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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?

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  • $\begingroup$ 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. $\endgroup$
    – Brandon Enright
    Commented Dec 30, 2014 at 1:19
  • $\begingroup$ My motivation is the answer to this question... I'm of the impression that they would have an attractive force. $\endgroup$
    – Xeren Narcy
    Commented Dec 30, 2014 at 1:27
  • $\begingroup$ 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. $\endgroup$
    – Xeren Narcy
    Commented Dec 30, 2014 at 1:34
  • $\begingroup$ You may be interested to ready up on gravitational solitons. $\endgroup$
    – CuriousOne
    Commented Dec 30, 2014 at 1:42
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    $\begingroup$ @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!" $\endgroup$
    – Hypnosifl
    Commented Dec 30, 2014 at 1:48

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A theorized object called a geon, "an electromagnetic or gravitational wave which is held together in a confined region by the gravitational attraction of its own field energy", would seem like a match for what you're talking about. The wiki article mentions that exact solutions involving geons have been found (one is discussed in this paper), though it's not clear if they would be stable. For numerical simulations of various scenarios involving strong gravitational waves whose behavior is highly nonlinear, see this pdf. And here is a pdf of John Wheeler's original 1955 paper proposing them, which contains an image of a toroidal electromagnetic geon (he later notes that gravitational wave geons would be spherical rather than toroidal) consisting of two electromagnetic waves traveling in opposite directions, held to their distorted paths by their own gravity:

enter image description here

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  • $\begingroup$ I have a followup question (will post it separately if not appropriate here) - if indeed a black hole can form by, in effect, 'runaway curvature', and since black holes are characterized by a few parameters (no hair theorem?), it means we shouldn't be able to tell apart a stellar-origin black hole and this type (perhaps angular momentum and charge will be telltale but otherwise I doubt it). Since this type of BH was not created by conventional mass, does it imply that a 'regular' BH would have the same 'composition'? What does this say about mass falling into each type of BH? $\endgroup$
    – Xeren Narcy
    Commented Dec 30, 2014 at 3:24
  • $\begingroup$ A black hole doesn't really have a "composition" in general relativity, it's a vacuum solution--a curved region of empty space, terminating in a singularity. $\endgroup$
    – Hypnosifl
    Commented Dec 30, 2014 at 4:27
  • $\begingroup$ It makes little sense to talk about the composition of a BH I know; I'm referring to the composition of the singularity (wherever all the mass-energy forming the BH 'ends up' after formation), but that makes even less sense to talk about... In any case there isn't any difference with the resulting BH, and in-falling matter is crushed / absorbed / pulverized indistinguishably between BH types? $\endgroup$
    – Xeren Narcy
    Commented Dec 30, 2014 at 5:05
  • $\begingroup$ In pure general relativity I don't think there'd be any difference (at least not if you wait a large time after the infalling matter or gravitational waves formed the black hole), but quantum gravity might turn out to be another story, since physicists often speculate that information will turn out to not really be "lost" when things fall into black holes. $\endgroup$
    – Hypnosifl
    Commented Dec 30, 2014 at 5:09
  • $\begingroup$ Related followup: this type of BH, I'm inclined to assume it will have large angular momentum (via propagation speed of gravity waves). It may give rise to a KN BH (rotating,charged) which violates the condition for an event horizon to exist - would this be closer to a Geon solution (ignoring the issue of a potentially naked singularity) than a BH? $\endgroup$
    – Xeren Narcy
    Commented Dec 30, 2014 at 5:32

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