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.

Gravitational waves provide a window on the universe of astronomical phenomena that is different from any in the electromagnetic spectrum. Mass in many different varieties of motion is a source of propagating ripples in spacetime curvature. In order to interpret the observations of gravitational wave detectors on Earth and in space, it is necessary to solve the Einstein equation for the gravitational radiation produced by given sources. Predicting the gravitational radiation from strong-curvature, rapidly varying sources is a problem generally tractable only by numerical simulation of the fully nonlinear Einstein equation – a subject well beyond the scope of this book. However, some insight into the production of gravitational waves can be obtained from examining the more tractable problem of the small ripples in spacetime emitted by weak, nonrelativistic sources.