Hamiltonian formulation of the conservative self-force dynamics in the Kerr geometry

Ryuichi Fujita, Soichiro Isoyama, Alexandre Le Tiec, Hiroyuki Nakano, Norichika Sago, Takahiro Tanaka

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We formulate a Hamiltonian description of the orbital motion of a point particle in Kerr spacetime for generic (eccentric, inclined) orbits, which accounts for the effects of the conservative part of the gravitational self-force. This formulation relies on a description of the particle's motion as geodesic in a certain smooth effective spacetime, in terms of (generalized) action-angle variables. Clarifying the role played by the gauge freedom in the Hamiltonian dynamics, we extract the gauge-invariant information contained in the conservative self-force. We also propose a possible gauge choice for which the orbital dynamics can be described by an effective Hamiltonian, written solely in terms of the action variables. As an application of our Hamiltonian formulation in this gauge, we derive the conservative self-force correction to the orbital frequencies of Kerr innermost stable spherical (inclined or circular) orbits. This gauge choice also allows us to establish a 'first law of mechanics' for black-hole-particle binary systems, at leading order beyond the test-mass approximation.

Original languageEnglish
Article number134001
JournalClassical and Quantum Gravity
Volume34
Issue number13
DOIs
Publication statusPublished - Jun 7 2017

Fingerprint

formulations
geometry
orbitals
eccentric orbits
circular orbits
particle motion
orbits
approximation

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

Cite this

Hamiltonian formulation of the conservative self-force dynamics in the Kerr geometry. / Fujita, Ryuichi; Isoyama, Soichiro; Le Tiec, Alexandre; Nakano, Hiroyuki; Sago, Norichika; Tanaka, Takahiro.

In: Classical and Quantum Gravity, Vol. 34, No. 13, 134001, 07.06.2017.

Research output: Contribution to journalArticle

Fujita, Ryuichi ; Isoyama, Soichiro ; Le Tiec, Alexandre ; Nakano, Hiroyuki ; Sago, Norichika ; Tanaka, Takahiro. / Hamiltonian formulation of the conservative self-force dynamics in the Kerr geometry. In: Classical and Quantum Gravity. 2017 ; Vol. 34, No. 13.
@article{7a9c1c9a65894b25a0a64d7ac0166dd8,
title = "Hamiltonian formulation of the conservative self-force dynamics in the Kerr geometry",
abstract = "We formulate a Hamiltonian description of the orbital motion of a point particle in Kerr spacetime for generic (eccentric, inclined) orbits, which accounts for the effects of the conservative part of the gravitational self-force. This formulation relies on a description of the particle's motion as geodesic in a certain smooth effective spacetime, in terms of (generalized) action-angle variables. Clarifying the role played by the gauge freedom in the Hamiltonian dynamics, we extract the gauge-invariant information contained in the conservative self-force. We also propose a possible gauge choice for which the orbital dynamics can be described by an effective Hamiltonian, written solely in terms of the action variables. As an application of our Hamiltonian formulation in this gauge, we derive the conservative self-force correction to the orbital frequencies of Kerr innermost stable spherical (inclined or circular) orbits. This gauge choice also allows us to establish a 'first law of mechanics' for black-hole-particle binary systems, at leading order beyond the test-mass approximation.",
author = "Ryuichi Fujita and Soichiro Isoyama and {Le Tiec}, Alexandre and Hiroyuki Nakano and Norichika Sago and Takahiro Tanaka",
year = "2017",
month = "6",
day = "7",
doi = "10.1088/1361-6382/aa7342",
language = "English",
volume = "34",
journal = "Classical and Quantum Gravity",
issn = "0264-9381",
publisher = "IOP Publishing Ltd.",
number = "13",

}

TY - JOUR

T1 - Hamiltonian formulation of the conservative self-force dynamics in the Kerr geometry

AU - Fujita, Ryuichi

AU - Isoyama, Soichiro

AU - Le Tiec, Alexandre

AU - Nakano, Hiroyuki

AU - Sago, Norichika

AU - Tanaka, Takahiro

PY - 2017/6/7

Y1 - 2017/6/7

N2 - We formulate a Hamiltonian description of the orbital motion of a point particle in Kerr spacetime for generic (eccentric, inclined) orbits, which accounts for the effects of the conservative part of the gravitational self-force. This formulation relies on a description of the particle's motion as geodesic in a certain smooth effective spacetime, in terms of (generalized) action-angle variables. Clarifying the role played by the gauge freedom in the Hamiltonian dynamics, we extract the gauge-invariant information contained in the conservative self-force. We also propose a possible gauge choice for which the orbital dynamics can be described by an effective Hamiltonian, written solely in terms of the action variables. As an application of our Hamiltonian formulation in this gauge, we derive the conservative self-force correction to the orbital frequencies of Kerr innermost stable spherical (inclined or circular) orbits. This gauge choice also allows us to establish a 'first law of mechanics' for black-hole-particle binary systems, at leading order beyond the test-mass approximation.

AB - We formulate a Hamiltonian description of the orbital motion of a point particle in Kerr spacetime for generic (eccentric, inclined) orbits, which accounts for the effects of the conservative part of the gravitational self-force. This formulation relies on a description of the particle's motion as geodesic in a certain smooth effective spacetime, in terms of (generalized) action-angle variables. Clarifying the role played by the gauge freedom in the Hamiltonian dynamics, we extract the gauge-invariant information contained in the conservative self-force. We also propose a possible gauge choice for which the orbital dynamics can be described by an effective Hamiltonian, written solely in terms of the action variables. As an application of our Hamiltonian formulation in this gauge, we derive the conservative self-force correction to the orbital frequencies of Kerr innermost stable spherical (inclined or circular) orbits. This gauge choice also allows us to establish a 'first law of mechanics' for black-hole-particle binary systems, at leading order beyond the test-mass approximation.

UR - http://www.scopus.com/inward/record.url?scp=85021050030&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021050030&partnerID=8YFLogxK

U2 - 10.1088/1361-6382/aa7342

DO - 10.1088/1361-6382/aa7342

M3 - Article

AN - SCOPUS:85021050030

VL - 34

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 13

M1 - 134001

ER -