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Fujita Ryuichi, Sago Norichika, Nakano Hiroyuki, Note on accuracy of the post-Newtonian approximation for extreme-mass ratio inspirals: retrograde orbits, *Classical and Quantum Gravity*, 10.1088/1361-6382/aa9ad5, 35, 027001, 2017.12. |

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Norichika Sago, Ryuichi Fujita, Hiroyuki Nakano, Accuracy of the Post-Newtonian Approximation for Extreme-Mass Ratio Inspirals from Black-hole Perturbation Approach, arXiv:1601.02174, We revisit the accuracy of the post-Newtonian (PN) approximation and its region of validity for quasi-circular orbits of a point particle in the Kerr spacetime, by using an analytically known highest post-Newtonian order gravitational energy flux and accurate numerical results in the black hole perturbation approach. It is found that regions of validity become larger for higher PN order results although there are several local maximums in regions of validity for relatively low-PN order results. This might imply that higher PN order calculations are also encouraged for comparable-mass binaries. . |

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Norichika Sago, Ryuichi Fujita, Calculation of radiation reaction effect on orbital parameters in Kerr spacetime, *Progress of Theoretical and Experimental Physics*, 2015, 073E03 , arXiv:1505.01600, 2015.07, We calculate the secular changes of the orbital parameters of a point particle orbiting a Kerr black hole, due to the gravitational radiation reaction. For this purpose, we use the post-Newtonian (PN) approximation in the first order black hole perturbation theory, with the expansion with respect to the orbital eccentricity. In this work, the calculation is done up to the fourth post-Newtonian (4PN) order and to the sixth order of the eccentricity, including the effect of the absorption of gravitational waves by the black hole. We confirm that, in the Kerr case, the effect of the absorption appears at the 2.5PN order beyond the leading order in the secular change of the particle's energy and may induce a superradiance, as known previously for circular orbits. In addition, we find that the superradiance may be suppressed when the orbital plane inclines with respect to the equatorial plane of the central black hole. We also investigate the accuracy of the 4PN formulae by comparing to numerical results. If we require that the relative errors in the 4PN formulae are less than $10^{-5}$, the parameter region to satisfy the condition will be $p\gtrsim 50$ for $e=0.1$, $p\gtrsim 80$ for $e=0.4$, and $p\gtrsim 120$ for $e=0.7$ almost irrespective of the inclination angle nor the spin of the black hole, where $p$ and $e$ are the semi-latus rectum and the eccentricity of the orbit. The region can further be extended using an exponential resummation method to $p\gtrsim 40$ for $e=0.1$, $p\gtrsim 60$ for $e=0.4$, and $p\gtrsim 100$ for $e=0.7$. Although we still need the higher order calculations of the PN approximation and the expansion with respect to the orbital eccentricity to apply for data analysis of gravitational waves, the results in this paper would be an important improvement from the previous work at the 2.5PN order, especially for large $p$ region.. |

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Soichiro Isoyama, Hiroyuki Nakano, Ryuichi Fujita, Sago Norichika, Takahiro Tanaka, Evolution of the Carter constant for a resonant inspiral into a Kerr black hole: I. The scalar case, *Progress of Theoretical and Experimental Physics*, 2013, 6, 063E01, arXiv:1302.4035 [gr-qc], 2013.06. |

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Soichiro Isoyama, Ryuichi Fujita, Norichika Sago, Hideyuki Tagoshi, Takahiro Tanaka, Impact of the second order self-forces on the dephasing of the gravitational waves from quasi-circular extreme mass-ratio inspirals, *Physical Review D*, 87, 2, 024010, 2013.01. |

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Sarp Akcay, Leor Barack, Thibault Damour, Norichika Sago , Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring, *Physical Review D*, 10.1103/PhysRevD.86.104041, 86, 104041, 2012.11. |