epovo
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- TL;DR
- In the derivation of the proof there is a step that I cannot make sense of
In Schutz 8.3, while proving that a Lorentz gauge exists, it is stated that
$$\bar h^{(new)}_{\mu\nu} = \bar h^{(old)}_{\mu\nu} - \xi_{\mu,\nu} - \xi_{\nu,\mu} + \eta_{\mu\nu}\xi^\alpha_{,\alpha}$$
where ##\bar h## is the trace reverse and ##\xi^\alpha## are the gauge functions. Then it follows with:
"Then the divergence is"
$$\bar h^{(new)\mu\nu}_{\,\,\,\,\,\,\,,\nu} = \bar h^{(old)\mu\nu}_{\,\,\,\,\,\,\,\,,\nu} - \xi^{\mu,\nu}_{\,\,\,,\nu}$$
I can't see why the divergence is that! I've tried and tried but I can't see it. Any help?
$$\bar h^{(new)}_{\mu\nu} = \bar h^{(old)}_{\mu\nu} - \xi_{\mu,\nu} - \xi_{\nu,\mu} + \eta_{\mu\nu}\xi^\alpha_{,\alpha}$$
where ##\bar h## is the trace reverse and ##\xi^\alpha## are the gauge functions. Then it follows with:
"Then the divergence is"
$$\bar h^{(new)\mu\nu}_{\,\,\,\,\,\,\,,\nu} = \bar h^{(old)\mu\nu}_{\,\,\,\,\,\,\,\,,\nu} - \xi^{\mu,\nu}_{\,\,\,,\nu}$$
I can't see why the divergence is that! I've tried and tried but I can't see it. Any help?