matt91a
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I was wondering if anyone could explain to me where the 2nd order terms in the gauge transformation
[itex]h_{\mu\nu}\rightarrow h_{\mu\nu}-\xi[/itex]_{\mu ,\nu}-\xi_{\nu, \mu}-\xi^{\alpha}h_{\mu\nu, \alpha}-\xi^{\alpha}_{,\mu}h_{\alpha\nu}-\xi^{\alpha}_{,\nu}h_{\mu\alpha}[/itex]
come from. The transformation is in Misner, Thorne and Wheeler's Gravitation (the section on the weak field approximation), but I'm not sure how they arrive at it. Is it through some kind of taylor expansion?
[itex]h_{\mu\nu}\rightarrow h_{\mu\nu}-\xi[/itex]_{\mu ,\nu}-\xi_{\nu, \mu}-\xi^{\alpha}h_{\mu\nu, \alpha}-\xi^{\alpha}_{,\mu}h_{\alpha\nu}-\xi^{\alpha}_{,\nu}h_{\mu\alpha}[/itex]
come from. The transformation is in Misner, Thorne and Wheeler's Gravitation (the section on the weak field approximation), but I'm not sure how they arrive at it. Is it through some kind of taylor expansion?