The double-series approximation method in general relativity I. Exact solution of the (24) approximation. II. Discussion of 'wave tails' in the (2s) approximation

In 1966 Bonnor and Rotenberg used the double-series approximation method, in conjunction with the Bondi metric, to study gravitational radiation from an isolated cohesive axisymmetric source vibrating smoothly during a finite interval u 1 0 and all u, is given of the (24) approximation step of Bonnor and Rotenberg's work. The quadrupole-quadrupole interaction is shown to satisfy Huygens' principle, but the monopole-2 4 -pole interaction gives rise to 'wave tails'. In part II it is shown that, for u>u 2 (end of the source vibration), the 'wave tails' resulting from the monopole-2 s -pole contribution of the (2s) approximation (s>or=2) represent incoming 2 s -pole radiation, at any rate for s=2, 3, 4.