Measuring gravitational waves in a humming universe with a coordinate-free approach

Gravitational waves are tiny ripples in spacetime. Their first direct detection in 2015 marked a revolutionary moment in astronomy. Today, we have a thorough understanding of signals that travel far from their sources through quiet, nearly empty space, such as those emitted when black holes merge. In this case, the wave can be considered a minor disturbance on a silent background. The distinction between "background" and "wave" is clear, and the quantity measured by the detector-...