# Black hole's delayed reactions

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1. Oct 14, 2015

### jartsa

Let's say I'm towing a black hole by using a spaceship, and a rope, and a mass that is attracting the black hole near its event horizon.

Let's say the mass unfastens at some moment, and I'm watching everything carefully.

Obviously I will notice that the mass has unfastened only after a long time after the unfastening happened.

As I'm watching carefully, I should be able to see what exactly happened, including the reason why I saw the black hole being accelerated by my pulling action when the mass was already unfastened.

So what might be the reason why I saw the black hole accelerating, when the mass was already unfastened?

2. Oct 14, 2015

### Staff: Mentor

I'm not sure this is actually possible; we certainly don't have a known solution of the Einstein Field Equation that describes it. So I'm not sure it's possible to have a meaningful discussion of this thought experiment, but I'll give it a try.

Some moment according to whose time? How do we determine which moment it is?

I take it you are assuming that you yourself are very far away from all this, so you expect light coming from the mass, which is close to the event horizon, to take a long time to get out to you, correct?

Also, you are implicitly using the Schwarzschild coordinate definition of "time" (more precisely, you are using that simultaneity convention). Since this scenario is not static, Schwarzschild coordinates don't actually apply, and I don't know offhand what coordinates would apply (since we don't have a known solution to begin with, as above); but I'm willing to assume for the sake of argument that we can find coordinates sufficiently similar to Schwarzschild coordinates for this scenario.

However, even if we can, we still have to be aware of the fact that a simultaneity convention is just that--a convention. There is no absolute answer to the question of "when" the mass detaches relative to you, sitting far away from it all.

Before we can even address this question, we first have to decide what it means to "see" the black hole at all. You can't literally see a black hole; light can't escape from it. All you can see is the hole's effects on light from objects around and behind it. Those effects will be time dilated, in general, by a factor that will vary depending on the path taken by the light. So before you can draw any conclusions from what you see, you have to adjust for this time dilation.

Once you've adjusted for time dilation, I don't see any reason why you would conclude that the hole was still accelerating after the mass unfastened. Can you give a reason why you think you would?

3. Oct 15, 2015

### jartsa

The release of the mass initiates a chain of causes and effects, and me noticing that the black hole has stopped accelerating is an event at the end of that chain. As I watch carefully, I can see those events in that chain happening, and I can see that there is a large delay between the release of the mass and me noticing any effect of that event.

So I know that the release of mass happened first, and then after a long time the event of me noticing a termination of acceleration happened. So it's reasonable for me to think that I was seeing the black hole accelerating when the mass had been already dumped.

Sure I am assuming that I know the real current position of the black hole. If I did not assume that, then what should I assume? Should I assume that a black hole looks like it's were it was million years ago?

For improved visibility the black hole may be replaced by a neutron star that is almost a black hole.

4. Oct 15, 2015

### Staff: Mentor

But you also took a long time to notice the release of the mass. What makes you think you wouldn't see the black hole stopping its acceleration at the same time as you saw the release of the mass?

If your answer is "because it takes longer for light to travel from the black hole to me, then from the mass to me", see below.

If you are talking about what you actually see, as in the light you receive at your location, you should assume that the light you receive reflects the state of the black hole when the light was emitted. Isn't that obvious?

But if you are trying to figure out the order in which things "actually happened", at least according to your simultaneity convention, then you have to first correct for light travel time. That means you can't just assume that the order in which you see things is the order in which they actually happened. If you receive light from two events, A and B, it is possible that A may have happened first even if you see the light from B first--if the light from A took longer to get to you. You don't appear to be taking this into account at all.

5. Oct 16, 2015

### jartsa

I agree that I would see the black hole stopping its acceleration at the same time as I saw the release of the mass. So there's nothing controversial there, I guess.

So the controversial part might be this part:

I am saying that a black hole is where it seems to be, and it has the velocity and the acceleration that it seems to have.
And this is my supporting argument: If it's not where it seems to be, then where is it?

The black hole at the center of our galaxy is at the center of our galaxy, because it seem to be at the center of our galaxy. No calculations have been done to find where it really is.

To assume that a black hole is were it seems to be is OK, because everybody assuming it. That's my argument for my controversial claim.

So we have a delay in the seen end of acceleration, and we have a delay in actual end of acceleration, as seen and actual are the same.

Last edited: Oct 16, 2015
6. Oct 16, 2015

### Staff: Mentor

Actually, you might not. You might see the mass released first, and then see the hole stopping.

But that doesn't mean the hole stopped after the mass was released. It only means that the light you see from the hole took longer to get to you than the light you see from the mass. In order to reconstruct what actually happened from what you see, you have to first correct for the travel time of the light, as I've already said.

What that correction should tell you, heuristically speaking, is that the hole stopped accelerating as soon as the information that the mass had been released reached it. In other words, it should tell you that changes in the gravitational field propagate at the speed of light.

And that's not correct. What is correct is that, when you see the black hole, and the image you see seems to be in a certain position and to have a certain velocity and acceleration, those are the parameters that described the black hole one light-travel time ago; they are not the parameters that describe the black hole "now".

You don't know for sure. The best you can do is to take the latest observation you have, which tells you where the hole was and what it was doing one light-travel time ago, and extrapolate those forward to tell you where the hole is "now".

This is, of course, not restricted to black holes; it's true of anything. We don't see the Sun as it is "now"; we see it as it was 500 seconds ago, and the best we can do at saying where it is "now", based on just that observation, is to extrapolate forward 500 seconds from what see. Of course, in the case of the Sun we don't just have one observation; we have a whole set of astronomical observations stretching over millennia, and a detailed model into which they all fit, so we can do much better at saying where the Sun is "now" than we could on the basis of just one observation. But it's still an extrapolation from data that can't tell us anything more recent than one light-travel time ago.

No, they're not. See above. Anyway, isn't it obvious? Do you always assume that you have instantaneous information about everything that happens in the universe, and that your information is always 100% accurate?

7. Oct 16, 2015

### rootone

8. Oct 17, 2015

### jartsa

When calculating the real position of Sagittarius A* from the light we receive, we take into account the delay of 26000 years that the light spends traveling through the empty space between Sagittarius A* and Earth, but we do not take into account a time, let's say 500000 years, that the light might have spent inside the black hole, where 'inside the black hole' means so deep in the gravity well that the coordinate speed of the black hole and the coordinate speed of said light are almost the same.

Hey now I know: As the rope is deep in the gravity well, the coordinate velocity of the rope and the coordinate velocity of the black hole must be almost the same ... that's why the black hole accelerates. The rope is pulled and the black hole follows the rope.

9. Oct 17, 2015

### Staff: Mentor

We don't? How do you know?

Also, not all of the light we receive from the area of Sagittarius came from an area so close to the horizon that it will be greatly time delayed by the hole's spacetime curvature. For example, light from the radius of the "photon sphere", at 3/2 the Schwarzschild radius, is only time dilated by a factor of $\sqrt{3}$, which is less than 2. And that already pins down the location of the hole pretty well.

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