I am using the schwartzchild metric given as [itex] ds^2 = (1 - \frac{2M}{r})dt^2 - (1 - \frac{2M}{r})^{-1} dr^2 [/itex], where I assume the angular coordinates are constant for simplicity.(adsbygoogle = window.adsbygoogle || []).push({});

So if a beam of light travels from radius r_{0}to smaller radius r_{1}, hits a mirror, and travels back to r_{0}, I am trying to find how much proper time has passed for an observer fixed at r_{0}. So far, i have that this path can be parametrized by r = r_{0}and t = x, where x is just my parameter. Therefore, r' = 0 and t' = 1. Using the formula for arc length, i have that the proper time is given by [itex] \int \sqrt{1 - \frac{2M}{r_0}} dx [/itex].

this is where i am stuck as i am having trouble determining the limits of my integral. can someone give me a hint or two in the right direction? thanks

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# Calculating proper time using schwartzchild metric

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