## Solution

This question concerns wristwatch time, tau-time i, proper time, and the correlation between this time and the r-coordinate Equation [19] gives us dt/dx, the correlation between time at infinity and spaceship proper time:

Equation [21] gives us dr/dt, the correlation between radial r-coordinate and far-away time.

We use equations [21] and [19] to find the correlation between changes in r-coordinate and wristwatch time:

This equation gives the change dx in proper time racked up during the shrinkage dr in the r-coordinate:

r dr

Integrate both sides of this expression from r = 2M to r = 0 0

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