Including gravity itself.
Neat, neat cite. Thanks.
I wonder what would’ve happened had Newton encouraged it?
I’m thinking of Einstein and the Mercury light deflection.
PKK-CHUUUWWWWW!
Mind blown. I assume this is according to the standard model, Higgs boson adding another particle to the mix, or something else?
No, even in classical GR. Gravitational waves have energy, for example, and energy is a source of gravitation. The wave equation is then non-linear, but you’d have to have very strong waves for the non-linearity to be noticeable.
Interesting.
I’m mean, I suppose I just took gravity for granted in the whole energy/matter equivalency. Just figured gravity was a manifestation of this energy as a whole.
Apparently I missing a finer point. Care to elucidate further?
Not sure what more to say. The energy-momentum tensor is the source of the gravitational field. Gravitational waves have energy and momentum, ergo they are sources of gravitational fields.
You don’t see something like this in EM, because photons have no charge, so they are not themselves a source for other photons. (At least, until you get extremely high field levels, that can pull electron positron pairs out of the vacuum.) But photons can be a source for gravitation, since they too have energy and momentum.
Here’s a question that maybe someone else can answer: gravitational waves are linear in the weak field approximation, but they travel at the speed of light. Can’t a Lorentz transformation make a strong gravitational wave arbitrarily low in energy, making it low enough energy for the weak field approximation to hold? If not, why not? Or does the non-linearity of gravitational waves not apply to plane waves?
Gravitational waves are sort of a bad example, since nobody actually knows how to properly deal with the nonlinearity. A better example would be a black hole, which could be said to be composed entirely of gravity.
And the Higgs boson has no particular relationship to gravity. Actually, nothing in particle physics has any known particular relationship to gravity. People often think that the Higgs is related to gravity because of the tremendous oversimplification that “it’s the cause of mass”, but mass can result from a great many sources (in fact, the vast majority of the mass we’re familiar with is due to sources unrelated to the Higgs), and gravity doesn’t care: It treats all mass the same.
The problem isn’t their energy per se, but their amplitude, and that’s unaffected by a Lorentz transformation.
Why does the amplitude of arbitrarily low frequency gravitational waves still cause the nonlinearity?
Thanks guys.
Actually, ZenBeam, I need to think about that one a bit more. I just realized that setting up the problem in different ways leads to different answers, which means that there’s obviously something I’m misunderstanding in my thinking.
(and as an aside, have I ever told you that you ask really great questions?)
It’s nice to be appreciated. 
Gravitational waves don’t have stress-energy in the normal sense: i.e. the description of a gravitational wave in a vacuum is a vacuum and the stress-energy tensor can be made to be zero everywhere just as in any vacuum. However of course if you’re concerned with the conservation of energy/momentum and you want to know how much energy/momentum they carry away with them you can assign a stress-energy pseudotensor.
In terms of the gravity and non-linearity of gravitational waves, that is really complicated territory, but in answer to Zen Beam’s question: a gravitational wave is actually an intrinsic part of spacetime itself rather than something that is defined on the spacetime. If we transform an em wave in flat spacetime then the wave transforms and the flat spacetime remains unchanged, however if we transform a gravitational wave against a flat ‘background metric’ only the actual (non-flat) spacetime remains unchanged and both the flat background metric and the gravitational wave transform. Choosing one flat background metric may get you a description of the gravitational wave which is a nice, well-behave plane wave, but the same gravitational wave against a different flat background metric may look nothing like a plane wave.
Additionally for a given spacetime, it is appropiate to use the weak-field approximation if there exists a global coordinate system that satisfies certain conditions. A coordinate transformation will not change the existance/nonexistance of such a global coordinate system on the spacetime.