# Does an accelerated particle emit gravitational waves?

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1. Sep 24, 2011

### bbbeard

Does a massive particle that is accelerated emit gravitational waves? What if the acceleration is due to a gravitational field?

2. Sep 24, 2011

### Andrew Mason

Re: Why do accelerated charges emits a photon?

Interesting question.

As far as I can tell, no one knows whether gravitational waves exist. GR seems to predict them and John Wheeler spent a good part of his life trying to find them. But none have ever been found. Mind you, it is a difficult task.

I am certainly not an expert in GR, but I don't see why the acceleration of a particle should cause emission of gravitational waves, regardless of the means by which acceleration is achieved. As far as I can tell, momentum is always conserved. The total momentum of the system (the momentum of the mass that is being accelerated plus the momentum of whatever it is that is supplying the acceleration) does not change. Assuming that all interactions are elastic, the mass/energy of the system would be conserved.

If the interaction was electromagnetic, say a photon of energy $E = h\nu \text{ and momentum } p = h/\lambda$ being absorbed by an atom of rest mass m, the absorbed energy would increase the rest mass of the absorbing atom by $\Delta m = h\nu\c^2$ and the momentum change of the atom would be $\Delta p = h/\lambda$. Where is there any room for momentum or energy being sent out as gravitational waves?

Perhaps someone who has a much better grasp of GR than I do should really answer this question.

AM

3. Sep 24, 2011

### PAllen

Real bodies (rather than ideal test bodies) follow 'almost geodesics', the difference being accounted for by gravitational waves. However, the amount can be ignored except for astronomic objects.

As to the free falling charge, I incline to agree with Andrew, but there have been long discussions in this forum about it. My summary would be: nobody knows, those who predict an effect find it too small to detect, almost in principle. However, experts in GR, and nobel prize winning physicists have come to opposite conclusions on this. Some say the equivalence principle should exclude charged bodies, others say they can be included.

4. Sep 24, 2011

### Bill_K

Yes, it is an ironclad prediction of general relativity that gravitational waves exist, and are produced by accelerating masses. It's true that momentum is conserved, however gravitational waves are quadrupole in nature and couple to any changing mass quadrupole moment.

Two masses orbiting about each other, for example, will generate gravitational waves. This has been observed in the case of PSR B1913+16, the binary pulsar, where changes in the orbital period are in close agreement with the prediction of general relativity.

5. Sep 24, 2011

### Naty1

6. Sep 24, 2011

### pervect

Staff Emeritus
You have to keep momentum conserved in GR, so you need to include the gravitation of whatever source is making the particle accelerate.

Kinnersley has a well known photon-rocket solution that doesn't have any gravitational radiation

You'll find a number of articles disussing the result - one author does a flat-space analysis http://arxiv.org/abs/gr-qc/9412063 and finds that it's due to a dipolar symmetry in Kinnersley's equations. You generally need a quadropole moment to generate gravity waves.

I haven't looked at the issue very closely, but this should get you started.

7. Sep 24, 2011

### PAllen

The photon rocket is an extremely idealized solution. Demonstrating that any 'real' body moving in a non-empty universe will radiate GW in principle is the following standard review:

http://relativity.livingreviews.org/Articles/lrr-2004-6/ [Broken]

Last edited by a moderator: May 5, 2017
8. Oct 10, 2011

### bbbeard

Re: Why do accelerated charges emits a photon?

I am so sorry, being a n00b, I had no idea where my post wound up after it got banned from the thread about electromagnetic interactions. Somehow I clicked on a link just now and got magically transported to this thread, which I now see several people commented on several weeks ago.

My post got banned because I was trying to examine the question about whether a charge freely falling in a gravitational field would emit radiation by asking the question whether a mass freely falling in a gravitational field would emit gravitational radiation. Somehow this was deemed "off-topic" and my post got sent through a wormhole, only to land in the SR/GR forum.

Well, shoot. At the risk of being accused of "thread hikacking" again, I am going to answer both questions. My gravity question was rhetorical. In my view, it is obvious that an object falling or orbiting in the gravitational field of another object is emitting gravitational quadrupole radiation. Someone else downthread pointed to the http://en.wikipedia.org/wiki/Hulse-Taylor_binary" [Broken] and that is exactly the paradigm I'm thinking of. We know gravitational radiation exists because (a) theory demands it, and (b) the rate of decay of the Hulse-Taylor system precisely matches the predictions of GR with no adjustable parameters. I don't mind that experimentalists want to build devices to measure passing gravity waves directly, but the Hulse-Taylor pulsar nailed down the case (which is why Hulse and Taylor won the Nobel Prize in 1993).

In the electromagnetic case, consider the heuristic picture of why accelerating charges generate outgoing electromagnetic radiation. Here's a typical picture:

[URL]http://physics.tamuk.edu/~suson/html/4323/gifs/photo013.gif[/URL]

[http://physics.tamuk.edu/~suson/html/4323/photons.html", which I can't vouch for, since I just grabbed the picture....]

The idea behind this picture is that a static charge will have radial E field lines that go out to infinity, but when the charge is accelerated, the field lines have to accommodate the change in geometry while remaining continuous and obeying special relativity. The region where the lines are distorted to where they are nearly transverse (and the slopes are discontinuous) is the outgoing EM wave. I assert that this picture suggests that a charge infalling toward the Earth will indeed generate outgoing electromagnetic radiation (albeit of very low energy). In fact, a charge in the lab frame will emit EM radiation simply by virtue of the Earth's rotation. The energy for this radiation (since someone is bound to ask) is extracted from the rotational energy of the Earth. This radiation loss contributes ever so slightly to the lengthening of the day....

BBB

Last edited by a moderator: May 5, 2017
9. Oct 10, 2011

### atyy

Re: Why do accelerated charges emits a photon?