New analytical methods for gravitational radiation and reaction in binaries with arbitrary mass ratio and relative velocity

Abstract

We present a new analytical framework for describing the dynamics of a gravitational binary system with unequal masses moving with arbitrary relative velocity, taking into account the backreaction from both compact objects in the form of tidal deformation, gravitational waves and self forces. Allowing all dynamical variables to interact with each other in a self-consistent manner this formalism ensures that all the dynamical quantities involved are conserved on the background spacetime and obey the gauge invariance under general coordinate transformations that preserve the background geometry. Because it is based on a generalized perturbation theory and the important new emphasis is on the self-consistency of all the dynamical variables involved we call it a gravitational perturbation theory with self-consistent backreaction (GP-SCB). As an illustration of how this formalism is implemented we construct perturbatively a self-consistent set of equations of motion for an inspiraling gravitational binary, which does not require extra assumptions such as slow motion, weak-field or small mass ratio for its formulation. This case should encompass the inspiral and possibly the plunge and merger phases of binaries with otherwise general parameters (e.g., mass ratio and relative velocity) though more investigation is needed to substantiate it. In the second part, we discuss how the mass ratio can be treated as a perturbation parameter in the post-Newtonian effective field theory (PN-EFT) approach, thus extending the work of Goldberger and Rothstein for equal mass binaries to variable mass ratios. We provide rough estimates for the higher post-Newtonian orders needed to determine the number of gravitational wave cycles, with a specified precision, that fall into a detector's bandwidth.