My notes give the variational principle for a geodesic in GR:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] c\tau_{AB} = c\int_A^B d\tau = c\int_A^B \frac{d\tau}{dp}dp = \int_A^B Ldp [/tex]

and then apply the Euler-Lagrange equations. By choosing p to be an "affine parameter" where [tex] \frac{d^2 p}{d\tau^2} [/tex] the Euler-Lagrange equations are then expressed as:

[tex] \frac{dL^2}{dx^\mu} + \frac{d}{dp}\left( \frac{dL^2}{d\dot{x}^\mu} \right) = 0 [/tex]

where the dot is wrt p. Apparently the affine parameter is usually chosen to be tau, but then L is just 1 and the equation holds trivially! In fact each term in the equation is zero individually. What am I missing here?

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# Confused by variational principle

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