Radiation reaction and gravitational waves in the effective field theory approach

TL;DR

This paper applies the effective field theory approach to compute radiation reaction forces and gravitational wave emission in binary systems, incorporating real-time dissipative effects and retarded boundary conditions within a post-Newtonian framework.

Contribution

It introduces a method to include real-time dissipative processes and retarded boundary conditions in the EFT approach for gravitational radiation, extending previous formalisms.

Findings

Computed 2.5 post-Newtonian radiation reaction contributions.

Described gravitational wave emission using EFT with retarded boundary conditions.

Clarified limitations of scattering formalism for dissipative processes.

Abstract

We compute the contribution to the Lagrangian from the leading order (2.5 post-Newtonian) radiation reaction and the quadrupolar gravitational waves emitted from a binary system using the effective field theory (EFT) approach of Goldberger and Rothstein. We use an initial value formulation of the underlying (quantum) framework to implement retarded boundary conditions and describe these real-time dissipative processes. We also demonstrate why the usual scattering formalism of quantum field theory inadequately accounts for these. The methods discussed here should be useful for deriving real-time quantities (including radiation reaction forces and gravitational wave emission) and hereditary terms in the post-Newtonian approximation (including memory, tail and other causal, history-dependent integrals) within the EFT approach. We also provide a consistent formulation of the radiation sector in the equivalent effective field theory approach of Kol and Smolkin.