- #1
Stella.Physics
- 63
- 13
So the Schwarzschild metric is given by
ds2= -(1-2M/r)dt2 + (1-2M/r)-1dr2+r2dθ2+r2sin2θ dφ2
and the Lagragian is ##{\frac{d}{dσ}}[{\frac{1}{L}}{\frac{dx^α}{dσ}}] + {\frac{∂L}{∂x^α}}=0##
with L = dτ/dσ. So for each α=0,1,2,3 we have
##{\frac{d^2 x^1}{dτ^2}}=0## for Minkowski spacetime
also the geadesic equation is ##{\frac{d^2 x^a}{dτ^2}}+Γ^a_{bc}{\frac{dx^b}{dτ}}{\frac{dx^c}{dτ}}=0##
So what happens in the Schwarzschild metric and how can I find the Christoffel symbols from the Schwarzschild metric and the geodesic equations?
ds2= -(1-2M/r)dt2 + (1-2M/r)-1dr2+r2dθ2+r2sin2θ dφ2
and the Lagragian is ##{\frac{d}{dσ}}[{\frac{1}{L}}{\frac{dx^α}{dσ}}] + {\frac{∂L}{∂x^α}}=0##
with L = dτ/dσ. So for each α=0,1,2,3 we have
##{\frac{d^2 x^1}{dτ^2}}=0## for Minkowski spacetime
also the geadesic equation is ##{\frac{d^2 x^a}{dτ^2}}+Γ^a_{bc}{\frac{dx^b}{dτ}}{\frac{dx^c}{dτ}}=0##
So what happens in the Schwarzschild metric and how can I find the Christoffel symbols from the Schwarzschild metric and the geodesic equations?
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