- #1

- 17

- 0

As a guess, I tried the take the time derivative:

[tex]\frac{d}{dt}\; g_{\mu \nu} u^{\mu} v^{\nu}+g_{\mu \nu} \dot{u^{\mu}} v^{\nu}+g_{\mu \nu} u^{\mu} \dot{v^{\nu}}=0[/tex]

I was assuming a stationary metric, so the first part would be zero, leaving

[tex]g_{\mu \nu} \dot{u^{\mu}} v^{\nu}+g_{\mu \nu} u^{\mu} \dot{v^{\nu}}=0[/tex]

From there I can substitute in for [tex]\dot{u^{\mu}}[/tex] and [tex]\dot{v^{\nu}}[/tex].

Is this the right path to take? It seems there's then some index trickery involved to solve this.

Thanks!