cross it. It does not matter if he is inertial or not (he can be stationary at some distance from black hole, orbiting around it, at infinity, or just far away), and it does not matter if Alice is (if Alice was falling non-inertialy - suppose, she was unsuccessfully trying to escape - the effects, seen by Bob would be quilitatively the same), it only matters how far from the horizon each of them is.

Same with the propeller, just on a smaller scale. Alice cannot see it cross the horizon, because the horizon is time-like. In this sense, the propeller will stop for her as well as it does for Bob, just not for as long, because as soon as she reaches horizon, it'll catch up.

Interestingly enough, they both (Alice, and propeller) will cross the horizon at the same time. And, once they do, time and space will switch places for them - the propeller will be later than Alice, but at the same spatial location

 

[weaselman]

Do we really need to argue semantics? You don't like that he says its flat at infinity.
I don't like that you say it actually hits infinity.

I was being sarcastic :)
If it is flat at infinity (and it, of course, is), and you don't like saying that it hits infinity (and you should not), then you realize that you can make the curvature as small as you want by moving farther away. In other words, you can make a reference frame as close to inertial as you need by increasing the distance from the black hole. Insisting that such observer is not inertial is even less reasonable than saying that Alice's propeller is non-inertial, because it rotates, and the Alice herself is non-inertial, because her propeller somehow affects her acceleration.
All three statements are actually true, but the effects are so totally and completely insignificant, that it is obvious that arguing them cannot possible have any constructive goal.And this is not semantics. Dale thinks that the difference between Bob and Alice is inertiality, which is incorrect. The real difference is the distance to the black whole.

The closer you are to the horizon, the slower your clock is ticking, compared to a more distant observer. At the horizon, the clock "stops", because the horizon itself is time-like. That is the real reason Bob cannot see anyone cross it. It does not matter if he is inertial or not (he can be stationary at some distance from black hole, orbiting around it, at infinity, or just far away), and it does not matter if Alice is (if Alice was falling non-inertialy - suppose, she was unsuccessfully trying to escape - the effects, seen by Bob would be quilitatively the same), it only matters how far from the horizon each of them is.

Same with the propeller, just on a smaller scale. Alice cannot see it cross the horizon, because the horizon is time-like. In this sense, the propeller will stop for her as well as it does for Bob, just not for as long, because as soon as she reaches horizon, it'll catch up.

Interestingly enough, they both (Alice, and propeller) will cross the horizon at the same time. And, once they do, time and space will switch places for them - the propeller will be later than Alice, but at the same spatial location

 

[JesseM]

The closer you are to the horizon, the slower your clock is ticking, compared to a more distant observer. At the horizon, the clock "stops", because the horizon itself is time-like.

Actually the horizon is light-like--entering the horizon is a bit like entering the future light cone of some event (and of course, once you enter an event's future light cone, you can never escape it!) As with a lot of aspects of nonrotating black holes, this is probably more intuitive if you use Kruskal-Szekeres coordinates.

Interestingly enough, they both (Alice, and propeller) will cross the horizon at the same time. And, once they do, time and space will switch places for them - the propeller will be later than Alice, but at the same spatial location

In Schwarzschild coordinates, which is what you're talking about, there is technically no time-coordinate where they cross the horizon (infinity is not a time coordinate!) And in a more physical sense, the event of Alice crossing the horizon lies in the future light cone of the event of the propeller crossing it.

 

[Dale]

I was being sarcastic :)
If it is flat at infinity (and it, of course, is), and you don't like saying that it hits infinity (and you should not), then you realize that you can make the curvature as small as you want by moving farther away. In other words, you can make a reference frame as close to inertial as you need by increasing the distance from the black hole. Insisting that such observer is not inertial is even less reasonable than saying that Alice's propeller is non-inertial, because it rotates, and the Alice herself is non-inertial, because her propeller somehow affects her acceleration.
All three statements are actually true, but the effects are so totally and completely insignificant, that it is obvious that arguing them cannot possible have any constructive goal.

