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The field equations are non-linear, that can be interpreted as gravity is coupling with itself, see for example here:

Non-linearity and self-coupling of gravity

I'm trying to understand what that means. What is self-coupling? Does that really mean that gravity gravitates? That the graviton (if it exists) underlies gravity as all other particles?

And, finally, could the fact that gravity can "escape" a black hole lead to the conclusion that the graviton would not interact with gravity? But then, going back to the entrance question, would that lead to the conclusion that gravity is not non-linear? Would it be linear then? Could one infer from that that gravitational fields just add up as a superposition? Is there probably a mistake in that reasoning?

Black holes have five "hairs": mass-energy, momentum, angular momentum, position and electric charge. Due to their mass-energy and their position, they interact with their surroundings through the gravitational field = the curvature of spacetime.

I'm really confused about the meaning of "gravity gravitates". If there were a graviton-particle, wouldn't it move at the speed of light (or below)? And shouldn't it then be blocked by the horizon? Therefore, there shouldn't be a graviton-particle, should it? The gravitation of the BH is simply engraved in the surrounding (infinite) spacetime, isn't it? However, then, how can one interpret the "gravity gravitates" = "EFE are nonlinear"- part of general relativity?

Related to this question is that question: How does gravity escape a black hole? There, the question is, how gravity can escape a black hole. One of the answers is, in short, that nothing moves out the black hole, the surrounding spacetime curvature is the gravitational field which is influenced by the bh but simply is there, and doesn't have to move. (and "it's easier to think about the question in purely classical terms (avoiding any mention of photons or gravitons)")

In contrast, MY question is: isn't the fact that gravity "escapes" a black hole a hint that gravity doesn't gravitate?

BarrierRemoval
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    related : https://physics.stackexchange.com/q/937/ – Jeanbaptiste Roux May 03 '22 at 16:52
  • @Jeanbaptiste Roux: Related to this question: Gravity is a field then (It is stated in your linked question)... But fields are not self-interacting, are they? At least one can superpose fields. - related to my question here, but different because here, it's about the superposition/linearity versus interacting/non-linearity. Completely different to that question there – BarrierRemoval May 03 '22 at 17:09
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    Fields can interact. A recommend you learn a bit of general relativity and quantum field theory. – Jeanbaptiste Roux May 03 '22 at 17:34
  • One CANNOT superpose fields if they are non-linear. Where did you get that idea? The graviton field self-interacts (as do many other fields (eg. the Higgs field)) and it is non-linear. You cannot superpose the graviton field. – Prahar May 03 '22 at 19:34
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    Gravity does not need to escape a black hole. The source of gravity of a black hole is the horizon, not anything “inside”. Nothing “inside” can have any influence on anything outside, including the influence by gravity. – safesphere May 04 '22 at 03:50
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    Does this answer your question? How does gravity escape a black hole? – Eric Smith May 16 '22 at 15:55
  • Gravitons, if they exist, play the same role for gravity that photons play for electromagnetism. In particular, real gravitons make up gravitational waves, and yes, gravitational waves cannot escape black holes (just as light cannot escape). Virtual gravitons that are used to describe gravity as a force are not real (hence the name "virtual"). – Eric Smith May 16 '22 at 15:58
  • @EricSmith no, that doesn't answer my question. However, my question builds up on that answer. Your linked question is regarding how gravity can "escape" a black hole. The answer there is, in short, it's an (infinite) field, it doesn't move out. My question is, isn't the fact that gravity "escapes" a black hole a hint that gravity doesn't gravitate? However, it's often stated that "gravity gravitates" which is a contradiction that I simply do not understand and hoped to get it sorted out here. – BarrierRemoval May 16 '22 at 16:43

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"Self-coupling" means that yes, gravity gravitates -- that for example gravitational waves would be affected by the gravitational field of objects they move past. Gravitons, if they exist, would interact with each other. Mathematically this is a consequence of the non-linearity of the Einstein field equations for gravity.

This has nothing to do with black holes. For example, photons are definitely affected by gravity (e.g. light is bent by the sun), as observed in many experiments. And yet black holes can be charged. This doesn't mean that photons can escape a black hole. Rather, it means that the naive view of the electromagnetic force as being "carried" by photons that is sometimes presented in pop-sci is incorrect. The electromagnetic force between charged particles is modelled by interacting virtual photons. This is a mathematical description of the force, and not at all an assertion that real photons are literally zipping back and forth between charges. The adjective virtual is really key there -- a virtual photon is not a real photon, and in most senses is not real at all.

Similarly, if gravitons exist then they will be observed as gravitational waves (analogous to how real photons are observed as EM waves). Gravitational waves, like anything else real, cannot escape black holes.

Eric Smith
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