B Propagation of changes in a gravitational field

[Lord Crc]

I thought gravitational waves were how changes in the gravitational field was propagated. The Insight https://www.physicsforums.com/insights/how-fast-do-changes-in-the-gravitational-field-propagate/ says so as well.

What got me confused was the following scenario: take a stationary black hole of suitable size (tens of solar masses?) with an orbiting companion body, a neutron star for example. Then shoot another suitably sized black hole into the system with such a velocity that it grazes the EH of the stationary black hole and escapes the system.

The intruder BH should cause the stationary BH to move no? If it does, the gravitational field felt by the companion mass would change too no? How is this change propagated?

 

[Vanadium 50]

with such a velocity that it grazes the EH of the stationary black hole

It can't both "graze" and "escape". You need to pick one or the other.

I don't see how this in any way contradicts gravitational perturbations traveling at c.

 

[Lord Crc]

It can't both "graze" and "escape". You need to pick one or the other.

Ok, I pick escape. The point being that the intruder should cause the stationary BH to move, or at least it would if they were regular stars. The intruder could be a neutron star if that is better.

Yes the effect is small, I'm trying to grasp the principle.

I don';t see how this in any way contradicts gravitational perturbations traveling at c.

I was told that gravitational waves does not escape the event horizon, which got me thinking about the above scenario. Clearly I'm missing something important.

 

[Ibix]

Ok, I pick escape. The point being that the intruder should cause the stationary BH to move, or at least it would if they were regular stars. The intruder could be a neutron star if that is better.

Yes the effect is small, I'm trying to grasp the principle.

The intruder seems to me to have a similar mass to the components of your binary. The effect will not be small. Why would you think the black hole wouldn't move? There's no "absolute rest" so a black hole moving isn't exactly surprising.

I was told that gravitational waves does not escape the event horizon, which got me thinking about the above scenario. Clearly I'm missing something important.

If you trace the gravitational waves backwards, you'll find that they come from somewhere outside the horizon (to the extent that you can localise the source of gravitational waves - it's complicated). In a sense, you could see it as the gravitational influence of the mass of the hole before it formed, with the pattern modified by later evolution of the "shape" of spacetime, which can depend on other things like other black holes/neutron stars/whatever.

 

[timmdeeg]

I was told that gravitational waves does not escape the event horizon, which got me thinking about the above scenario. Clearly I'm missing something important.

I think if two black holes are flying past each other - so no merger - their horizons will be deformed and emit gravitational waves then (until being spherical again).

 

[Vanadium 50]

I am still unclear about what the question is. If you are asking if gravitational changes propagate at c, they do. If you are trying to imagine a situation where you get changes in gravitational sources and could think about measuring this speed, why do you need such a complicated situation? If you are asking about event horizons, why isn't that in the title? And this situation doesn't really involve event horizons.

 

[Lord Crc]

I am still unclear about what the question is.

I was told gravitational waves do not escape the EH. Based on what I've read, such as the Insight I linked, gravitational waves propagates changes to the gravitational field. Assuming both are true, I don't understand how objects external to a black hole, such as the orbiting planet in my OP, "can tell" if the black hole moves due to an external pertubance.

I'm entirely comfortable with gravitational waves propagating at c, that was never any doubt.

 

[Lord Crc]

The intruder seems to me to have a similar mass to the components of your binary. The effect will not be small. Why would you think the black hole wouldn't move? There's no "absolute rest" so a black hole moving isn't exactly surprising.

I meant to say "might be small". I would expect it to move, but clearly I'm missing some pieces to the puzzle.

If you trace the gravitational waves backwards, you'll find that they come from somewhere outside the horizon (to the extent that you can localise the source of gravitational waves - it's complicated). In a sense, you could see it as the gravitational influence of the mass of the hole before it formed, with the pattern modified by later evolution of the "shape" of spacetime, which can depend on other things like other black holes/neutron stars/whatever.

Was that a response to the question I linked? Just want to verify before I interpret it all wrong.

 

[LURCH]

So the question you’re asking would be something like, “if changes in the gravitational field are propagated by gravitational waves, and gravitational waves travel at c, then how can anything that happens to the mass within the EH have any effect on things outside of the Horizon?” Is that an accurate paraphrase?