I already addressed this in post 44. Yes, you can make the proper acceleration arbitrarily small, but you are incorrect that the effects are insignificant. Remember, we are looking at effects on Bob's observations of Alice, not on effects that are local to Bob. As you arbitrarily reduce the acceleration you must also arbitrarily increase the distance to Alice, which makes Bob's observations arbitrarily sensitive to his acceleration (see the Rindler metric). The net effect is that the distance cancels out and only the acceleration matters. I will work it out completely, but probably not today.

Your basic error is the assumption that because an effect is locally insignificant it must also be globally insignificant.

And this is not semantics. Dale thinks that the difference between Bob and Alice is inertiality, which is incorrect. The real difference is the distance to the black whole.

The closer you are to the horizon, the slower your clock is ticking, compared to a more distant observer. At the horizon, the clock "stops", because the horizon itself is time-like. That is the real reason Bob cannot see anyone cross it. It does not matter if he is inertial or not (he can be stationary at some distance from black hole, orbiting around it, at infinity, or just far away), and it does not matter if Alice is (if Alice was falling non-inertialy - suppose, she was unsuccessfully trying to escape - the effects, seen by Bob would be quilitatively the same), it only matters how far from the horizon each of them is.

OK, then at what initial distance does an inertial Bob have to be in order for him to never see Alice cross? And what is the minimum distance for a stationary Bob below which he will eventually see Alice cross?

Alice cannot see it cross the horizon, because the horizon is time-like. In this sense, the propeller will stop for her as well as it does for Bob

This is factually incorrect, particularly for a super-massive black hole as we have been discussing here. Alice will not notice anything unusual about the propeller crossing the event horizon provided that the tidal forces are negligible.

 

[weaselman]

Your basic error is the assumption that because an effect is locally insignificant it must also be globally insignificant.

You already agreed, that they are globally insignificant at infinity. Unless, you really believe, that they all just "jump" to insignificance when you "hit infinity", you have to admit, that they are becoming less and less significant as you approach it. There is no third possibility (no first possibility either realy, as dubsed pointed out, which leaves us only one choice). If the distance "cancels out", it can't possibly matter, even if it is infinite.

 

[Dale]

You already agreed, that they are globally insignificant at infinity. Unless, you really believe, that they all just "jump" to insignificance when you "hit infinity", you have to admit, that they are becoming less and less significant as you approach it. There is no third possibility (no first possibility either realy, as dubsed pointed out, which leaves us only one choice). If the distance "cancels out", it can't possibly matter, even if it is infinite.

Look at what I actually said in #44, you are misreading what I wrote. I agreed that the metric is locally flat "at infinity", not that the global effects wrt observations of Alice ever became insignificant. In fact, I explained exactly the fact that the global effects were significant at any finite distance.

 

[weaselman]

Look at what I actually said in #44, you are misreading what I wrote. I agreed that the metric is locally flat "at infinity", not that the global effects wrt observations of Alice ever became insignificant. In fact, I explained exactly the fact that the global effects were significant at any finite distance.

Take a look at the link I quoted in the post you were responding to. It explains the specifics of Alice's free fall from the stand point of an inertial observer at infinity. Those are exactly the observations we are discussing here (clocks/propellers slowing down and "stopping" eventually). You replied to that post and conceded that an observer at infinity would indeed be inertial and observe these effects.

 

[kj30]

Interesting thread. I'm still confused on several points:

1. If a black hole is sufficiently large to minimize the effect of tidal forces, how is it possible for someone to not notice any change in local physics after passing through the event horizon? If you were falling in feet first, how could you see your feet with your eyes? Light can't go in that direction inside the event horizon.

2. Is there a simple way to understand why someone falling through the event horizon does not experience the entire future of the universe "falling in" and burning them up in a brilliant super-high blueshift flash? If someone were suspended right above the event horizon (by massive rocket thrusters, etc.) it seems clear that this would happen. What is it about traveling into the event horizon that allows the traveler to escape this flash? I don't find the explanation in the FAQ convincing, namely that there wouldn't be enough time for light in distant parts of the universe to reach you as you pass through the event horizon. If the whole future passes before your eyes, there WILL be enough time for light anywhere to reach you. Or does that not apply if you are in an inertial frame falling freely into the black hole?

