### Abstract

In a previous paper, based on the black hole perturbation approach, we formulated a new analytical method for regularizing the self-force acting on a particle of small mass μ orbiting a Schwarzschild black hole of mass M, where μ ≪ M. In our method, we divide the self-force into the S̃-part and R̃-part. All the singular behavior is contained in the S̃-part, and hence the R̃-part is guaranteed to be regular. In this paper, focusing on the case of a scalar-charged particle for simplicity, we investigate the precision of both the regularized S̃-part and the R̃-part required for the construction of sufficiently accurate waveforms for almost circular inspirai orbits. We calculate the regularized S̃-part for circular orbits to 18th post-Newtonian (PN) order and investigate the convergence of the post-Newtonian expansion. We also study the convergence of the remaining R̃-part in the spherical harmonic expansion. We find that a sufficiently accurate Green function can be obtained by keeping the terms up to l = 13.

Original language | English |
---|---|

Pages (from-to) | 283-303 |

Number of pages | 21 |

Journal | Progress of Theoretical Physics |

Volume | 113 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 1 2005 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)

### Cite this

*Progress of Theoretical Physics*,

*113*(2), 283-303. https://doi.org/10.1143/PTP.113.283

**A new analytical method for self-force regularization. II - Testing the efficiency for circular orbits.** / Hikida, Wataru; Jhingan, Sanjay; Nakano, Hiroyuki; Sago, Norichika; Sasaki, Misao; Tanaka, Takahiro.

Research output: Contribution to journal › Article

*Progress of Theoretical Physics*, vol. 113, no. 2, pp. 283-303. https://doi.org/10.1143/PTP.113.283

}

TY - JOUR

T1 - A new analytical method for self-force regularization. II - Testing the efficiency for circular orbits

AU - Hikida, Wataru

AU - Jhingan, Sanjay

AU - Nakano, Hiroyuki

AU - Sago, Norichika

AU - Sasaki, Misao

AU - Tanaka, Takahiro

PY - 2005/2/1

Y1 - 2005/2/1

N2 - In a previous paper, based on the black hole perturbation approach, we formulated a new analytical method for regularizing the self-force acting on a particle of small mass μ orbiting a Schwarzschild black hole of mass M, where μ ≪ M. In our method, we divide the self-force into the S̃-part and R̃-part. All the singular behavior is contained in the S̃-part, and hence the R̃-part is guaranteed to be regular. In this paper, focusing on the case of a scalar-charged particle for simplicity, we investigate the precision of both the regularized S̃-part and the R̃-part required for the construction of sufficiently accurate waveforms for almost circular inspirai orbits. We calculate the regularized S̃-part for circular orbits to 18th post-Newtonian (PN) order and investigate the convergence of the post-Newtonian expansion. We also study the convergence of the remaining R̃-part in the spherical harmonic expansion. We find that a sufficiently accurate Green function can be obtained by keeping the terms up to l = 13.

AB - In a previous paper, based on the black hole perturbation approach, we formulated a new analytical method for regularizing the self-force acting on a particle of small mass μ orbiting a Schwarzschild black hole of mass M, where μ ≪ M. In our method, we divide the self-force into the S̃-part and R̃-part. All the singular behavior is contained in the S̃-part, and hence the R̃-part is guaranteed to be regular. In this paper, focusing on the case of a scalar-charged particle for simplicity, we investigate the precision of both the regularized S̃-part and the R̃-part required for the construction of sufficiently accurate waveforms for almost circular inspirai orbits. We calculate the regularized S̃-part for circular orbits to 18th post-Newtonian (PN) order and investigate the convergence of the post-Newtonian expansion. We also study the convergence of the remaining R̃-part in the spherical harmonic expansion. We find that a sufficiently accurate Green function can be obtained by keeping the terms up to l = 13.

UR - http://www.scopus.com/inward/record.url?scp=18544383931&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18544383931&partnerID=8YFLogxK

U2 - 10.1143/PTP.113.283

DO - 10.1143/PTP.113.283

M3 - Article

AN - SCOPUS:18544383931

VL - 113

SP - 283

EP - 303

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 2

ER -