Equivalence Principle in Action

Abstract

Having introduced the equivalence principle in the previous chapter, we now apply it. We want to find out, how gravity bends space-time around ball-shaped objects like stars or planets. We free-fall towards the ball, starting far away from the ball. The equivalence principle tells us that we do not feel any acceleration. However, the more we approach the ball, the faster we fall towards it. From the falling speed we can deduce how the pace of clocks and the length of rods resting near the ball change relative to us, and therefore how space-time is bending. In other words, once we know this speed, we know how gravity bends space-time near heavy masses like planets or stars. Exactly how the falling speed is increasing, we will see in Chap. 8, after we learned about the Einstein equation of gravity.