Hello! I am a bit confused about the geodesic equation. So for a massive particle it is given by: ##\frac{d}{d\tau}\frac{dx^\alpha}{d\tau}+\Gamma^\alpha_{\mu\beta}\frac{dx^\mu}{d\tau}\frac{dx^\beta}{d\tau}=0##, where ##\tau## is the proper time, but in general can be any affine parameter. I am confused about ##x^\alpha##. In which coordinate is this measured i.e. where is the observer located. I am actually doing the Schwarzchild metric now, and from the geodesic equation you can get ##\frac{dx^\alpha}{d\tau}##, but I am not sure for who do you get this, as all the values of the geodesic equations are evaluated at the position of the moving object, so for example ##\frac{dt}{d\tau}##, connects the time of the observer, with the proper time of the object, however, different observers, in Schwarzchild metric, measure different times, yet the geodesic equation gives just a value for it. Can someone explain this to me please? Thank you!(adsbygoogle = window.adsbygoogle || []).push({});

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# I Geodesic equation

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