 

[PAllen]

Look, it really doesn’t matter whether one or both objects in a binary system are BH, a or whether an intruder is a BH or neutron star. For all combinations you may think of, the escaping intruder will result in displacement of both members of the orbital system, with interactions among all three being required to fully describe the result. In addition, gravitational radiation will be released ( distinguishable from that released by the unperturbed binary system). There is essentially no difference which of the three bodies you consider to be a BH vs. neutron stars. No part of this requires propagation of anything across an event horizon, nor propagation of anything faster than c.

Given the above, please try to explain CLEARLY which part is bothering you. I truly have no understanding of what is bothering you about this scenario.

 

[Lord Crc]

Ok, let me try again.

We have a very massive body A at rest (not absolutely of course) being orbited by a piece of dust D. Another massive body B moves from infinity, goes near enough A to perturb it and escapes the system.

AFAIK this event should cause A to accelerate for a bit and start moving, and thus change the gravitational field around it, as "felt" by D. However assuming the acceleration is sufficiently low, D should keep orbiting A as it moves.

AFAIK the change to the gravitational field that keeps D orbiting A, rather than orbiting the initial position of A, is propagated by gravitational waves emitted by A.

My question is, is the above correct?The reason I ask is because I don't see how can it if A is a black hole and gravitational waves does not escape the event horizon.

 

[Ibix]

My question is, is the above correct?

Yes, essentially. A simpler example would be two orbiting black holes. Both move around their common centre of mass and continuously emit gravitational radiation.

The reason I ask is because I don't see how can it if A is a black hole and gravitational waves does not escape the event horizon.

The thing to understand is that at any event in spacetime you can only be affected by things in your past light cone. And the past light cone of any event outside an event horizon cannot include the event horizon. So the point I was making in my previous post is that you can always trace gravitational influence "now" back to the time before the event horizon existed. So the gravitational waves are, in some sense, the gravitational influence of the stars that collapsed to form the holes distorted by the later motion of the holes.

I don't know if that picture helps you. Formally, you could say that GR is, at its core, a system of differential equations. If you set up some initial conditions including collapsing stars and work out what happens if you let them collapse, gravitational radiation from their mutual orbit is implied already.

 

[Lord Crc]

The thing to understand is that at any event in spacetime you can only be affected by things in your past light cone. And the past light cone of any event outside an event horizon cannot include the event horizon. So the point I was making in my previous post is that you can always trace gravitational influence "now" back to the time before the event horizon existed. So the gravitational waves are, in some sense, the gravitational influence of the stars that collapsed to form the holes distorted by the later motion of the holes.

I kinda get it but then I don't. In my example, B can linger at infinity for whatever time before it enters the system. How would D know the new trajectory of A, once it starts moving?

 

[Lord Crc]

Btw forgot to say thanks guys. It's probably some silly thing, but the disconnect I'm clearly having makes it difficult.

 

[Ibix]

I kinda get it but then I don't. In my example, B can linger at infinity for whatever time before it enters the system.

Can it? Why does it start moving then? And how was it hovering in the first place?

 

[LURCH]

Maybe it will help if we get rid of the third body, and just say that “for some reason” the black hole moves. I think that the mention of gravitational waves has caused people to think of the type of gravitational waves that we have observed so far. Specifically, the idea that the BH is already radiating gravity waves before the experiment begins, because it is orbiting something. OP, correct me if I’m wrong, but I think this is not the situation you are trying to describe. You mean to say that the BH emits a single gravitational wave when it changes course, right? And that change in gravition causes the orbiting body to change its orbit?

I present the following modification of the question, to which I will then propose an answer (to check if my own understanding is correct). Hope this brings clarity. Suppose the BH in question is of such mass that it has a diameter of ten light minutes. Let us further suppose that the orbiter is just five light minutes outside the Event Horizon. Now, for some reason, the BH moves. Does the The orbit of the orbiting body change five minutes later (the time for a “change” to travel at light speed from the EH), or does the orbit change after 15 minutes?

My tentative answer is that it would take only five minutes for the orbiter to be effected, because he effect is being caused by a change to the space at, or just outside of, the EH, and NOT by any change of conditions inside the EH. Would that be correct? And does it help you answer your original question, @Lord Crc ?

 

[Vanadium 50]

I still don't understand what you are asking.

Is it about black holes or not?
Is it about gravitational radiation or the gravitational force?

