Problems for week 17

Problems for week 17:

Take another look at exercise 6.6. from the textbook ("The tidal force pendulum and the curvature of space") and use the hints given in the problem session.

To round off our discussion about the curvature tensor and flat/curved spacetime, show that the vanishing of the Riemann tensor is a sufficient condition for spacetime to be flat everywhere. Does this imply that spacetime is a globally trivial flat space?