Theory of post-Newtonian radiation and reaction

Abstract: We address issues with extant formulations of dissipative effects in the effective field theory (EFT) which describes the post-Newtonian (PN) inspiral of two gravitating bodies by (re)formulating several parts of the theory. Novel ingredients include gauge invariant spherical fields in the radiation zone; a system zone which preserves time reversal such that its violation arises not from local odd propagation but rather from interaction with the radiation sector in a way which resembles the balayage method; 2-way multipoles to perform zone matching within the EFT action; and a double-field radiation-reaction action which is the non-quantum version of the Closed Time Path formalism and generalizes to any theory with directed propagators including theories which are defined by equations of motion rather than an action. This formulation unifies the treatment of outgoing radiation and its reaction force. We demonstrate the theory in the scalar, electromagnetic and gravitational cases by economizing the following: the expression for the radiation source multipoles; the derivation of the leading outgoing radiation and associated reaction force such that it is maximally reduced to mere multiplication; and the derivation of the gravitational next to leading PN order. In fact we present a novel expression for the +1PN correction to all mass multipoles. We introduce useful definitions for multi-index summation, for the normalization of Bessel functions and for the normalization of the gravito-magnetic vector potential.