We examine two problems in gravitational radiation reaction by the method of Matched Asymptotic Expansions (MAE). In the first problem, we use the method of MAE to calculate the leading orders of gravitational radiation reaction from a system of two slowly moving bodies scattering through a small angle. The leading time odd secular effect corresponds to a slight decrease in the Newtonian mechanical energy of the system. The magnitude of this decrease agrees with the gravitational energy loss predicted by the Landau -Lifschitz quadrupole formula. Our solution satisfies a condition to exclude incoming radiation. In the second problem, we examine the causes of divergent integrals in the post-Newtonian (PN) treatments of radiation reaction in slow motion, bound systems. The PN methods implicitly assume that the near zone metric has an analytic dependence on the slow motion parameter (epsilon). We show explicitly that a PN approximation method leads to a divergent integral at the 4-PN order. We then examine the wave zone metric. By use of matching arguments, we find a term that matches to the near zone that is an 0(log (epsilon)) larger than the 4-PN divergence. All terms that match in are finite. We conclude that the PN divergences signal a breakdown of the assumption of analytic dependence upon (epsilon). Therefore, the inner zone must have a non-analytic dependence on (epsilon) , and such dependence can only be found by singular perturbation methods such as MAE. We also show that our wave zone metric can be matched, after a gauge transformation, to the inner zone metric of Chandrasekhar and Esposito. Our results suggests that the PN calculations give the correct answers at least up to the orders at which the divergences occur.
- Pub Date:
- Physics: Astronomy and Astrophysics