Wouldn't gravitons themselves theoretically be affected by gravity?

Question

(I wrote this using the assumption that the graviton exists, which I know is not necessarily true; this is asked from a theoretical standpoint)

It is my understanding that General Relativity states all massive and/or energetic particles must be affected by the curvature of spacetime; this stipulation aligns with all known elementary particles. I understand that the graviton, being a particle that reliably interacts with photons, is going to be virtually impossible to detect experimentally. It is almost certainly massless and of a remarkably low energy, but it must possess energy nonetheless. As such, shouldn't gravitons themselves be affected by gravity, creating a paradox in which (increasingly virtual ?) gravitons must interact with other gravitons? Also, assuming that our conception that massless particles always travel at the speed of light holds true for gravitons, wouldn't gravitons themselves not be able to escape from a black hole, annulling the gravitational force of the black hole in the process?

Answer 1

Yes, gravitons must necessarily respond to each other via gravity. This means that in addition to communicating forces between objects that bend spacetime, the force carrier particles bend spacetime themselves.

But for very weak gravitational fields, the math gets easier to deal with because in this simplified case, the effect of the gravitons themselves on the curvature of spacetime can be ignored.