 

[A.T.]

We have a very massive body A at rest (not absolutely of course) being orbited by a piece of dust D. Another massive body B moves from infinity, goes near enough A to perturb it and escapes the system.

AFAIK this event should cause A to accelerate for a bit and start moving, and thus change the gravitational field around it, as "felt" by D. ...

I don't understand why you describe the effect on D as coming via A only. If B affects A then it also affects D, which will move according to the space-time geometry resulting from the A & B combined.

 

[stevendaryl]

I was told gravitational waves do not escape the EH.

I think that maybe you have the intuition that for one object's gravity to affect another object, then gravity waves have to propagate from one to the other. That's not true. Gravity is described in General Relativity as a field (a tensor field, actually) extended throughout spacetime. The details of how that field varies from place to place shows the presence of matter. But outside the event horizon of a black hole, the effects of gravity are no different than the effects of any other spherically symmetric object of the same mass.

 

[stevendaryl]

I still don't understand what you are asking.

Is it about black holes or not?
Is it about gravitational radiation or the gravitational force?

I think his confusion is that he has the intuition that gravitational force between two objects is due to gravitational waves propagating from one to the other. Black holes contradict this intuition.

On the other hand, if this is his confusion, I don't quite understand why one black hole zooming past another is more relevant than just something orbiting a black hole.

 

[Lord Crc]

Can it? Why does it start moving then? And how was it hovering in the first place?

Say it was orbiting at infinity, and it started moving because I triggered a giant rocket engine pushing it into the A-D system.

Specifically, the idea that the BH is already radiating gravity waves before the experiment begins, because it is orbiting something. OP, correct me if I’m wrong, but I think this is not the situation you are trying to describe.

Indeed, I assume the original system is free of gravitational waves (D being of negligible mass).

You mean to say that the BH emits a single gravitational wave when it changes course, right? And that change in gravition causes the orbiting body to change its orbit?

Yes, that was what I was trying to ask (though not sure if it would be a single wave or not).

My tentative answer is that it would take only five minutes for the orbiter to be effected, because he effect is being caused by a change to the space at, or just outside of, the EH, and NOT by any change of conditions inside the EH. Would that be correct? And does it help you answer your original question, @Lord Crc ?

I'll have to chew on that one.

I don't understand why you describe the effect on D as coming via A only. If B affects A then it also affects D, which will move according to the space-time geometry resulting from the A & B combined.

Of course B will perturb D as well, but I was focusing on what happens to D due to the acceleration of A.

Is it about gravitational radiation or the gravitational force?

It's about changes to the gravitational field, and how these changes are propagated.

I think his confusion is that he has the intuition that gravitational force between two objects is due to gravitational waves propagating from one to the other. Black holes contradict this intuition.

AFAIK, a test particle orbiting a mass at rest (relative to the test particle) does so due to the static gravitational field, no waves involved. This I get, I think. When the mass is accelerated, the gravitational field changes. AFAIK the acceleration causes the mass to emit gravitational waves. When the acceleration stops the field is static again. Assuming the acceleration is slight enough then the test particle should still orbit the mass, though, I assume, the orbit would be perturbed.

I had assumed the perturbation of the orbit of the test particle, causing it to orbit in the new, static field, was due to the gravitational wave emitted by the mass when it was accelerated, but I got doubts about this when I was told gravitational waves do not escape a black hole.

My apparently confusing three-body problem was just the first thing that popped into mind as I contemplated this.

 

[stevendaryl]

AFAIK, a test particle orbiting a mass at rest (relative to the test particle) does so due to the static gravitational field, no waves involved. This I get, I think. When the mass is accelerated, the gravitational field changes. AFAIK the acceleration causes the mass to emit gravitational waves. When the acceleration stops the field is static again. Assuming the acceleration is slight enough then the test particle should still orbit the mass, though, I assume, the orbit would be perturbed.

That intuition is almost right, but not quite. In sort of the same way that a planet can have a stable orbit around a star, the gravitational field itself can change in time in a smooth, predictable way. Those changes are not due to gravitational waves. It's only higher-order changes that propagate as gravitational waves.

 

[A.T.]

Of course B will perturb D as well, but I was focusing on what happens to D due to the acceleration of A.

