# General Relativity Lorentz-like equation

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?

• 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. – AoZora Apr 18 at 12:12
• Which literature? What is a "Lorentz-like" equation? – Avantgarde Apr 18 at 13:35