 

[George Jones]

1. The event horizon is a lightlike hypersurface. When my eyes are outside the event horizon, they see my feet outside the event horizon; when my eyes are on the event horizon, they see my feet on the event horizon; when my eyes are inside the event horizon, they see my feet inside the event horizon.

2. Suppose observer that A hovers at a great distance from a black hole, and that observer B hovers very close to the event horizon. The light that B receives from A is tremendously blueshifted. Now suppose that observer C falls freely from a great distance. C whizzes by B with great speed, and, just past B, light sent from B to C is tremendously Doppler reshifted. What about light from A to C. The gravitation blueshift from A to B is less that the Doppler redshift from B to C. As C crosses the event horizon, C sees light from distant stars redshifted, not blueshifted.

 

[sheaf]

When my eyes are outside the event horizon, they see my feet outside the event horizon; when my eyes are on the event horizon, they see my feet on the event horizon; when my eyes are inside the event horizon, they see my feet inside the event horizon.

That's a good point, I never thought of it like that before :)

 

[Naty1]

"When my eyes are outside the event horizon, they see my feet outside the event horizon; when my eyes are on the event horizon, they see my feet on the event horizon; when my eyes are inside the event horizon, they see my feet inside the event horizon."

George, I'm surprised at you! First time ever I have disagreed...

That statement is not correct...or is terribly misleading...what is observed depends on whether the observer is free falling or nearby stationary...the description covers neither...for the free falling observer, there is no event horizon, all appears rather normal except perhaps for some tidal effects...

 

[Naty1]

" If a black hole is sufficiently large to minimize the effect of tidal forces, how is it possible for someone to not notice any change in local physics after passing through the event horizon? If you were falling in feet first, how could you see your feet with your eyes? Light can't go in that direction inside the event horizon..."

If you are free falling, there is no event horizon...and that has nothing to do with the effects of tidal forces be they large or small...As you fall you are gradually streched and squeezed to a more "spagehtti" configuration...longer and thinnner.

The ananomoly is akin to asking about two passing observers in relative motion: each sees the others time dilated and length contracted...who is "right"??...each is correct in in her own reference frame...there is no absolute...

Or when a stationary observer measures one temperature at some point and an accelerating observer (Unruh effect) measures a higher temperature...who is "right"...again, each is in their own reference frame...

 

[George Jones]

The definition of the event horizon of a black hole is observer-independent.

The standard definition of the black hole region of an asymptotically flat spacetime is the region of spacetime from which it is impossible to escape to future null infinity. An event horizon is the boundary of this region.

No mention of observers. It is this standard definition of event horizon that I used implicitly in my previous post.

 

[Naty1]

Here is a great explanation I saved from a similar discussion...my notes show it from Dalespam...

"For example, in the curved spacetime around a nonrotating black hole, if you use Schwarzschild coordinates the coordinate velocity of light decreases as you approach the horizon and actually reaches zero on it, whereas if you use Kruskal-Szekeres coordinates in the same spacetime, the coordinate speed of light is the same everywhere (see this page for a discussion of different coordinate systems that can be used in a spacetime containing a nonrotating black hole).

a while ago I scanned some diagrams from Gravitation by Misner/Thorne/Wheeler for part of another discussion. You don't really need to know too much about the math (I don't) to get a basic conceptual understanding of the meaning of the diagrams.

First of all, it helps to understand some of the weaknesses of Schwarzschild coordinates which are "fixed" by Kruskal-Szekeres coordinates. The first is that in Schwarzschild coordinates it takes an infinite coordinate time for anything to cross the horizon, even though physically it only takes a finite proper time for a falling object to cross the horizon. The second is that inside the horizon, Schwarzschild coordinates reverse the role of time and space--the radial coordinate in Schwarzschild coordinates is physically spacelike outside the horizon but timelike inside, while the time coordinate in Schwarzschild coordinates is physically timelike outside the horizon but spacelike inside. In Kruskal-Szekeres coordinates, in contrast, objects crossing the horizon will cross it in a finite coordinate time, and the Kruskal-Szekeres time coordinate is always timelike while its radial coordinate is always spacelike. And light rays in Kruskal-Szekeres coordinates always look like straight diagonal lines at 45 degree angles, while the timelike worldlines of massive objects always have a slope that's closer to vertical than 45 degrees.

