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 journalArticlepeer-review

16 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

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

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