I have some problem understanding the section on "Geodesic deviation" in schutz, more specifically I'm confused by eq. 6.84:(adsbygoogle = window.adsbygoogle || []).push({});

Eq 6.84 reads (ξ is the 'connecting vector' from one geodesic to Another, V is the tangent vector):

We can use (6.48) to obtain

∇_{V}∇_{V}ξ^{α}= ∇_{V}(∇_{V}ξ^{α}) = (d/dλ)(∇_{V}ξ^{α}) = Γ^{α}_{β0}(∇_{V}ξ^{α})

(Eq 6.48 gives the second equality, but I fail to see why the last equality is true)

Eq 6.48 says the following:

U^{β}V^{α}_{;β}= 0 ⇔ (d/dλ)V = ∇_{U}V = 0

(U is tangent to the curve, λ is the parameter along it)

Can someone please help me and explain what's going on?

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

Dismiss Notice

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!

# I Schutz: question regarding geodesic deviation

Have something to add?

Draft saved
Draft deleted

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