Gravitational Radiation Reaction in Axially Symmetric Systems with Possibly Strong Fields

The leading radiation reaction in quasistatic, axially symmetric systems is calculated by matched asymptotic expansions. Earlier results on inductive transfer of near-zone "energy" are combined via matching with a wave-zone expansion in the Regge-Wheeler gauge. Two independent measures of the damping are computed: (1) the change of the 1/R coefficient in a Weyl-Levi-Civitfi type of multipole expansion in the near zone and (2) the change in Bondi energy at future null infinity. When an averaging process is justified, such as in (nearly) periodic systems, both quantities yield a generalized version of the usual quadrupole formula, provided the radiation is outgoing at future null infinity. It is also shown that terms nonanalytic in the slow-motion parameter e make a time-even contribution to the near-zone monopole coefficient. The principal advantage of this calculation over previous work is that the sources are permitted to have strong gravitational fields. Moreover, no specific model for the sources is assumed.