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I am trying to find the Christoffel connections of this metric:

ds^{2}= -(1+2∅)dt^{2}+(1-2∅)[dx^{2}+dy^{2}+dz^{2}]

where ∅ is a general function of x,y,z,t.

I tried to solve this through the least action principle, but some of my results(t-related terms) were different from the answer with a minus sign. So, I guess it's a problem about the part of t of the action.

I regarded this part as -1/2(1+2∅)[itex]\dot{t}[/itex]^{2}, should I remove the minus sign to get the correct answer?

[itex]\dot{t}[/itex]: the derivative of t regard to the affine parameter λ

Thanks for your help!

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# Need to calculate Christoffel connection from a given metrics

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