Can black holes grow if nothing can enter them?

[sillycow]

You can still calculate the distance to the mirror using the time it takes for the light to reflect off the mirror, but the calculation is a lot more complicated than just dividing the time by $c$

I would have to divide by 2C as the light travels in both directions, and what are the complications? Does anything else take time besides the passage of light through space? Does it take time for the mirror to locally start reflecting light? I do not understand?
I thought according to the theory of relativity, every observer allways sees light traveling at C relative to herself. Isn't that the whole point of space-time dialation: Light travels at the same speed, but it's time-space being warped.
This is not the only solution to "I'll never see an object fall through an event horizon". The other is saying that I'd see the object slow down, and *almost* freeze at the horizon's "distance". As such it keeps getting closer at an ever slower rate. But it's distance to me is not "without bound", as there is an analytical solution to the limit.

it stops working completely as the object reaches the horizon

How can you say this after saying:

you'll never see an object falling through the horizon.

If no observer can ever observe anything reaching an event horizon? I mean, it would literally take forever to see something reach an event horizon. So how can you say that observer A can ever see anything stop emitting light "as the object reaches the event horizon"? I mean there can exist no object B which an outside observer, A, can ever witness falling past an event horizon. Can something "happen", if no-one can ever witness it, or be affected by it? Isn't that the "philosophy" of singularities? Namely: what you can't observe is meaningless.

 

[Dale]

Can something "happen", if no-one can ever witness it, or be affected by it?

Let's not get into philosophy here. GR predicts that there are classes of observers that can witness it and it predicts what other classes of observers will witness. That is scientifically sufficient.

 

[sillycow]

GR predicts that there are classes of observers that can witness it

So far we have dealt with 2 classes of objects:
One that does not accelerate: This is the observer. (is it standing still? Is it orbiting the black hole, or being pulled inside at a lower speed?, I'm not sure that it matters [does it?]).
The other object starts moving wit a higher speed towards the black hole. This is the mirror
They both start out at the same point.

We know that this class of observer would ever never observe the mirror to reach the horizon. (it would take infinite time)
We know that the mirror would not observe itself reaching the horizon, because the horizon keeps "backing off" from it.

So this "class" of observer cannot see it happen.

Can you define a different class of observer that would see the mirror reach the event horizon.

 

[Dale]

Can you define a different class of observer that would see the mirror reach the event horizon.

Yes. The class of observers that also cross the horizon.

 

[stevebd1]

It's probably worth pointing out that if you fall into a BH with any kind of velocity then the radial length expansion is reduced and in the case of falling from rest at infinity, when your velocity would be v=\sqrt(2M/r), then (rudimentally) the length contraction (due to SR) would cancel out the length expansion (due to GR, i.e. gravity) and coordinate distance would equal proper distance from the perspective of the infalling observer. This is taken into account with Gullstrand Painleve coordinates, it also removes the singularity at the event horizon. Basically the view of the BH would be very different for an observer hovering above it and for an observer falling in with some speed.

 

[Nugatory]

How can you say this after saying:

If no observer can ever observe anything reaching an event horizon? I mean, it would literally take forever to see something reach an event horizon. So how can you say that observer A can ever see anything stop emitting light "as the object reaches the event horizon"? I mean there can exist no object B which an outside observer, A, can ever witness falling past an event horizon. Can something "happen", if no-one can ever witness it, or be affected by it? Isn't that the "philosophy" of singularities? Namely: what you can't observe is meaningless.

It sounds as if you've skipped over post #5 in this thread? It explains this.

We know that the mirror would not observe itself reaching the horizon, because the horizon keeps "backing off" from it.

That's not what happens. An observer riding along with the mirror will find himself and the infalling mirror reaching the horizon quite quickly... Also covered in post #5.

 

[PeterDonis]

if we continue with the ruler analogy, if the "printed length" on the rullers (the centimeter marks), never converge. How can you say that the length of the tape measure converges?

You are misunderstanding how the word "converge" is being used here. My advice is to forget we ever used that word, and go back to the description of the tape measure being slowly lowered towards the horizon. The key point there is that, as the lower end of the tape measure gets closer and closer to the horizon, the length recorded by the tape measure does not increase without bound; it approaches some fixed value. That fixed value is the distance to the horizon. (The word "converge" is a technical term that means the same, in this context, as what I just said; but if that still confuses you, again, just forget the word "converge" and focus on what I just described.)

I think that the conclusion should be that rulers and tape measures are not good measurements of distance.

No, the conclusion is, as A.T. pointed out, that rulers and tape measures have to be at rest relative to you, to be good measurements of distance for you. Distance is relative.

In the tape measure scenario as I described it in post #18, to be completely precise and correct, we should imagine the tape measure being slowly lowered in very small increments; after each increment, we stop lowering the tape measure, so it is completely at rest relative to us, and record the length it registers. That ensures that it is giving us proper measurements of length relative to us.

When examaning the time it takes for the laser to reflect off the mirror, this time converges to some fixed value.

No, it won't. The laser light reflected off the mirror behaves exactly like light emitted from an emitter traveling with the mirror; as Nugatory said, it takes longer and longer to get out to the detector as the mirror/emitter gets closer and closer to the horizon.

