期刊
CLASSICAL AND QUANTUM GRAVITY
卷 34, 期 13, 页码 -出版社
IOP Publishing Ltd
DOI: 10.1088/1361-6382/aa7342
关键词
approximation methods; equations of motion; wave generation and sources; post-Newtonian approximation; perturbation theory
类别
资金
- European Research Council under the European Union's Seventh Framework Programme [304978]
- H ERC Consolidator Grant 'Matter and strong-field gravity: New frontiers in Einstein's theory' [MaGRaTh-646597]
- Marie Curie FP7 Integration Grant [PCIG13-GA-2013-630210]
- MEXT [24103001, 24103006, 15H02087]
- JSPS [16K05347, 25800154, 16K05356]
- Grants-in-Aid for Scientific Research [16K05347, 16K05356, 25800154] Funding Source: KAKEN
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.
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