Consider lightlike radial trajectories in the Schwarzschild spacetime in Schwarzschild coordinates. They are just like my Problem 3.2 with a → 2M, so look at the solution to that one.

(a) Verify that it takes an infinite coordinate time to go outward from r = 2M to r :— ЗМ. (b) How much coordinate time does it take to go outward from r = 3M to r = 6M?