 

[sillycow]

the tape measure does not increase without bound; it approaches some fixed value

1. Let's say the distance to the black hole is 100 meters.
2. The tape accelerates to speed V and position X (Did I push it, or was it being pulled?)
3. I measure the meter mark on my end. (at my observation point)
4. I repeat 1-3 99 times.
5. Now comes the last meter. Does it accelerate more slowly than the first? What are the pehenomena at work? What does it "feel" like to me? Is it because the far end of the tape is getting very massive/heavy?
5b. Does this change if I am talking about a sequence of disconnected rulers?

 

[sillycow]

Tonly if I send it before a certain time. After that, you won't get my message until you've crossed the horizon and it's too late.
c) There is another point in time, only slightly after the one in #b, such that I have to send my message before then or you won't even receive it because you've died at the central singularity before it got to you.

Putting all of these together, it's hard to see how your conclusion in #2c above makes sense. It's much more natural to say that you do in fact fall through the horizon and hit the central singularity - I just don't get to see it.
.

Thanks. I need to digest this.

 

[PeterDonis]

The tape accelerates to speed V and position X (Did I push it, or was it being pulled?)

The tape is lowered in a controlled fashion. It has a natural tendency to free-fall downward, so you don't have to push it; you just need to pull on it enough to counteract most of its tendency to free-fall, so that it just goes down a little bit at a time. Think of lowering a weight using a winch and pulley mechanism that allows you to precisely control its movement.

Now comes the last meter. Does it accelerate more slowly than the first?

The amount of force that must be exerted at the top of the tape (where the pulley/winch mechanism is, or whatever you are using to control the descent) in order to keep the descent under control, increases as the tape is lowered. But it is always a finite amount of force as long as the lower end of the tape is above the horizon.

Is it because the far end of the tape is getting very massive/heavy?

Not really. The proper acceleration at the lower end of the tape--the "weight" it feels because it is not in free fall--increases as the tape is lowered. But the force in question is the force exerted by the part of the tape just above the lower end--and ultimately, the force exerted by the mechanism at the top that is controlling the descent, transmitted through the tape. It's not due to any increase in mass of the tape itself. If you measured the mass of a small piece of the tape, using a device right next to it, it would be unchanged.

Does this change if I am talking about a sequence of disconnected rulers?

There is no way to control the descent of a sequence of disconnected rulers, so this thought experiment can't be realized using them. You need a single continuous object like a tape, so a force exerted at the top can control the descent of the entire object.

 

[jartsa]

1. Let's say the distance to the black hole is 100 meters.
2. The tape accelerates to speed V and position X (Did I push it, or was it being pulled?)
3. I measure the meter mark on my end. (at my observation point)
4. I repeat 1-3 99 times.
5. Now comes the last meter. Does it accelerate more slowly than the first? What are the pehenomena at work? What does it "feel" like to me? Is it because the far end of the tape is getting very massive/heavy?
5b. Does this change if I am talking about a sequence of disconnected rulers?

What are we doing with the tape? Lowering it towards an event horizon? If so, then it will be difficult to lower the tape slowly enough. The problem with too much speed is not that the tape tends to twist to one side. Instead it tends to Lorentz-contract.

 

[PeterDonis]

What are we doing with the tape? Lowering it towards an event horizon?

Yes.

If so, then it will be difficult to lower the tape slowly enough.

Difficult, yes, but not impossible. This is an idealized thought experiment, so as long as it's not impossible, we can do it.

The problem with too much speed is not that the tape tends to twist to one side. Instead it tends to Lorentz-contract.

Yes, that's why we lower the tape very slowly and only a little bit at a time; then we stop it and take a measurement. Then we repeat the process.

 

[eltodesukane]

"Distance, in physics is defined by the time it takes light from point A to reach point B. "
No, distance between A and B is how many meter sticks you need between A and B.
In a varying gravitational field, your method doesn't work.

 

[PAllen]

"Distance, in physics is defined by the time it takes light from point A to reach point B. "
No, distance between A and B is how many meter sticks you need between A and B.
In a varying gravitational field, your method doesn't work.

Neither does the meter stick method work, in general, in GR. For example, you presumably want to require that each meter stick is 'at rest' relative to its immediate neighbors. Then you find that you can't (always) meet that condition over a large distance - applying this ruler by ruler, you end up forced to make a ruler move on lightlike curve at some point or have infinite proper acceleration. A trivial case is spanning the horizon of a BH. There is also a non-uniqueness issue for varying gravitational field.

A correct statement is that non-locally, both relative velocity and distance are ambiguous in GR.

 

[IngemarAEH]

One question was how a black hole can grow, if approaching objects take infinite time to enter the black hole, as seen from far away ?

I haven't studied the math on this, but I believe it's a test particle, with negligible mass, that is never seen to enter the black hole.
My intuition tells me that a massive object, such as a star, would make the horizon of the black hole expand, when sufficiently close, hence it will enter the black hole in finite time.

 

[PeterDonis]

One question was how a black hole can grow, if approaching objects take infinite time to enter the black hole, as seen from far away ?

There have been plenty of threads already on this. Here is a good one:

https://www.physicsforums.com/threads/how-do-black-holes-grow.652845/#post-4163966