Wednesday, February 20, 2019

general relativity - Equation of motion of a photon in a given metric


I have this metric: ds2=dt2+etdx2

and I want to find the equation of motion (of x). for that i thought I have two options:




  1. using E.L. with the Lagrangian: L=˙t2+et˙x2.





  2. using the fact that for a photon ds2=0 to get: 0=dt2+etdx2 and then: dt=±et/2dx.




The problem is that (1) gives me x=aet+b and (2) gives me x=aet/2+b.




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