Evolution of the Carter constant for resonant inspirals into a Kerr black hole: I. the scalar case

Soichiro Isoyama, Ryuichi Fujita, Hiroyuki Nakano, Norichika Sago, Takahiro Tanaka

Research output: Contribution to journalReview article

10 Citations (Scopus)

Abstract

We discuss the inspiral of a small body around a Kerr black hole. When the time scale of the radiation reaction is sufficiently longer than its orbital period, the leading-order orbital evolution is described only by the knowledge of the averaged evolution of constants of motion, i.e., the energy, azimuthal angular momentum, and the Carter constant. Although there is no conserved current composed of the perturbation field corresponding to the Carter constant, it has been shown that the averaged rate of change of the Carter constant can be given by a simple formula, when there exists a simultaneous turning point of the radial and polar oscillations. However, an inspiraling orbit may cross a resonance point, where the frequencies of the radial and polar orbital oscillations are in a rational ratio. At the resonance point, one cannot find a simultaneous turning point in general. Hence, even for the averaged rate of change of the Carter constant, a direct computation of the self-force, which is still challenging especially in the case of the Kerr background, seems to be necessary. In this paper, we present amethod of computing the averaged rate of change of the Carter constant in a relatively simple manner at the resonance point.

Original languageEnglish
Article number063E01
JournalProgress of Theoretical and Experimental Physics
Volume2013
Issue number6
DOIs
Publication statusPublished - Jun 1 2013

Fingerprint

scalars
orbitals
oscillations
angular momentum
orbits
perturbation
radiation
energy

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Evolution of the Carter constant for resonant inspirals into a Kerr black hole : I. the scalar case. / Isoyama, Soichiro; Fujita, Ryuichi; Nakano, Hiroyuki; Sago, Norichika; Tanaka, Takahiro.

In: Progress of Theoretical and Experimental Physics, Vol. 2013, No. 6, 063E01, 01.06.2013.

Research output: Contribution to journalReview article

@article{cdb06c4b3a8744b0a8a6f02ff1562dc2,
title = "Evolution of the Carter constant for resonant inspirals into a Kerr black hole: I. the scalar case",
abstract = "We discuss the inspiral of a small body around a Kerr black hole. When the time scale of the radiation reaction is sufficiently longer than its orbital period, the leading-order orbital evolution is described only by the knowledge of the averaged evolution of constants of motion, i.e., the energy, azimuthal angular momentum, and the Carter constant. Although there is no conserved current composed of the perturbation field corresponding to the Carter constant, it has been shown that the averaged rate of change of the Carter constant can be given by a simple formula, when there exists a simultaneous turning point of the radial and polar oscillations. However, an inspiraling orbit may cross a resonance point, where the frequencies of the radial and polar orbital oscillations are in a rational ratio. At the resonance point, one cannot find a simultaneous turning point in general. Hence, even for the averaged rate of change of the Carter constant, a direct computation of the self-force, which is still challenging especially in the case of the Kerr background, seems to be necessary. In this paper, we present amethod of computing the averaged rate of change of the Carter constant in a relatively simple manner at the resonance point.",
author = "Soichiro Isoyama and Ryuichi Fujita and Hiroyuki Nakano and Norichika Sago and Takahiro Tanaka",
year = "2013",
month = "6",
day = "1",
doi = "10.1093/ptep/ptt034",
language = "English",
volume = "2013",
journal = "Progress of Theoretical and Experimental Physics",
issn = "2050-3911",
publisher = "Oxford University Press",
number = "6",

}

TY - JOUR

T1 - Evolution of the Carter constant for resonant inspirals into a Kerr black hole

T2 - I. the scalar case

AU - Isoyama, Soichiro

AU - Fujita, Ryuichi

AU - Nakano, Hiroyuki

AU - Sago, Norichika

AU - Tanaka, Takahiro

PY - 2013/6/1

Y1 - 2013/6/1

N2 - We discuss the inspiral of a small body around a Kerr black hole. When the time scale of the radiation reaction is sufficiently longer than its orbital period, the leading-order orbital evolution is described only by the knowledge of the averaged evolution of constants of motion, i.e., the energy, azimuthal angular momentum, and the Carter constant. Although there is no conserved current composed of the perturbation field corresponding to the Carter constant, it has been shown that the averaged rate of change of the Carter constant can be given by a simple formula, when there exists a simultaneous turning point of the radial and polar oscillations. However, an inspiraling orbit may cross a resonance point, where the frequencies of the radial and polar orbital oscillations are in a rational ratio. At the resonance point, one cannot find a simultaneous turning point in general. Hence, even for the averaged rate of change of the Carter constant, a direct computation of the self-force, which is still challenging especially in the case of the Kerr background, seems to be necessary. In this paper, we present amethod of computing the averaged rate of change of the Carter constant in a relatively simple manner at the resonance point.

AB - We discuss the inspiral of a small body around a Kerr black hole. When the time scale of the radiation reaction is sufficiently longer than its orbital period, the leading-order orbital evolution is described only by the knowledge of the averaged evolution of constants of motion, i.e., the energy, azimuthal angular momentum, and the Carter constant. Although there is no conserved current composed of the perturbation field corresponding to the Carter constant, it has been shown that the averaged rate of change of the Carter constant can be given by a simple formula, when there exists a simultaneous turning point of the radial and polar oscillations. However, an inspiraling orbit may cross a resonance point, where the frequencies of the radial and polar orbital oscillations are in a rational ratio. At the resonance point, one cannot find a simultaneous turning point in general. Hence, even for the averaged rate of change of the Carter constant, a direct computation of the self-force, which is still challenging especially in the case of the Kerr background, seems to be necessary. In this paper, we present amethod of computing the averaged rate of change of the Carter constant in a relatively simple manner at the resonance point.

UR - http://www.scopus.com/inward/record.url?scp=84879164111&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84879164111&partnerID=8YFLogxK

U2 - 10.1093/ptep/ptt034

DO - 10.1093/ptep/ptt034

M3 - Review article

AN - SCOPUS:84879164111

VL - 2013

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 6

M1 - 063E01

ER -