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In the literature, it says that, in the weak-field, $$g_{µν} = η_{µν} +h_{µν},$$ slow-motion limit, the Geodesic equation reduces to the Lorentz-like equation.

Can anyone explain this?

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  • $\begingroup$ Maybe it is related to the fact that is you keep only first order in h (which is almost always what books do) you are neglecting some of the backreaction effects? Right now I don't know if the geodesic equation becomes really algebraically similar to the Lorentz eqs, but I'll check. $\endgroup$ – AoZora Apr 18 at 12:12
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    $\begingroup$ Which literature? What is a "Lorentz-like" equation? $\endgroup$ – Avantgarde Apr 18 at 13:35

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