This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Supplement on the geodesic equation Im writing up this brief supplement because I noticed a lot of people get ting things wrong when finding the geodesic equation via Hartles Lagrangian method. This method is a little tricky since there are a few steps you must follow that he doesnt explicitly state. This is best illustrated by example: Consider the hyperbolic plane (problem 8.12 on the last hw): dS 2 = y 2 ( dx 2 + dy 2 ) Since geodesics are paths of extremal length, we want to extremize S = dS = 1 y dx d 2 + dy d 2 d where we have parametrized our path by some paramter  its not important what this parameter is since we will switch to an affine parameter during the calculation (rememeber an affine parameter is just one that make the RHS of the geodesic equation 0). Now, if we identify L = 1 y dx d 2 + dy d 2 = dS d then finding geodesics looks a lot like solving the EulerLagrange equations from classical mechanics....
View Full
Document
 Spring '08
 KEVIN
 General Relativity

Click to edit the document details