I always thought the non-linearity of Einsteins field equations implies that there should be direct graviton-graviton interactions. But I stumbled upon Wikipedia which argues:
If gravitons exist, then, like photons and unlike gluons, gravitons do not interact with other particles of their kind. That is, gravitons carry the force of gravitation but are not affected by it. This is apparent due to gravity being the only thing which escapes from black holes, in addition to having an infinite range and traveling in straight lines, similarly to electromagnetism.
Is Wikipedia correct? If not, why not? And what then are the arguments that there must be graviton-graviton interactions?
(As of this question being asked, the above paragraph has been removed from Wikipedia.)
Answer
I'm pretty sure that you are right and Wikipedia is wrong. In the linearized gravity approximation at weak curvature, you ignore the gravitational self-back-reaction, but in general gravitons carry energy (as evidenced by the work done by gravitational waves on the LIGO detectors) and therefore contribute to the stress-energy tensor of general relativity, therefore sourcing more gravitons. Also, some quick Googling finds lots of references to multiple-graviton vertices in effective quantum gravity field theories, whereas the Wikipedia article paragraph you quote has no references.
The issue of how gravitons can "escape" from a black hole without needing to travel faster than light is discussed at How does gravity escape a black hole?. The short answer is that gravitons can't escape from a black hole, but that's okay because they only carry information about gravitational radiation (which also can't escape from inside a black hole), not about static gravitational fields.
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