Assume we have a free-falling particle in gravity in a static metric. Its worldline is described by:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu} [/tex]

where ##|h_{\mu \nu} << 1|##.

Taken from Hobson's book:

Why did they let ##g^{k\mu} = \eta^{k\mu}##?

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# Weak gravity and the Newtonian limit

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