By introducing a specific but arbitrary coordinate system, show that among all timelike world lines that a particle could take to get from event P 0 to event P 1 , the one or ones whose proper time lapse is stationary under small variations of path are the freefall geodesics In other words, an acti...

By introducing a specific but arbitrary coordinate system, show that among all timelike world lines that a

Question:

By introducing a specific but arbitrary coordinate system, show that among all timelike world lines that a particle could take to get from event P₀ to event P₁, the one or ones whose proper time lapse is stationary under small variations of path are the freefall geodesics. In other words, an action principle for a timelike geodesic P(λ) [i.e., x^α(λ) in any coordinate system x^α] is