"We consider the motion of nonspinning, compact objects orbiting around a Kerr black hole with tidal couplings. The tide-indcued quadrupole moment modifies both the orbital energy and out-going fluxes, so that over the inspiral timescale there is an accumulative shift in the orbital and gravitational wave phase. Previous studies on compact object tidal effects have been carried out in the Post-Newtonian (PN) and Effetive-One-Body (EOB) formalisms. In this work, within the black hole perturbation framework, we propose to characterize the tidal influence in the expansion
of mass ratios, while higher-order PN corrections are naturally included. For the equatorial and circular orbit, we derive the leading order, frequency depedent tidal phase shift which agrees with the Post-Newtonian result at low frequencies but deviates at high frequencies. We also find that such phase shift has weak dependence (≤ 10%) on the spin of the primary black hole. Combining this black hole perturbation waveform with the Post-Newtonian waveform, we propose a frequency-domain, hybrid waveform that shows comparable accuracy as the EOB waveform in characterizing
the tidal effects, as calibrated by numerical relativity simulations. Further improvement is expected as the next-leading order in mass ratio and the 2PN tidal corections are included. This hybrid approach is also applicable for generating binary black hole waveforms."