The book helps -- clocks deeper in a gravitational potential run slow relative to those higher in the potential.
As I recall from Hartle, to paraphrase: "The experimentalists in the basement live longer than the theorists upstairs, but the view is worth it." My recollection from the associated problem is that the difference, over a lifetime, is microseconds.
MTW won't give even that much aid :). Good luck with your studies; there's a lot to learn.