Tail-transported temporal correlations in the dynamics of a gravitating system

The existence of retarded correlations over arbitrarily large time spans in the dynamics of a gravitating system, namely, the influence of the past evolution of a material system on its present gravitational internal dynamics, is investigated. This ‘‘hereditary’’ influence can be thought of as transported by the gravitational waves emitted by the system in the past and subsequently scattered off the curvature of spacetime back onto the system (‘‘backscattered waves’’ or ‘‘tails’’). The method used here applies to weakly self-gravitating slowly varying sources. It is a combination of a multipolar post-Minkowskian expansion for the metric in the weak-field region outside the system, and of a post-Newtonian-type expansion for the metric in the near zone. The two expansions are then ‘‘matched’’ in the weak-field-near-zone overlap region. The lowest-order nonlinear piece in the near-zone metric which depends on the full past history of the source (‘‘hereditary’’ term) is determined. This term arises at the fourth post-Newtonian (PN) level. The arising of this ‘‘hereditary’’ term signifies the breakdown of one of the fundamental tenets of the post-Newtonian approximation schemes. Indeed, at the 4PN level it becomes impossible to express the near-zone metric as a functional of the instantaneous state of the material source. This means also that there is a fundamental breakdown of the concept of near zone versus the concept of wave zone. The direct dynamical influence of the above-determined hereditary, or tail, term on the evolution of the material system is then studied. This term is found to modify the Burke-Thorne gravitational radiation quadrupole damping force. This modification, although quite small in absolute magnitude, is rather large relative to the usual damping force, being ∼(v/c${)}^3$ smaller (1(1/2PN relative level). It could be important in the dynamics of inspiralling binaries. Finally, it is shown that the hereditary term is predominantly sensitive to the recent past evolution of the system and only negligibly dependent on its very remote past history.