- #1

- 1,734

- 13

[tex] \frac{d^2 x^{\mu}}{d \tau^2} + \Gamma_{00}^{\mu} \left( \frac{dx^0}{d\tau} \right)^2 = 0 [/tex]

I know that ## \Gamma_{\alpha \beta}^{\mu} = \frac{\partial x^{\mu}}{\partial y^{\lambda}} \frac{\partial^2 y^{\lambda}}{\partial x^{\alpha} \partial x^{\beta}}##, so

[tex]\Gamma_{00}^{\mu} = \frac{\partial x^{\mu}}{\partial y^{\lambda}} \frac{\partial^2 y^{\lambda}}{\partial t^2} [/tex]

How did they get the relation ##\Gamma_{00}^{\mu} = -\frac{1}{2} g^{\mu \lambda} \frac{\partial g_{00}}{\partial x^{\lambda}}##?