Analytical Effective One-Body Formalism For Extreme-Mass-Ratio Inspirals With Eccentric Orbits

Extreme-mass-ratio inspirals (EMRIs) are among the most important sources for future spaceborne gravitational wave detectors. In this kind of system, compact objects usually orbit around central supermassive black holes on complicated trajectories. Usually, these trajectories are approximated as the geodesics of Kerr space-times, and orbital evolution is simulated with the help of the adiabatic approximation. However, this approach omits the influence of the compact object on its background. In this paper, using the effective one-body formalism, we analytically calculate the trajectory of a nonspinning compact object around a massive Kerr black hole in an equatorial eccentric orbit (omitting the orbital inclination) and express the fundamental orbital frequencies in explicit forms. Our formalism includes the first-order corrections for the mass ratio in the conservative orbital motion. Furthermore, we insert the mass-ratio-related terms into the first post-Newtonian energy fluxes. By calculating the gravitational waves using the Teukolsky equations, we quantitatively reveal the influence of the mass of the compact object on the data analysis. We find that the shrinking of geodesic motion by taking small objects as test particles may not be appropriate for the detection of EMRIs.