8 - Gravitational Waves: Curvature in Motion

Summary

Gravitational waves are simply the solutions of the linearized Einstein equations, that is, the solution of the Einstein equations in weak gravitational fields or, equivalently, in spacetimes that are 'almost flat'. In this respect, they are not very different from the sound waves we hear when we listen to music or from the electromagnetic waves we receive when looking at the screen of our cellphone. However, it is not pressure or electromagnetic fields that are propagated, but rather the very same curvature we have encountered already. Hence, gravitational waves represent the propagation at the speed of light of small ripples in the curvature in spacetime. This chapter will make use of simple mechanical analogues to explain how gravitational waves are produced every time a mass or energy is set in motion, and how the amplitude of gravitational waves produced on Earth can only be extremely small.