Can two gravitational waves orbit each other?

[friend]

Since gravitational waves have energy, they can curve space all by themselves. I wonder in what conditions, if any, two gravitational waves could orbit each other. Thanks.

 

[PeterDonis]

Since gravitational waves have energy, they can curve space all by themselves.

Actually, no, because you are conflating two different meanings for "have energy". Gravitational waves have zero stress-energy, and it is stress-energy that curves spacetime. Gravitational waves carry energy in the sense that they can do work (for example, they can heat up an object if they pass through it). But that is not the same as having stress-energy and curving spacetime all by themselves. This is one of the more counterintuitive areas of GR.

I wonder in what conditions, if any, two gravitational waves could orbit each other.

They can't. See above.

 

[pervect]

Since gravitational waves have energy, they can curve space all by themselves. I wonder in what conditions, if any, two gravitational waves could orbit each other. Thanks.

My recollection is that gravitational waves can orbit each other, like light pencils. Like light pencils, they only attract each other when they go in opposite directions (but if the waves are traveling in a circle, this condition is met). However, it is believed not to be a stable configuration in either case. The concept is called a geon, the name is due to Wheeler. I was trying to find some references to support my recollection, while I've f I've found some they are not very specific on this point or not of great quality or both. Besides the Wiki article on Geon, there was one youtube video of Wheeler (the originator of the name geon) who mentioned near the end of the video that it could apply to GW's as well as pencils of radiation. (This was near the end of the video if you dig it up). The name itself originated from the electromagnetic case, not the GW case. I'll save Peter the trouble of mentioning that youtube vidoes aren't in general good references for PF, even if they are purported to be of a famous figure. Sadly, one has to be really careful of "facts" on the internet.

If you can get past the paywall to some of Wheeler's papers (see the Wiki article on Geons for a start of a bibliography), there might be some good info in there.

I'll agree that GW's under consideration are a vacuum solution to Einstein's field equations, and as such have a zero stress-energy tensor. But the "effective stress energy tensor", the result of linearizing the nonlinear equations, is nonzero. My recollection is that the effective stress energy tensor can cause the waves to attract in linearized theory. In the full non-linear theory, one would use something like the De Donder gauge so that the Einstein's field equations were a wave equation to get a similar reslut. Sorry I don't have a better source, but I thought I'd post what I could recall, which isn't the same as what Peter said :(.

 

[friend]

Do you remember approximately what size range they might possibly be? Was this supposed to be a large or small effect? Did they have a large amount of energy or small? Did they radiate their energy away? Thanks.

 

[PeterDonis]

The concept is called a geon

I don't know if a geon would be properly described as "gravitational waves orbiting each other". But that's more a matter of language than physics; you are right that the concept exists.

 

[haael]

Actually, no, because you are conflating two different meanings for "have energy". Gravitational waves have zero stress-energy, and it is stress-energy that curves spacetime. Gravitational waves carry energy in the sense that they can do work (for example, they can heat up an object if they pass through it). But that is not the same as having stress-energy and curving spacetime all by themselves. This is one of the more counterintuitive areas of GR.

The above statement is in contradiction to all I know about GR.

Could you point me to some paper or could you derive the stress-energy of a g-wave to show it is zero?

I have read more than once that gravitational waves do carry the charge of gravity. The gravitational waves interact with each other through self-interaction. This does not mean that they can orbit or even attract each other, but nevertheless they will interact. Two g-waves passing through each other will not only interfere linearily, but also will show some diffraction. That is what I understand. I'm open to be proven wrong.

 

[martinbn]

The above statement is in contradiction to all I know about GR.

Could you point me to some paper or could you derive the stress-energy of a g-wave to show it is zero?

I have read more than once that gravitational waves do carry the charge of gravity. The gravitational waves interact with each other through self-interaction. This does not mean that they can orbit or even attract each other, but nevertheless they will interact. Two g-waves passing through each other will not only interfere linearily, but also will show some diffraction. That is what I understand. I'm open to be proven wrong.

Non of this means that the stess energy tensor isn't zero.

 

[PeterDonis]

Could you point me to some paper or could you derive the stress-energy of a g-wave to show it is zero?

Try any GR textbook. The fact that gravitational waves contain zero stress-energy is one of the most basic facts about them.

I have read more than once that gravitational waves do carry the charge of gravity.

Please give a specific reference--textbook or peer-reviewed paper. "I have read" is not sufficient.

The gravitational waves interact with each other through self-interaction.

That is correct. But it doesn't mean gravitational waves have nonzero stress-energy. It just means they're nonlinear--which is to be expected since the Einstein Field Equation, even in vacuum (which is what we use to describe gravitational waves), is nonlinear.

 

[PeterDonis]

Non of this means that the stess energy tensor isn't zero.

That's not quite correct. The "charge of gravity" is stress-energy, so if gravitational waves did carry the charge of gravity, they would have nonzero stress-energy. But they don't, just as electromagnetic waves don't carry the charge of electromagnetism.

 

[martinbn]

That's not quite correct. The "charge of gravity" is stress-energy, so if gravitational waves did carry the charge of gravity, they would have nonzero stress-energy. But they don't, just as electromagnetic waves don't carry the charge of electromagnetism.

I should have said almost none.

 

[pervect]

The above statement is in contradiction to all I know about GR.

Could you point me to some paper or could you derive the stress-energy of a g-wave to show it is zero?

I have read more than once that gravitational waves do carry the charge of gravity. The gravitational waves interact with each other through self-interaction. This does not mean that they can orbit or even attract each other, but nevertheless they will interact. Two g-waves passing through each other will not only interfere linearily, but also will show some diffraction. That is what I understand. I'm open to be proven wrong.

If we restrict ourselves to GW's in a vacuum (no matter, just GW's), then the stress energy $T_{\mu\nu}$ is zero because we are in a vacuum.

 

[calinvass]

Gravitational waves spread-out in all directions. How is it possible to have them spinning around each other? Light can modeled as plane waves where all individual waves are parallel to each other, as part of a beam. Will gravitational waves do the same thing in principle? I suppose they can travel exactly like light does, especially if we consider that the waves can be modeled by gravitons, because gravitons, as far as I know travel, like any other particle.