Discuss the below:
Light signals and time differences in Schwarzchild geometry
Q: An observer at r = r1 in Schwarzchild geometry sends a light signal in the radial direction toward r = r2 where r2 > r1.
(a) Determine the instantaneous coordinate velocity dr/dt of the signal.
(b) Suppose the signal is reflected at r = r2 and returns to r1. Determine how long, as measured in coordinate time t, it takes the signal to return.
(c) Determine how long it takes as measured by the clock of the observer at r1.