Researching, I found that gravitational waves are generated by the changing in time of the quadrupole moment of mass of a system - source. They travel at speed of light, and they perturbate the spacetime where they are. But the spacetime is statically deformed when a mass is present in it, even if the mass has not a time-varying quadrupole moment.

These characteristics are very similar to that of an electric field which can be static if in presence of a non-moving charged particle and has perturbations whenever a charge is accelerated.

Can spacetime be thought as a field exerted by mass and perturbated by gravitons?

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    $\begingroup$ There's a section in "Gravitation" (section 5 starting on page 424) where one starts with a spin 2 ('graviton') field on flat spacetime and, through an (infinite) series of corrections to account for the self-interaction, one arrives at the full background free general relativity. Are you thinking of something along these lines? $\endgroup$ – Alfred Centauri Aug 30 '18 at 1:49
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    $\begingroup$ Possibly useful: physics.stackexchange.com/q/336360/133418 $\endgroup$ – Avantgarde Aug 30 '18 at 2:26
  • $\begingroup$ Yes. There are difficult passages in those lines, but basically I really felt interesting the idea of having a field with a matter stress-tensor as the cause of a deformation in a flat spacetime-field, as the matter stress-tensor must be coupled with the total stress-tensor. Similar to what I thought about a mass and gravitons influencing "their" field. Just the demonstration doesn't stand up when trying to couple the stress-tensor of a dynamic system as a source and it leads to the use of the geometric interpretation. $\endgroup$ – Costantino Aug 30 '18 at 2:36
  • $\begingroup$ But I didn't understand very well, the guy tried to put series in the formula and then just cut at the third order and it doesn't work aswell...? Ugh, help. This question is still active for me $\endgroup$ – Costantino Aug 30 '18 at 2:43
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    $\begingroup$ You are describing the difference between a field and a wave. The field is static (moving slower than light) and "consists" of virtual photons (or hypothetically virtual gravitons). The wave moves with the speed of light and "consists" of real photons (or hypothetically real gravitons). Photons don't interact with the electromagnetic field or other photons. Gravitons hypothetically do interact with the gravitational field and other gravitons in standard General Relativity. Spacetime is not the gravitational field. The spacetime curvature is the gravitational field (the time curvature mostly). $\endgroup$ – safesphere Aug 30 '18 at 3:27

Actually it seems so. There is this theory done by M. Novello and R. P. Neves which gives a solid structure to this idea, differently from the attempt Gravitation book. It is quite recent, march 2018, and this is the link to the article.


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