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Linearizing gravity as follows:

$$ g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu} $$

Up to this point, everything is a 4x4 matrice.

How does one eventually recover a spin-2 particle which, according to https://en.wikipedia.org/wiki/Spin_(physics), has for basis three 5x5 matrices?

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    $\begingroup$ An even better question is how does this lead to a massless spin-2 particle with 2, not 5, degrees of freedom. $\endgroup$ – G. Smith Aug 6 at 19:31
  • $\begingroup$ Related, and also. $\endgroup$ – Cosmas Zachos Aug 7 at 1:22
  • $\begingroup$ This answer may well be helpful. $\endgroup$ – Cosmas Zachos Aug 13 at 15:15

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