GR is non-linear, so you it's not so easy to decompose the effect of multiple sources, as if it was were a linear superposition.

 

[PeterDonis]

I was told gravitational waves do not escape the EH.

First, "I was told" is not a valid reference. You need to tell us what specific reference you got this from.

Second, when black holes merge, gravitational waves are emitted. Those waves do not come from inside the horizon. But they do come from the black hole merger. So the actual intuition you are using here, which is something more like "black holes can't emit gravitational waves" is clearly wrong.

The scenario you described in your OP is basically a weaker version of a black hole merger, where the holes don't merge, they just make a close approach and then separate. Yes, gravitational waves should be emitted from this process, but they will be much weaker than the gravitational waves emitted from a black hole merger.

 

[Lord Crc]

That intuition is almost right, but not quite. In sort of the same way that a planet can have a stable orbit around a star, the gravitational field itself can change in time in a smooth, predictable way. Those changes are not due to gravitational waves. It's only higher-order changes that propagate as gravitational waves.

Ok, now we're getting somewhere. So presumably these changes propagates at c as well?

GR is non-linear, so you it's not so easy to decompose the effect of multiple sources, as if it was were a linear superposition.

Point taken!

First, "I was told" is not a valid reference. You need to tell us what specific reference you got this from.

I did link to the relevant post in my reply #3. Though the current theme doesn't make it abundantly clear IMO.

Second, when black holes merge, gravitational waves are emitted. Those waves do not come from inside the horizon. But they do come from the black hole merger. So the actual intuition you are using here, which is something more like "black holes can't emit gravitational waves" is clearly wrong.

I thought it was the mass inside the black hole that emitted the waves, and that these waves escaped the event horizon.

 

[Lord Crc]

I am still unclear about what the question is.

I see now that it was confusing to link to the Insight without specifying better that I was really just using a single line as a reference, and that my question wasn't really about the speed of gravity. Sorry about that.

 

[PeterDonis]

I thought it was the mass inside the black hole that emitted the waves, and that these waves escaped the event horizon.

No, it isn't. The waves are emitted from the region of fluctuating spacetime curvature outside the horizon; basically they carry away the fluctuating spacetime curvature so that what remains is the smooth horizon of the new, merged black hole.

 

[Lord Crc]

No, it isn't. The waves are emitted from the region of fluctuating spacetime curvature outside the horizon; basically they carry away the fluctuating spacetime curvature so that what remains is the smooth horizon of the new, merged black hole.

So the mental image I have now is that the EH is like a Neumann boundary in regular PDEs. And the waves come from the exterior reacting to this boundary moving and changing. Is that closer or even more wrong?

 

[PeterDonis]

the mental image I have now is that the EH is like a Neumann boundary in regular PDEs

I don't think this is a good way to think about it. The EH can't even be locally defined; to know exactly where the EH is, you have to know the entire future of the spacetime.

 

[Lord Crc]

Oh shoot, forgot about that point.

 

[stevendaryl]

Ok, now we're getting somewhere. So presumably these changes propagates at c as well?

It depends on what you mean by "propagate". The gravitational field can change with time. That doesn't imply anything "propagating". Propagation is really applicable to perturbations. If you jiggle a mass, then that will cause a jiggle in the gravitational field, and that will propagate out at the speed of light.

I thought it was the mass inside the black hole that emitted the waves, and that these waves escaped the event horizon.

No, gravitational waves are disturbances in the gravitational field. The "source" of a gravitational wave isn't a mass, it's a little jiggle in a gravitational field. So the waves don't propagate from the center of the black hole; they propagate from the field surrounding the black hole.

 

[Lord Crc]

It depends on what you mean by "propagate". The gravitational field can change with time. That doesn't imply anything "propagating". Propagation is really applicable to perturbations. If you jiggle a mass, then that will cause a jiggle in the gravitational field, and that will propagate out at the speed of light.

Right, and my misunderstanding was equating that jiggle with gravitational waves.

No, gravitational waves are disturbances in the gravitational field. The "source" of a gravitational wave isn't a mass, it's a little jiggle in a gravitational field. So the waves don't propagate from the center of the black hole; they propagate from the field surrounding the black hole.

Gotcha. I'll have to spend some time reprogramming my brain but I think I got the point now.

Thank you all for your input and patience. Clearly I need to work on my question-asking skills.