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General Relativity and Quantum Cosmology, gr-qc
Abstract:
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. We use the same approach as is commonly employed in
black-hole perturbation theory by introducing a 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
evolution equations and compute the binary's radiative multipole moments that
determine the gravitational waves through a decomposition into the fundamental
frequencies of the motion. The major differences between our treatment and the
quasi-Keplerian approach often used in post-Newtonian (PN) calculations are
that the orbital parameters describe strong-field dynamics, and that expressing
the multipole moments in terms of the frequencies simplifies the calculations
and also results in 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 of energy and
angular momentum 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.
