# I Schutz: question regarding geodesic deviation

1. Mar 21, 2017

### patrik1982

I have some problem understanding the section on "Geodesic deviation" in schutz, more specifically I'm confused by eq. 6.84:

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
VVξα = ∇V(∇Vξα) = (d/dλ)(∇Vξα) = Γαβ0(∇Vξα)

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

Eq 6.48 says the following:
UβVα = 0 ⇔ (d/dλ)V = ∇UV = 0
(U is tangent to the curve, λ is the parameter along it)

2. Mar 21, 2017

### martinbn

In the book it is

$\nabla_V(\nabla_V\xi^\alpha)=\frac{d}{d\lambda}(\nabla_V\xi^\alpha)+\Gamma^\alpha_{\beta 0}(\nabla_V\xi^\beta)$

3. Mar 21, 2017

### patrik1982

Nope. At least not in my book. (Photo attached)
So, this is a misprint then?

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4. Mar 21, 2017

### RockyMarciano

No, the relaevant equation, equivalent to the one martinbn wrote, is the next one:6.85