1. The problem statement, all variables and given/known data Consider the two-dimensional spacetime with the line element dS2 = -X2dT2+dX2. Find the shapes X(T) of all timelike geodesics in this spacetime. 2. The attempt at a solution I have the solution to this problem but I don't understand one step. For timelike worldlines dS2 = -dt2 = 0 (where dt is the proper time) We also have that the Lagrangian is L = (X2(dT/dσ)2 - (dX/dσ)2)1/2 The Euler-Lagrange equation gives us that ∂L/(∂(dT/dσ)) = const. In the solutions, it is stated that this constant is identically equal to "e", and I do not understand why this is. Could anyone explain this or point me in the right direction? Thanks.