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If a light beam were to parallel the rope's path, the wavelength of the light would shorten as the light got deeper into the gravity well. Would the light be shortening with respect to the rope?

Sorry... I wasn't clear. I was imagining hanging the ideal rope down from a platform toward the event horizon and shining a light beam in parallel, downward.

The light beam's wavelength will definitely shorten as it approaches the event horizon (zero wavelength at the event horizon).

Quote from: AndroidNeox on 22/10/2013 22:23:08Sorry... I wasn't clear. I was imagining hanging the ideal rope down from a platform toward the event horizon and shining a light beam in parallel, downward.That's what I thought you meant. Seems to me, for the local observer, the light leaving his torch will appear unchanged, although the tidal gradient will mean it becomes more quickly red-shifted the closer he gets to the BH. The distant observer sees the local observer's time run slow and his light red-shifted. QuoteThe light beam's wavelength will definitely shorten as it approaches the event horizon (zero wavelength at the event horizon).From who's viewpoint will it shorten?

Sorry... I wasn't clear. I was imagining hanging the ideal rope down from a platform toward the event horizon and shining a light beam in parallel, downward. The light beam's wavelength will definitely shorten as it approaches the event horizon (zero wavelength at the event horizon). Time will slow. I think time will slow so that, for a local observer, the frequency of the light will appear unchanged, but I'm not positive.

If the mirror is stationary, the returning light should be the same frequency as it had originally.

Quote from: AndroidNeox on 23/10/2013 00:11:03If the mirror is stationary, the returning light should be the same frequency as it had originally.This may be the key. I usually see discussions about free-falling objects & observers.

I've seen a number of Relativity thought experiments that use idealized rope in lowering an object (like Hawking's box of light/radiation) to the vicinity of an event horizon. What I'm not sure about is how the rope gets altered relativistically. If a light beam were to parallel the rope's path, the wavelength of the light would shorten as the light got deeper into the gravity well. Would the light be shortening with respect to the rope?

It's my understanding that as you approach and cross the event horizon nothing particularly changes to the light you are observing.

Even after crossing the event horizon you would still be able to see light from the outside coming in since it is acting as a kind of "one way" valve only allowing light in but not out.

To an observer situated at some distance away, however, the light coming from you would be stretched and stretched to the point of becoming infrared and eventually stop being light at all and become radio waves, etc., which is why to an observer you would ultimately disappear.

You would also appear to an observer to become ever increasingly slowed to the point where you would seem frozen although to you, nothing would seem different. This is because the closer you get to the event horizon the harder light has to work to overcome the tidal forces of the BH, taking longer than normal.

Despite your "on board" clocks seeming normal if you could suddenly travel back to where the observer is sitting you would find they have aged much more than you because your time flowed relatively much slower than theirs. Another way to look at it is that at some point, when about to cross the event horizon, there will be a final photon that is able to escape the gravity of the BH, after which, all the photons will be trapped inside the BH at which point you will appear to an observer to be frozen, although in reality you keep going.

I'm not quite clear on this point but we have to remember that a BH is not only sucking in material objects but space itself too, …

…so presumably this contributes to the slowing of light to reach an observer.

I'm not quite clear on this point but we have to remember that a BH is not only sucking in material objects but space itself too, …QuoteWhere did you get that idea? It’s news to me. In fact I can’t even imagine what it means.

Where did you get that idea? It’s news to me. In fact I can’t even imagine what it means.

The URL you posted had a space in it which made it unworkable so I http://www.bbc.co.uk/science/space/universe/sights/black_holes/#p00frjln [nofollow]

Is there a widely used definition of "idealized rope"? If not, please explain how the rope is idealized. The rope I am imagining has zero mass, infinite strength and tensile modulus, and the light-travel time between its distance markers is constant in the reference frame of an imaginary observer clinging to the rope. Is that an accurate description of the rope in the thought experiment?

Pmb, there has to be a moment when all light is no longer able to escape the pull of the black hole else why does the image of something that is about to cross the event horizon become frozen? If light continued to travel from such an object it would be seen as moving away.

The following diagram shows a foolish observer's worldline in the outside region, venturing into the black hole. This observer is periodically sending out light-pulses. However, notice that the closer our foolish observer gets, the longer it takes for his pulses to reach an outside observer. Before he reaches the event horizon, the observer can still return to the outer regions of the outside region... but the longer he waits, the longer it will take him to return. Just after the foolish observer crosses the event horizon (at event u), his light-pulses never reach an outside observer. And since his light-pulses can't reach the outside, no particle (for example, his spaceship) can reach the outside. Now, once inside, the light cones now direct him to the singularity. His life will soon be over: his worldline will end.

