- #1

- 156

- 4

[itex]\ddot x^{\mu} + \Gamma^{\mu}{}_{\alpha \beta} \dot x^{\alpha} \dot x^{\beta} = 0 [/itex] where differentiation is with respect to some path parameter [itex]\lambda[/itex].

If we choose [itex]\lambda[/itex] equal to proper time [itex]\tau[/itex] then it can be readily proved that

[itex]c^2 = g_{\mu \nu}(x) \frac{dx^{\mu}}{d\tau} \frac{dx^{\nu}}{d\tau}[/itex]

Only problem is I can't quite see how to go from the first to the second, can someone explain for me please?