Gravitational radiation, or gravitational waves, are often described as "ripples in the fabric of spacetime", and depicted using rubber-membrane images like the one shown here. This description is certainly poetic, and fits well with the geometric gravity-as-curvature interpretation of Einstein's General Theory of Relativity (GR). However, this imagery is not necessarily the best approach to a deeper understanding of the mechanics and properties of gravitational waves.
In fact, gravitational radiation is not unique to GR, but is a necessary consequence of nearly any theory of gravity that is consistent with the more basic rules of Special Relativity. It arises from the simple fact that a change in the gravitational field of an object takes time to be felt at large distances: the effect cannot propagate instantaneously or at any speed greater than the speed of light.
This fact is true for other fields besides gravity, and gravitational radiation can be viewed as analogous to electromagnetic radiation: a more familiar phenomenon that covers everything from radio waves, through visible light, to x-rays and gamma rays. The following pages will therefore begin with a discussion of how electromagnetic radiation occurs, and how a similar underlying mechanism leads to gravitational radiation. I will then go on to explain how gravity differs from electromagnetism, and how this affects the generation and detection of gravitational waves.
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additional mathematical detail.
Start: Gravitational waves demystified
Analogy: Electromagnetic fields
Electromagnetic field of an accelerated charge
Derivation of the radiative electromagnetic field
Gravitational tidal field
Equivalence between dipole and tidal field
Formulae and details
Differences between gravitational and electromagnetic radiation
Gravitational wave spectrum