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(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?

QuaternionsRock
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    I don't see where the paradox is. Gluons self-interact too. Also, possible duplicate of How does gravity escape a black hole? and links therein. – AccidentalFourierTransform Jun 29 '19 at 17:24
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    Photons are also massless, but black holes can have electric and magnetic fields. – G. Smith Jun 29 '19 at 18:11
  • @AccidentalFourierTransform it is my current understanding that, in QFT, electric fields can be thought of in terms virtual photons, and that this conceptualization should theoretically extend to all of the fundamental forces, including gravity. Shouldn’t this mean that gravitons emitting from a massive object must be affected by a slightly more virtual graviton, which in turn must be affected by an slightly more virtual graviton than that, so on and so forth? Anyways, I’m grateful for the link; I’ll dig into it when I get a chance. Cheers! – QuaternionsRock Jun 29 '19 at 19:42
  • @G.Smith wait... what? How? – QuaternionsRock Jun 29 '19 at 19:43
  • @QuaternionsRock Your picture of gravitons being affected by virtual gravitons is not wrong. The formalisation of that intuition is what we call the loop expansion. There is nothing paradoxical about that. – AccidentalFourierTransform Jun 29 '19 at 19:54
  • @QuaternionsRock What do you mean by '..paradox in which (increasingly virtual ?) gravitons must interact with other gravitons..'? The picture of virtual 'particles' is a useful mnemonic in perturbation theory. You don't have to talk about them in a non-perturbative setup. – Avantgarde Jun 29 '19 at 19:55
  • You can read about Reissner-Nordström and Kerr-Newman black holes. – G. Smith Jun 29 '19 at 22:08
  • "energetic particles must be affected by the curvature of spacetime" - According to the Einstein equivalence principle, a particle doesn't have to curve spacetime to be affected by a curved spacetime. A feather and a hammer fall with the same acceleration in the gravity of a planet (as long as the hammer is much smaller than the planet). "wouldn't gravitons themselves not be able to escape from a black hole, annulling the gravitational force of the black hole in the process?" - The gravity of a black hole is sourced from outside the event horizon, not from inside. – safesphere Jun 30 '19 at 02:40
  • All theories are actually non linear, so their normal modes (elementary excitations) are free (independent) only approximately. Graviton energy is not small; it is $\hbar\omega$ and can be as big as the photon energy in the bremstrahlung processes. What is really smal is the emission probabiliy :-( – Vladimir Kalitvianski Jun 30 '19 at 10:49

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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.

niels nielsen
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