Value of g near a black hole (re-visited)

Spin-Analyser

Could you clarify this please? Are you saying that an in-faller would see the in-fallers in front of them ( who were of course outside the horizon from a distance ) cross the event horizon as they approach, at which point they disappear from this this observers perspective only to reemerge once the event horizon is reached? This doesn't seem right?

PAllen

As long as an infaller is outside the horizon, they see prior infallers as they were closer to the horizon than they are. Note that distances perceived by this infaller are very different from the r coordinate value - there is "lot's of room". Passing the horizon by our chosen infaller is experienced as seeing prior infallers pass the horizon.

There is no disappearance or reappearance.

I came up with an analogy on another thread. Imagine a chain of infalling observers. Imagine a pink flashbulb goes off beyond one end of this chain. Prior to the pink light reaching (say) the last observer in the chain, all prior infallers are seen as before the flash reached them. The moment the flash reaches the last observer is exactly the moment when this observer sees all prior observers flash pink. Thus, the moment the this observer crosses the horizon is the moment they see earlier infallers as of when they crossed the horizon. Factoring light delay, you deduce they all got hit with the flash before you, but you only see them flash pink the same time you do. Similarly, factoring in light delay, this trailing infaller deduces the earlier infallers crossed the horizon before they did.

Spin-Analyser

Okay I kind of see, but if the in-faller were to get very close to the horizon (say one plank length away) and then move away, would that mean that they observed the previous in-fallers crossing the event horizon twice, once on the way towards it and them reemerging on the return journey?

PAllen

No. Until the moment the event horizon 'passes them' they sell all prior infallers as of before they passed the horizon. In my analogy, if the pink flash is 1 planck length from the trailing observer:

- no earlier observer is seen to have flashed pink
- the trailing observer can still, in principle, accelerate away from the light, and without ever quite exceeding c, stay ahead of it: see Rindler Horizon.

At precisely the moment the flash reaches the trailing observer, all prior observer's flash pink, and no acceleration at all will catch light that has already passed.

Sufficiently locally, all 'near horizon' phenomena are accurately described by a passing flash of light - because the event horizon is a light like surface.

Passionflower

You are wrong.

A free falling observer (free falling from infinity) will measure his distance to the EH to be exactly equal to r - rs (where rs is the event horizon).

Contrast this with a stationary observer close to EH he will measure his distance from the EH to be more than r - rs

Spin-Analyser

What if the in-faller stops one plank length away? They will see the event horizon as just in front of them, but also just in front of every other object that hasn't crossed the horizon yet but who are closer to the singularity than they are? This seems very paradoxical!

PAllen

I wasn't actually thinking of infalling from infinity. In these scenarios of changing mind at the last second, I think in terms of observers hovering near the horizon, then shutting off fuel. However, I failed to specify this, and certainly you are right about an infaller from infinity.

[Edit: this observation does clarify that I needn't have said anything about comparative distances, as it is not relevant to the main issues - see next post.]

PAllen

No, they will see earlier infallers a 'normal' distance away, as of before they passed the horizon. Think of it this way: if they could know where the horizon was just before it hit them, they would see earlier infallers at a distance such that they could deduce they must be already inside; however, if each earlier infaller had a watch, the image they would see on the watch would be of a moment just before each earlier infaller crossed the horizon. Think more about the passing flash of light example. Further, if at this last moment, they accelerated away frantically, they would never see the earlier infaller's watches reach their infall moment.

Spin-Analyser

So let me clarify.

1). It is perfectly possible to observe objects crossing the event horizon of a black hole.
2). It is not possible to observe them at a time after they reached the event horizon.

Think very carefully about your next answer.

PAllen

Both your statements are not quite right.

It is perfectly possible to see objects cross the horizon when you cross the horizon. It will be obvious (at that moment) that they crossed before you. Further, you can deduce for possible infallers ahead of you, that 'if they are still where they appear to be', and you know where the horizon is, they are inside the horizon. However, since you are seeing an 'old' image of them, you cannot tell if they made a last moment decision to escape (and thus are closer to you than they appear) unless you also make such a decision, and later see that they did. Further, as long as you remain outside the horizon, you cannot tell for sure whether they crossed or not.

Spin-Analyser

I'm talking about an observer who never reaches the horizon themselves. As they approach they will see objects crossing the event horizon, but they will be seeing them as they were before they reached the horizon?

PAllen

Let's talk about a supermassive BH, and let's say you are following 10 feet behind your partner, approaching the horizon. Let's say you know exactly where it is all times (by computation and knowledge of the region). Let's say you fall to 3 feet from the horizon and stop. At this moment, it is possible to still see an image of your partner that looks 10 feet from you. Now consider two cases:

1) Your partner crossed the horizon. You will see their image fade to black, and their wristwatch will never quite reach the time they crossed the horizon.

2) Your partner stopped 1 foot from the horizon. Some time after you stop, you will see that your partner started accelerating to hover before you did, getting closer to you in the process, and are now stopped 2 feet away.


The closer to the horizon your partner makes decision (2), the longer before you can distinguish it from (1).

Spin-Analyser

So if you are close enough to the horizon you can observe objects crossing it?

They both hover just above the horizon. One of them turns off their engines. Does the other one see them disappear passed the horizon?

PAllen

This is getting repetitive. You are seeing an old image from before they crossed. It is from when they were still (in my prior example) 10 feet from you but right near the horizon. This light takes a while (up to forever) to reach you.
The one that remains hovering sees the other one approach the horizon, effectively going black before reaching it. The image history here is quite different from tandem infallers. The image history (past world lines + light null paths) makes for the difference these cases.

Passionflower

Basically an observer can detect a signal from another observer who passed the event horizon if he passes the event horizon as well in time. He will observe the signal only after he passed the horizon himself.

An observer who never passes the event horizon cannot receive a signal from an observer passed the event horizon.

Spin-Analyser

I'm just trying to be absolutely clear that you're saying you can see an object turn black, effectively crossing the horizon. But at this point you're still not sure if they reached the horizon or not? If they accelerated at the last moment they would presumably reappear from the others perspective after a time. And if they cross the horizon they would suddenly see all the other objects that had fell in earlier?

The one that remains hovering will see them approaching the horizon as they are falling towards the singularity, meaning the event horizon will always be falling in ahead of them?

PAllen

I think I will have to let someone else answer your questions after this. Somehow, I think I'm being clear and you get something quite different from what I said out of it. Someone else may express it in a way you get it.

Repeating yet again: You don't see them actually cross the horizon if you remain outside. No exception. The turning black is just a matter of infinite red shift and time dilation relative to you if you are hovering further away.

If they divert from crossing at the last minute, sometime before infinite redshift, you see them turn on their thrusters and (as in my tandem example) get closer to you (you having already hovered). All this is due to light delay. You never see turning fully black and reappearing[edit: you can see someone have arbitrarily close to infinite redshift, then approach you becoming less redshifted, even pass you]. Ultimately, after infinite time, you can infer they crossed if you never detect that they stopped and hovered.

Finally, yes, the moment you cross you see prior infallers as of the moment they crossed.
I don't understand this at all. The one that is hovering simply sees the one that turns off thrusters fall towards the horizon, get redder, ultimately black, just outside the horizon. Nothing about the history from horizon to singularity can be seen by the one remaining outside.