- #1
Apashanka
- 429
- 15
From the geodesic equation
d2xμ/dΓ2+Γμ00(dt/dΓ)2=0,for non-relativistic case ,where Γ is the proper time and vi<<c implying dxi/dΓ<<dt/dΓ.
Now if we assume that the metric tensor doesn't evolve with time (e,g gij≠f(t) ) then Γμ00=-1/2gμs∂g00/∂xs.
If we here assume that the metric components of the curved part is a perturbation on the flat part
Then gμϑ=ημϑ(flat part)+hμϑ(perturbation)
After which I got stuck in calculating the inverse components of the metric tensor gϑμ which is needed in Γμ00 above.
Can anyone please help me in sort put this.
Thank you.
d2xμ/dΓ2+Γμ00(dt/dΓ)2=0,for non-relativistic case ,where Γ is the proper time and vi<<c implying dxi/dΓ<<dt/dΓ.
Now if we assume that the metric tensor doesn't evolve with time (e,g gij≠f(t) ) then Γμ00=-1/2gμs∂g00/∂xs.
If we here assume that the metric components of the curved part is a perturbation on the flat part
Then gμϑ=ημϑ(flat part)+hμϑ(perturbation)
After which I got stuck in calculating the inverse components of the metric tensor gϑμ which is needed in Γμ00 above.
Can anyone please help me in sort put this.
Thank you.