Gravitational radiation damping of a binary system containing compact objects calculated using matched asymptotic expansions

Abstract

This paper calculates the secular changes in orbital period, semimajor axis, and eccentricity for a gravitationally bound, slow-motion system of two compact bodies, directly from the Einstein field equation, using matched asymptotic expansions. Burke previously derived the radiation damping of a weak-field, slow-motion system, also using matched asymptotic expansions. However, no previous derivations extend to systems, such as the binary pulsar PSR 1913 + 16, containing objects with strong internal gravity. This calculation uses distinct wave-, near-, and body-zone expansions to seek a uniformly valid, one-parameter family of approximate space-times representing a bound system of compact objects undergoing gravitational radiation reaction. As in Burke's work, matching outward gives the lowest-order near-zone and radiation fields, and then matching back inward yields near-zone resistive potentials of $\frac{5}{2}$-post-Newtonian order, which contain the lowest-order time-odd effects of radiation. Matching inward again using my earlier technique for the problem of motion in external fields then gives the resulting deflections of the bodies from the world lines that they would otherwise follow. The secular changes in orbital parameters derived for the system of compact objects treated here agree with the standard formulas obeyed by weak-field systems.