Here's one of the diagrams from Gravitation, showing the surface of a collapsing star (the black line bounding the gray area which represents the inside of the star) in both Schwarzschild coordinates and Kruskal-Szekeres coordinates. They've also drawn in bits of light cones from events alone the worldline of the surface, and the event horizon is shown as a vertical dotted line in the Schwarzschild diagram on the left, while it's shown as the line labeled r=2M at 45 degrees in the Kruskal-Szekeres diagram on the right (the sawtoothed line in that diagram represents the singularity)."

 

[Naty1]

Hi George, your post #65...

The definition of the event horizon of a black hole is observer-independent.

All I can say is that in a half a dozen books or so and other references on black hole horizons and never heard of such a thing...or never recognized it, anyway. But knowing your posts, I accept what you say is correct in your context...I just don't understand it.
They all say a free falling observer has no observational evidence of a horizon...

The standard definition of the black hole region of an asymptotically flat spacetime is the region of spacetime from which it is impossible to escape to future null infinity. An event horizon is the boundary of this region.

...but the implications are likely too subtle for an aging engineer...This seems like the definition of the apparent horizon??

Leonard Susskind in THE BLACK HOLE WAR PAGE 237 discusses Black Hole Complementarity...in which a free falling observer passes an "event horizon" unaffected while the stationary observer is annihilated by radiation...and he clearly explains both versions are true...that's the perspective I posted. And that's the repeated perspective I've seen in other references...like Kip Thorne's BLACK hOLES AND TIME WARPS...

Unfortunately for me, there are too many type horizons to be positive how each differs from the other..I know of a fixed (or stationary or Absolute, of Hawking) type, stretched (of Susskind) , and Apparent (Of Penrose, among others) are I think the big three...

anyway, thanks for the reply...

 

[Naty1]

Dalespam...just read in detail your explanations to Weaselman..posts 37 to 47 or thereabouts...again, thanks...
getting a proper understanding of these subetlies is one hurdle, trying to express them is another...and interpretating what someone else means still another.

for example, your post,

I agreed that the metric is locally flat "at infinity", not that the global effects wrt observations of Alice ever became insignificant.

clarified a fine point that like Weaselman, I likely did not pick up...

this is tooooooo much for Christmas eve, Merry Christmas all...time to walk my Yorkies, then time for a drink!

 

[Dale]

Merry Christmas (eve), Naty1! Don't worry too much about it, GR is a very subtle topic and I make mistakes often too and still feel like a novice most of the time.

 

[George Jones]

They all say a free falling observer has no observational evidence of a horizon...

Yes, this is true, but this doesn't mean that we can't calculate what an observer would see on when on the event horizon.

This seems like the definition of the apparent horizon??

No, the definition I gave is for the absolute event horizon, which is a global concept. The definition of the apparent horizon is based on trapped surfaces, and is a more local concept. For stationary black holes (e.g., spherical black holes and rotating black holes) these two horizons coincide. In general (for positive mass/energy), the apparent horizon is at or inside the event horizon.

 

[Passionflower]

Yes, this is true, but this doesn't mean that we can't calculate what an observer would see on when on the event horizon.

Right.

If an observer, free falling at escape velocity, knows the mass of the non rotating black hole he can calculate how much time he is away from reaching the singularity and where he is wrt the event horizon by measuring the tidal acceleration between the floor and ceiling of his spaceship.

If he does not know the mass he can still determine how much time he has left until he reaches the singularity.

 

[Naty1]

From George:

For stationary black holes (e.g., spherical black holes and rotating black holes) these two horizons coincide. In general (for positive mass/energy), the apparent horizon is at or inside the event horizon.

Kip Thorne's BLACK HOLES AND TIME WARPS, page 415, Box 12.1 seems to have a slightly different description:

The absolute horizon is created at the star's center...well before the star's surface shrinks through the critical circumference. The absolute horizon is just a point when created but it then expands smoothly and emerges through the star's surface precisely when the surface shrinks through the critical circumference. It then stops expanding and thereafter coincides with the suddenly created apparent horizon.

