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## Main Question or Discussion Point

**self-interactions in "linearized" gravity**

This question is really about the gauge invariance seen in linearized gravity. I'm trying to derive the 3-point self-interaction term in the GR lagrangian (in the weak field limit), and the algebra is just a nightmare. I finally gave up and determined that I could find it by just writing down the most general terms, and requiring gauge invariance. By inspecting the Ricci tensor, it is clear that all of these terms are of the form [TEX]h\partial{h}\partial{h}[/TEX]. The most general lagrangian has 10 terms, but under the infinitesimal gauge transformation [TEX]h_{\mu\nu}\rightarrow h_{\mu\nu} + \partial_\mu\alpha_\nu + \partial_\nu\alpha_\mu[/TEX], it can not be made invariant. In fact, even the 4 point term seems to break gauge invariance. Is this gauge invariance purely a feature of the linear terms or am I doing something wrong?

*edit* and if anyone knows this lowest order self-interaction term that would be incredibly helpful.

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