Generalized Perturbed Kepler Problem: Gravitational Wave Imprints from Eccentric Compact Binaries

TL;DR

This paper introduces a unified, physically transparent framework to analyze how environmental effects and new physics perturb the orbits and gravitational wave signals of eccentric compact binaries.

Contribution

It develops a source-specific modeling approach for perturbed Keplerian orbits, enabling detailed study of deviations from standard gravitational dynamics in gravitational wave data.

Findings

Derived modified orbital dynamics from a general perturbed potential.

Computed gravitational fluxes and phase evolution for perturbed orbits.

Assessed the observational relevance for current and future detectors.

Abstract

Observations of astrophysical binaries may reveal departures from pure Keplerian orbits due to environmental influences, modifications to the underlying gravitational dynamics, or signatures of new physics. In this work, we develop a unified framework to systematically study such perturbations in the ambit of the perturbed Kepler problem and explore their impact on eccentric orbital dynamics and gravitational wave emission. Unlike traditional parametrized frameworks such as post-Newtonian and post-Einsteinian expansions, our approach offers a more source-specific modeling strategy, making it more natural to trace the physical origins of eccentric binary model parameters. Starting from a general perturbed potential, we derive the modified orbit and compute the associated gravitational fluxes and phase evolution, assessing their observational relevance for both current and future detectors. This framework thus offers a general and physically transparent toolkit for probing such subtle deviations from standard dynamics in gravitational wave data.