Post-Newtonian templates for phase evolution of spherical extreme mass ratio inspirals

We present various post-Newtonian (PN) models for the phase evolution of compact objects moving along quasispherical orbits in Kerr spacetime. The models are derived by using the 12PN analytic formulas of the energy, angular momentum and their averaged rates of change calculated in the framework of the black hole perturbation theory. To examine the convergence of time-domain PN models (TaylorT families), we evaluate the dephasing between approximants with different PN orders. We found that the TaylorT1 model shows the best performance and the performance of the TaylorT2 model is the next best. To evaluate the convergence of frequency-domain PN models (TaylorF families), we evaluate the mismatch between approximants with different orders. We found that the performance of the TaylorF2 model is comparable with the TaylorT2 model. Although the TaylorT2 and TaylorF2 models are not so accurate as the TaylorT1 model, the fully analytical expressions give us easy-to-handle templates and are useful to discuss effects beyond general relativity.