The question whether gravitational radiation exists is of great interest, both theoretically and experimentally. In the weak field approximation Einstein's field equations lead to a wave equation, which, in analogy with the situation with Maxwell's equations of electrodynamics, clearly suggests that gravitational waves exist; and, it would be hoped, again in analogy with the electrodynamic case, that they carry energy. We recall the crucial discovery by Hertz of electromagnetic waves, which convinced him, as well as the general public, of the reality of the field. From the 1960s Weber pioneered experiments to search for gravitational waves, but they have not yet been found. On the other hand there is some very convincing, though indirect, evidence that the gravitational field may radiate energy, which comes from the discovery that the period of the binary pulsar PSR 1913+16 is decreasing. One may feel justified in taking an optimistic view that gravitational radiation exists and might soon be discovered.

On the theoretical side there is a problem which is totally absent in the electromagnetic case. General Relativity is a non-linear theory, and this has the physical consequence that the gravitational field itself carries energy – witness the pseudo-energy-momentum tensor discussed earlier – which then acts as a source for more gravitational field. In contrast the electromagnetic field carries no electric charge so is not a source of further field. In the language of quantum theory, there is a graviton–graviton coupling but no photon–photon coupling.