# Can gravitational waves orbit each other to form a standing wave?

Since gravitational waves are a type of propagation of energy of some sort, they ought to induce their own gravitational field. I'm assuming this extra gravitational force / curvature is independent from the wave itself, so there ought to be an observer that would 'feel' or 'observe' the wave pass, and in addition 'feel' or 'observe' a secondary attractive force towards the 'densest' part of the wave. I'm not sure if it is possible to discern these two effects without experiencing them as a whole but I'm assuming one could somehow.

Regarding the secondary attractive force, could this be used / amassed to a sufficient degree to allow two (or more) gravitational waves to orbit each other, with the extremal case being a gravitational standing wave arranged in a loop (held together by its own mass-energy)? Is such a system capable of collapsing into a black hole given enough energy in the wave(s) and sufficiently small orbit?

• I'm no expert here but I suspect they can't. I think your premise that gravity waves are energy and therefor should have a gravitational field is not totally correct. I think the energy to distort the gravitational field in the first place is all the "gravity" they need. They should be able to interfere with each other but I don't see how they could attract each other. Dec 30, 2014 at 1:19
• My motivation is the answer to this question... I'm of the impression that they would have an attractive force. Dec 30, 2014 at 1:27
• Which I followed up with this question here. So from these two questions (and their answers) I'm reasoning that gravitational waves ought to have their own attractive force / self-energy. Dec 30, 2014 at 1:34
• You may be interested to ready up on gravitational solitons. Dec 30, 2014 at 1:42
• @Brandon Enright - Unlike the waves in EM and quantum theory, gravitational waves don't add linearly, so you can't just think in terms of superposition. See the last section of this article which notes that "when two gravitational waves meet, they do not just pass through each other, they interact. If both waves are weak, the interaction will be almost unnoticeable, but for stronger waves, the consequences can be quite dramatic - in some cases, the collision of two gravitational waves could lead to the formation of a black hole!" Dec 30, 2014 at 1:48