Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Need to calculate Christoffel connection from a given metrics

**Physics Forums | Science Articles, Homework Help, Discussion**