Comments on gravitational radiation damping and energy loss in binary systems

Sources of Gravitational Waves: Theory and Observations

“…During the last thirty years there have been significant advances on the problems emphasised in the historic discussion organised and moderated by A. Ashtekar at the end of the school. The validity of the quadrupole formula for gravitational radiation far away from a binary source was questioned by some of the participants at the Les Houches school, appealing to the ongoing debate at that time [22][23][24][25][26][27][28][29] relating to the difficulties in describing nonlinearities in GR within a precise mathematical framework. At the Les Houches school, the Paris group (Damour, Deruelle, ...) proposed a consistent framework in terms of which to formulate questions about the two-body dynamics and GW emission.…”

Post-Newtonian Gravitational Radiation

“…As an example, within the rigorous approach, one was not permitted, by the end of the seventies, to apply the standard quadrupole formula to the binary pulsar. Indeed, as pointed out by Ehlers et al [7], it was not clear that gravitational radiation reaction on a self-gravitating system implies the standard quadrupole formula for the energy flux, notably because computing the radiation reaction demands a priori three non-linear iterations of the field equations [8], which were not fully available at that time. Ehlers and collaborators [7] remarked also that the exact results concerning the structure of the field at infinity (notably the asymptotic shear of null geodesics whose variation determines the flux of radiation) were not connected to the actual dynamics of the binary.…”

“…The important remarks of Jürgen Ehlers et al [7] on the applicability of the quadrupole formula to the binary pulsar stimulated research to settle down this question with (al least) acceptable mathematical rigor. The question was finally answered positively by Damour and collaborators [16][17][18][19], who obtained in algebraically closed form the general-relativistic equations of motion of two compact objects, up to the requisite 5/2 post-Newtonian order (2.5PN order or 1/c 5 ) where the gravitational radiation reaction force appears.…”

The Confrontation Between General Relativity and Experiment

“…However, the discovery revealed an ugly truth about the "problem of motion". As Ehlers et al pointed out in an influential 1976 paper [142], the general relativistic problem of motion and radiation was full of holes large enough to drive trucks through. They pointed out that most treatments of the problem used "delta functions" as a way to approximate the bodies in the system as point masses.…”