Would the light be shortening with respect to the rope?

Therefore the frequency of the light, as measured by any single observer, does not change as the light moves through the gravitational field!

It's hard to know how much of a popular science programme is analogy and how much is hard physics, but Cox does explicitly say that space flows into the black hole with increasing velocity.

Quote from: AndroidNeoxWould the light be shortening with respect to the rope? No. The reason for all of this confusion is a misunderstanding about gravitational redshift. Students of GR often make the mistake of thinking that the frequency of an EM wave changes as it moves through a gravitational wave wherein fact there is no change in frequency. In fact the energy of the photon doesn't change either.See ...sorry, you cannot view external links. To see them, please REGISTER or LOGINNotice the conclusion arrived at after Eq. (2) - QuoteTherefore the frequency of the light, as measured by any single observer, does not change as the light moves through the gravitational field!

It's hard to know how much of a popular science programme is analogy and how much is hard physics, but Cox does explicitly say that space flows into the black hole with increasing velocity. It occurs to me that in that model the tidal force spahettification is due to the increasing 'stretching' of space, which should lead to the wavelength of infalling light lengthening...

But where does it say that. I did a search on that page for the phase space flows and found nothing.I then simplified it to search for "flow" and also found nothing.

... Well it's the same close to a black hole, because space flows faster, faster and faster towards the black hole. Literally, this stuff [gestures around himself], my space that I'm in, flowing over the edge, into the black hole; and at the very special point, called the event horizon, space is flowing at the speed of light into the black hole...

A singularity is warping spacetime to a much greater degree than an ordinary mass, such as a star, therefore, I would have thought one could refer to spacetime crossing the event horizon and entering the singularity. Or is this misguided?

Quote from: dlorde on 23/10/2013 21:07:17It's hard to know how much of a popular science programme is analogy and how much is hard physics, but Cox does explicitly say that space flows into the black hole with increasing velocity. It occurs to me that in that model the tidal force spahettification is due to the increasing 'stretching' of space, which should lead to the wavelength of infalling light lengthening... It works the other way. When spacetime is stretched (e.g. gravity well) objects in spacetime shrink and slow.

Quote from: webplodder on 24/10/2013 10:15:18A singularity is warping spacetime to a much greater degree than an ordinary mass, such as a star, therefore, I would have thought one could refer to spacetime crossing the event horizon and entering the singularity. Or is this misguided?I'm not qualified to say. When I first heard this as the river & waterfall analogy, I assumed the analogy was just with the effects of gravity on matter falling towards a black hole. Subsequently I've seen several articles by people who should know (and now Cox's video) who talk of space literally 'flowing' into the black hole, moving at c at the event horizon, and continuing to accelerate past it (this sounds analogous to the expansion of space by dark energy, that causes the most distant galaxies to recede from us faster than c). In this case, I'd expect infalling light to be red-shifted due to the acceleration expanding or stretching of space towards the black hole and outgoing light (above the EH) also red-shifted climbing out of the gravity well.I'm still not clear whether they're saying the acceleration due to gravity is actually physically equivalent to space flowing (i.e. the physics is the same), or whether it is simply an overblown analogy and a misuse of 'literally' (never mind what the OED says)...I'd be grateful for an authoritative view on this.

You're mistaken.

The River Model of Black Holes by Hamilton & Lisle, Am J. Phys., 76 (6), June 2008).

It becomes a bit odd for rotating black holes, because instead of an overall spiraling vortex, there is a twist, or shear of the metric, at each point of the flow.

Are you familiar with frame dragging? This flowing stuff (which I'm totally ignorant about right now) sounds similar to frame dragging.

Quote from: Pmb on 24/10/2013 16:44:08Are you familiar with frame dragging? This flowing stuff (which I'm totally ignorant about right now) sounds similar to frame dragging.Yes; I suppose they both refer to distortions of the spacetime metric, but the river model is based in an analogy for gravitational distortion; I don't know of an equivalent analogy for frame-dragging.

... Frame-dragging doesn't neccesarily refer to spacetime curvature. ...

Quote from: AndroidNeox on 23/10/2013 22:33:09Quote from: dlorde on 23/10/2013 21:07:17It's hard to know how much of a popular science programme is analogy and how much is hard physics, but Cox does explicitly say that space flows into the black hole with increasing velocity. It occurs to me that in that model the tidal force spahettification is due to the increasing 'stretching' of space, which should lead to the wavelength of infalling light lengthening... It works the other way. When spacetime is stretched (e.g. gravity well) objects in spacetime shrink and slow.What works the other way? and from who's point of view? are you talking about stationary or infalling objects? in which directions or dimensions do they shrink?

