Alice Observes Bob at Event Horizon: DarkLink's Question

[Felix Fowler]

Hello physics forum. I am not very well versed in physics, so this question could be a misfire, but I just wanted to clear this up.

I watched one of Susskinds holographic principle lectures. So I get that Bob would see Alice turn into a hot mush of energy as she approaches an event horizon. But what would Alice observe Bob to be doing?

My thinking is that because Alice's clock is slowing down so much relative to Bob (due to the relativsitic effects of the black hole), that light would be taking an increasingly long time to reach Alice. So Bob would appear to be accelerating away from Alice as the light takes longer and longer to reach her. Would Bob at some point dim and then disappear, according to Alice, when the relative speed is more than the speed of light? (as if the whole universe had expanded away from Alice as she neared the event horizon)

Kind of concluding that event horizon of the black hole is similar/same as edge of observable universe.

Thanks,
DarkLink

 

[PeterDonis]

I watched one of Susskinds holographic principle lectures.

Note that the viewpoint in these lectures is not based on classical GR; it's based on one particular proposal for a quantum theory of gravity. So if you want an answer based on that, this thread really belongs in either the quantum forum or the beyond the standard model forum (since the proposal Susskind is discussing is not an experimentally established theory, it's just a proposal).

The answer based on classical GR, which is what I'll assume for the rest of this post, is simple: Bob would see Alice slow down more and more and never quite reach the horizon. Alice would observe nothing unusual at all as she crossed the horizon, which she would do in a finite time by her clock.

Alice's clock is slowing down so much relative to Bob (due to the relativsitic effects of the black hole)

This is not correct, because Alice is not stationary; she is falling into the hole. If she were stationary at some fixed height above the horizon, your statement would be correct. But because she is falling in, there is no well-defined way to compare her clock with Bob's, so there is no well-defined meaning to her clock rate relative to Bob.

What Alice would see of Bob is that light signals from him would be increasingly redshifted. As she crossed the horizon, assuming Bob is at some constant height that is very far away from the hole, the redshift factor she observes would be approximately 2. It would continue to increase as she fell further below the horizon.

when the relative speed is more than the speed of light?

There is no well-defined meaning to "relative speed" between spatially separated observers in a curved spacetime. The "speeds" you sometimes see quoted in pop science articles are coordinate speeds and have no physical meaning. The only well-defined observable is the redshift Alice observes in light signals coming from Bob, as described above.

as if the whole universe had expanded away from Alice as she neared the event horizon)

No, this is not what Alice will observe. She will observe light coming in from the universe being increasingly redshifted, just like Bob's light is. But other aspects will be quite different from the expanding universe we see here on Earth.

Kind of concluding that event horizon of the black hole is similar/same as edge of observable universe.

There are some respects in which it is, and some in which it isn't. See above.

 

[Felix Fowler]

Thank you for the lengthy response, Peter! Just want to know a little more.

She will observe light coming in from the universe being increasingly redshifted, just like Bob's light is. But other aspects will be quite different from the expanding universe we see here on Earth.
.

What other aspects would be quite different? Does everything get increasingly redshifted from Alice's perspective?

Thanks

 

[Ibix]

The black hole expands to fill more and more of the sky as you get close - apparently reaching up around you. The whole rest of the sky gets squished into a smaller and smaller circle above you, including possibly more than one image of stuff nearly directly behind the hole from your position. Close to the black hole, if you look out of one window you may even be able to see your own ship if you are able to control your descent enough. This is all due to the strong curving of light near the black hole - light may even orbit one.

The sky may be red shifted or blue shifted. There will be a blue shift due to gravitational time dilation and a red shift due to Doppler. Which effect is stronger depends on how you approach the hole. The effect will vary by angle. If the sky is blue shifted it will also appear bright; if red shifted it will appear dim.

 

[PeterDonis]

What other aspects would be quite different?

Light that is coming from parts of the universe not directly overhead of Alice will be bent by the hole's gravity, so that it appears to Alice to be coming from a narrower and narrower portion of the sky, centered on the direction that is directly overhead.

Does everything get increasingly redshifted from Alice's perspective?

I already answered that: yes.

 

[m4r35n357]

Thank you for the lengthy response, Peter! Just want to know a little more.
What other aspects would be quite different? Does everything get increasingly redshifted from Alice's perspective?

Thanks

Explore Andrew Hamilton's site for some great visuals and explanations.

 

[Flo Tur]

You said: "Bob would see Alice slow down more and more and never quite reach the horizon." This must be valid for any object attracted by the hole: rocks, gases, stars.So instead of a black hole, Bob will see a static image of all it's engulfing history. What's wrong here?

 

[phinds]

You said: "Bob would see Alice slow down more and more and never quite reach the horizon." This must be valid for any object attracted by the hole: rocks, gases, stars.So instead of a black hole, Bob will see a static image of all it's engulfing history. What's wrong here?

Well for one thing, for much of the "engulfing history", there is not yet an event horizon. Once the EH forms then Bob sees that portion of the engulfing history that is not yet red-shifted out of his ability to detect it. If he COULD detect them, yes he would see all the objects, but so what? There's nothing "wrong". The objects don't care what he can see, they've already fallen into the BH.

 

[Flo Tur]

What red-shift appear to Bob?

 

[phinds]

What red-shift appear to Bob?

I have no idea what you are asking

 

[Flo Tur]

Please explain what do you mean by: "...Bob sees that portion of the engulfing history that is not yet red-shifted out of his ability to detect it. If he COULD detect them,..."

 

[Ibix]

As you get closer to the event horizon you are deeper and deeper in the gravitational field and the radiation you emit is progressively further redshifted as viewed by a distant observer. Classically, a distant observer sees this continue forever with light you emit getting dimmer and redder as you get closer to the horizon. Eventually the light will be too dim and long wave for detection, so things that fell into the hole a long time ago will no longer be detectable in practice although in principle radiation is still coming up from you.

 

[Flo Tur]

Happy New Year!

If the BH continuously attract gases, dust, debris, we could expect to see a lot of red-shifted objects covering the BH? Which will no longer be black at all. Maybe we should use this when searching for BHs?

 

[Ibix]

You can certainly see gas and dust as it heats up and spirals into the hole. This is called an accretion disc and can be very very bright. But the hole itself is black because in the final stages of infall to the horizon things approaching it get ever more red and dim until they are undetectable to a distant observer.