Conditions for Sustained Orbital Resonances in Extreme Mass Ratio Inspirals

Abstract

We investigate the possibility of sustained orbital resonances in extreme mass ratio inspirals. Using a near-identity averaging transformation, we reduce the equations of motion for a particle moving in Kerr spacetime with self-force corrections in the neighbourhood of a resonant geodesic to a one dimensional equation for a particle moving in an effective potential. From this effective equation we obtain the necessary and sufficient conditions that the self-force needs to satisfy to allow inspiralling orbits to be captured in sustained resonance. Along the way we also obtain the full non-linear expression for the jump in the adiabatic constants of motion incurred as an inspiral transiently evolves through a strong resonance to first-order in the mass ratio. Finally, we find that if the resonance is strong enough to allow capture in sustained resonance, only a small fraction (order of the square root of mass-ratio) of all inspirals will indeed be captured. This makes observation of sustained resonances in EMRIs -- if they exist -- very unlikely for space based observatories like eLisa.

14 pages, 6 figures, corrected a number of typesetting errors in Sec. IIID

References in corpus (6)

• Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors
• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• Resonantly enhanced and diminished strong-field gravitational-wave fluxes
• A census of transient orbital resonances encountered during binary inspiral
• Isofrequency pairing of geodesic orbits in Kerr geometry
• Evolution of the Carter constant for a resonant inspiral into a Kerr black hole: I. The scalar case

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