He goes on to say
...

the areas of absolute horizons (but not necessarily apparent horizons) will increase not only when black holes collide and coalesce but also also when they are born, when matter or gravitational waves fall into them...

and so forth.

which may relate to George's description.

One thing I have never read is whether when an additional bit(s) is added to a black hole, does the absolute horizon area increase "smoothly" and the apparent horizon discontinuously. Why wouldn't the apparent horizon grow?? If there is a theoretical difference, what does it mean?

Thorne continues:

Hawking was well aware the choice of definition of horizon, absolute or apparent, could not influence in any way any predictions for the outcome of experiments...however, the choice of definition could influence the ease with which physicsts deduce...the properties and behaviors of black holes...

 

[George Jones]

See Figure 5.7 on page 134 (pdf page 150) and Figure 5.16 on page 155 (pdf page 171) of Eric Poisson's notes,

http://www.physics.uoguelph.ca/poisson/research/agr.pdf,

which evolved into the excellent book, A Relativist's Toolkit: The Mathematics of Black Hole Mechanics.

 

[nismaratwork]

See Figure 5.7 on page 134 (pdf page 150) and Figure 5.16 on page 155 (pdf page 171) of Eric Poisson's notes,

http://www.physics.uoguelph.ca/poisson/research/agr.pdf,

which evolved into the excellent book, A Relativist's Toolkit: The Mathematics of Black Hole Mechanics.

If I'm reading this correctly then the answer is: 'It's all inside the hole, so you don't get to see it anyway'... which is what you said without diagrams in the first place... right?

 

[kj30]

2. Suppose observer that A hovers at a great distance from a black hole, and that observer B hovers very close to the event horizon. The light that B receives from A is tremendously blueshifted. Now suppose that observer C falls freely from a great distance. C whizzes by B with great speed, and, just past B, light sent from B to C is tremendously Doppler reshifted. What about light from A to C. The gravitation blueshift from A to B is less that the Doppler redshift from B to C. As C crosses the event horizon, C sees light from distant stars redshifted, not blueshifted.

Thanks for the clarification! I guess my conceptual hangup was that C must pass through a point where a suspended observer, B, would see the whole future of the universe pass in a short time and get burned up in a flash of gamma radiation. But somehow C gets through that same point without suffering that experience. But by equivalence, I guess that's no different from the fact that I would not share the experience of a galactic traveler accelerating back and forth across the galaxy merely because he passes very close to me. He might see the entire future of the galaxy in a few seconds, and burn up from the radiation, and I would not. That fact that we were at the same point in space for an instant of time during which he was getting burned with gamma radiation is irrelevant. Is that a somewhat correct analogy?

Can I surmise that if a mirror were suspended very close to the event horizon, and I sent a flash of light towards the black hole, it might take a very LONG time for the reflection to come back to me? And in the local physics of the mirror, the flash of light would appear as high-end gamma radiation?

 

[Naty1]

George, unsure whether to thank you or cuss you for the reference in your post #73...
I think I'll "thank you" now, perhaps saving the cussing for later when I try to plow thru that book...

 

[kj30]

Just bumping up my unanswered question (my pervious post of Dec25-10). Either it stumped the experts, or it was too boring and sophomoric for the experts! Probably the latter, ;-)

Basically, if you suspend a mirror very near (but above) the event horizon, and you send a flash of light towards the black hole from a "safe" distance away from the black hole, it might take a very long time for the light flash to come back. Correct?

 

[George Jones]

Just bumping up my unanswered question (my pervious post of Dec25-10). Either it stumped the experts, or it was too boring and sophomoric for the experts! Probably the latter, ;-)

Basically, if you suspend a mirror very near (but above) the event horizon, and you send a flash of light towards the black hole from a "safe" distance away from the black hole, it might take a very long time for the light flash to come back. Correct?

Yes. For quantitative details, see

https://www.physicsforums.com/showthread.php?p=928277#post928277.