- #1

- 429

- 15

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.