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A while ago, I read a proof in a book on GR that when using the proper-time parametrization, the two conditions ## \delta \int_{\lambda_1}^{\lambda_2} \sqrt{-g_{\mu\nu} \dot{x}^\mu \dot{x}^\nu} d\lambda=0## and ## \delta \int_{\lambda_1}^{\lambda_2} (-g_{\mu\nu} \dot{x}^\mu \dot{x}^\nu) d\lambda=0## are equilvalent. But then I forgot which book was it. I was able to reconstruct the proof but now I'm really curious what book was that! Does anyone know? I've checked several books so I know that not many books on GR contain such a proof.
Thanks
Thanks
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