Chapter 21 Ray D'Inverno Scalar Optics, congruence of null geodesics

[portugal]

First of all this is my first thread, so I apologize for any mistake.
Perhaps this is a stupid question, but i need some help in exercise 21.10 of D'Inverno, to write down geodesic equation for l^a, which is a vector tangent to a congruence of null geodesics and then by a rescaling of l^a:

l^a -> A l^a how we conclude that l^a;b l^b=0 ?

 

[btphysics]

Hello, try to use general geodesic equation and then simplify the connection term with the definition of covariant derivative. Read about affine parameters.

I'll try to post a solution attempt. ( Ray D'inverno is a nice book has introduction to general relativity aspects).