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?

Staff Emeritus
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.

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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

Gold Member
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).

Staff Emeritus
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.

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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 ?

Staff Emeritus
I still don't understand what you are asking.

Is it about black holes or not?

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

Staff Emeritus
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

Staff Emeritus
I still don't understand what you are asking.

Is it about black holes or not?
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.

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