Quote from: AndroidNeoxYou're mistaken.The proof that you're wrong is found at...sorry, you cannot view external links. To see them, please REGISTER or LOGINSee Eq. (12) in that page. Other sources of proof, such as the American Journal of Physics, are quoted below.Quote from: AndroidNeoxLight dropping into a gravity well increases in energy... wavelength shortens/frequency increases.This too is a common mistake. The frequency of light does not change as it moves through a gravitational field as reckoned by any single observer. It’s only when you later compare measurements made by observers located at different gravitational potentials does the spectral shift manifest itself.

Light dropping into a gravity well increases in energy... wavelength shortens/frequency increases.

By working "the other way" I meant that when light (or anything else) passes into a region where spacetime is stretched, as in a gravity well, relative to another frame where spacetime is less stretched (or not stretched at all in the case of inertial reference frames) then the object (or wavelength of light) is observed to shrink and time is observed to slow. Time passes more slowly on Earth with respect to (WRT) an observer outside of our gravity well, maybe floating out in space. Because acceleration changes the nature of one's reference frame, an observer on Earth can see that time is passing more quickly for the observer out in space. In the case where there is no acceleration but two observers are moving WRT each other, they will both see that the other observer's clock is going more slowly than their local clock.

That suggests frame dragging and the river model are not as similar as they might sound - but I'm at my depth limit here.

It seems to me that rather than trying to clarify things, you just like to nit-pick and argue.

... I'd be more than happy to get back to you after I understand it to chat about it if you'd like?

He's shown why he thinks what you said is mistaken. If you feel his proofs and arguments are wrong and the error is his, you just have to show how they're wrong. You can't both be right, but an assertion can't stand without some evidence, plausible argument or mathematical proof.

The clock at the top of the tower emits two flashes radially downward (emission events A and B) differentially close together in global t-coordinate: dt_{AB}. For the stationary tower clock, dr = 0 and dphi = 0, the metric tells us the corresponding wristwatch time lapse d H recorded on the tower clock: (#eq:1A)dT_{H} = (1 - 2M/r_{H})^{1/2} dt_{AB} (dphi = 0; dr = 0) (4.2)Figure 4.2 traces the radially-downward global worldlines of the two flashes emitted by the tower clock at events A and B. The Earth clock receives these flashes at events C and D with map t-coordinate separation dt_{CD}. Map t-lapse Equation (4.1) tells us that these worldlines have identical slopes (the radial map speed of light has the same value) at every intermediate value of r-coordinate. As a result, the two worldlines are parallel at every radius on the map spacetime diagram, so the global t-coordinate separation between them maintains its initial value dt_{AB}.

okay. I found it. It's described in the articleThe River Model of Black Holes by Hamilton & Lisle, Am J. Phys., 76 (6), June 2008).as well as in the new version of Exploring Black Holes - Second Version. I never heard of this before and I may get drive heaves after I learn about it.

Quote from: AndroidNeox on 24/10/2013 21:49:10It seems to me that rather than trying to clarify things, you just like to nit-pick and argue.But correcting errors is clarifying... He's shown why he thinks what you said is mistaken. If you feel his proofs and arguments are wrong and the error is his, you just have to show how they're wrong. You can't both be right, but an assertion can't stand without some evidence, plausible argument or mathematical proof.

... Einstein was right that event horizons cannot form (in finite time).

Quote from: AndroidNeox on 28/10/2013 17:52:56... Einstein was right that event horizons cannot form (in finite time). The event horizon isn't a special place in terms of physical characteristics, it just happens to be where the escape velocity exceeds 'c'. For a large black hole, you could pass through it without noticing. Although I've heard that to an infalling observer, the event horizon always appears to remain ahead. Did you mean the singularity?

Ask a physicist to present an actual calculated result based on Relativity for the amount of time it would take for some object to pass the event horizon and they won't be able to.

How long does the whole process take? Well, of course, it depends on how far away you start from. Let's say you start at rest from a point whose distance from the singularity is ten times the black hole's radius. Then for a million-solar-mass black hole, it takes you about 8 minutes to reach the horizon. Once you've gotten that far, it takes you only another seven seconds to hit the singularity. By the way, this time scales with the size of the black hole, so if you'd jumped into a smaller black hole, your time of death would be that much sooner.