Foundations of an effective-one-body model for coalescing binaries on eccentric orbits

We develop the foundations of an effective-one-body (EOB) model for eccentric binary coalescences that includes the conservative dynamics, radiation reaction, and gravitational waveform modes from the inspiral and the merger-ringdown signals. Our approach uses the strategy that is commonly employed in black-hole perturbation theory: we introduce an efficient, relativistic parameterization of the dynamics that is defined by the orbital geometry and consists of a set of phase variables and quantities that evolve only due to gravitational radiation reaction. Specializing to nonspinning binaries, we derive the EOB equations of motion for the new variables and make use of the fundamental frequencies of the motion to compute the binary's radiative multipole moments that determine the gravitational waves. Our treatment has several advantages over the quasi-Keplerian approach that is often used in post-Newtonian (PN) calculations: a smaller set of variables, parameters that reflect the features of strong-field dynamics, and a greater transparency of the calculations when using the fundamental frequencies that leads to simplifications and an unambiguous orbit-averaging operation. While our description of the conservative dynamics is fully relativistic, we limit explicit derivations in the radiative sector to 1.5PN order for simplicity. This already enables us to establish methods for computing both instantaneous and hereditary contributions to the gravitational radiation in EOB coordinates that have straightforward extensions to higher PN order. The weak-field, small eccentricity limit of our results for the orbit-averaged fluxes agrees with known PN results when expressed in terms of gauge-invariant quantities. We further address considerations for the numerical implementation of the model and the completion of the waveforms to include the merger and ringdown signals, and provide illustrative results.