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## Main Question or Discussion Point

From the geodesic equation

d

Now if we assume that the metric tensor doesn't evolve with time (e,g g

If we here assume that the metric components of the curved part is a perturbation on the flat part

Then g

After which I got stuck in calculating the inverse components of the metric tensor g

Can anyone please help me in sort put this.

Thank you.

d

^{2}x^{μ}/dΓ^{2}+Γ^{μ}_{00}(dt/dΓ)^{2}=0,for non-relativistic case ,where Γ is the proper time and v_{i}<<c implying dx^{i}/dΓ<<dt/dΓ.Now if we assume that the metric tensor doesn't evolve with time (e,g g

_{ij}≠f(t) ) then Γ^{μ}_{00}=-1/2g^{μs}∂g_{00}/∂x^{s}.If we here assume that the metric components of the curved part is a perturbation on the flat part

Then g

_{μϑ}=η_{μϑ}(flat part)+h_{μϑ}(perturbation)After which I got stuck in calculating the inverse components of the metric tensor g

^{ϑμ}which is needed in Γ^{μ}_{00}above.Can anyone please help me in sort put this.

Thank you.