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Thytanium

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- TL;DR Summary
- The inertial acceleration in free fall is zero but the ordinary acceleration is not zero in free fall due to the relative movement and for this reason there are differences between the two that I want to know and above all to be able to obtain Newton's kinematic equations using the parametric geodesic equations of relativity.

Hello friends of the Forum. I want to ask you why the inertial acceleration in free fall in the relativistic geodesic equations is assumed equal to zero in free fall and equal to 9.8 m/s at rest on the earth's surface. On the other hand, assuming that zero acceleration in free fall, what would be the metric tensor g(ij) to use in Christoffel Symbols and obtain x¨β(τ)=Γijβx˙i(τ)x˙j(τ)=9.8m/s in the vicinity of the earth's surface in free fall so that when doing the double integration of x¨β(τ) obtain the parametric equation x(t)=v.t+9.8.t22 assuming τ=t and v a constant.