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evaluated along some path connecting fixed points A and B in spacetime. Here f is regarded as a function of 8 independent variables and . By varying the path , show that A is extremized for
where . These are the Euler- Lagrange equations.
holds for any parameter along the curve such that , being the proper time measured along the curve.
[ Note that in two dimensions the Riemann tensor has only one independent component, so calculate and obtain all other components in terms of it.]
(6b) Prove that
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