It is known that all particles follow a geodesic in spacetime. Presumably gravitons follow geodesics as well. However, how does one describe that mathematically? For the case of other particles it is more straight forward as their energy-momentum tensor would couple to the metric. The case of graviton seems to be more complicated as graviton is the fluctuation of the metric itself. So, is it inherently some sort of self-coupling of the metric? Where can one find a more rigorous mathematical description of this?
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2$\begingroup$ You probably mean gravitational waves. $\endgroup$– my2ctsCommented Jan 17 at 23:16
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1$\begingroup$ Because gravitons are not known to exist yet. $\endgroup$– ProscionexiumCommented Jan 18 at 5:11
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$\begingroup$ It automatically drops out of general relativity, just not in the flat background approximation that is usually used to motivate the existence of gravitational waves. The proper procedure would be a perturbation Ansatz around a non-flat metric, I suppose. One of the theorists will probably write an answer for you that shows the mathematics of it. Gravitons are NOT gravitational waves, by the way. Quantization is a totally different beast from linearization and/or perturbation around the classical metric. $\endgroup$– FlatterMannCommented Jan 18 at 5:54
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1$\begingroup$ Just like photons? There are only three types of geodesics: timelike (tardyons), spacelike (tachyons) and lightlike (luxons). Gravitational waves should propagate on lightlike geodesics as electromagnetic waves do it. $\endgroup$– JanGCommented Jan 18 at 11:52
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$\begingroup$ Well yeah, you are right, gravity is well-known for having self-coupling. $\endgroup$– AvantgardeCommented Jan 19 at 22:31
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