Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole

Isoyama, Soichiro; Barack, Leor; Dolan, Sam R.; Tiec, Alexandre Le; Nakano, Hiroyuki; Shah, Abhay; Tanaka, Takahiro; Warburton, Niels

doi:10.1103/physrevlett.113.161101

Cited by 79 publications

(115 citation statements)

References 88 publications

(142 reference statements)

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“…This important result extends to non-equatorial orbits the innermost stable circular orbit condition derived in Ref. [78] for equatorial orbits. In particular, as will be shown below, the renormalized redshiftz is related to the gaugeinvariant interaction Hamiltonian…”

Section: Frequency Shift Of Innermost Stable Spherical Orbitssupporting

confidence: 74%

“…It is also supported by a variety of calculations comparing self-force, post-Newtonian and numericalrelativity predictions [78,94,132]. In particular, the recent results of Ref.…”

mentioning

confidence: 56%

“…Moreover, the equivalence between the conditions (7.1) and (8.29) generalizes to inclined orbits the results of Refs. [78,127], which established the equivalence between the notions of innermost stable circular orbit (ISCO) and minimum energy circular orbit (MECO).…”

Section: E Minimum Energy Spherical Orbitsmentioning

confidence: 99%

See 2 more Smart Citations

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

Fujita

Isoyama

Tiec

et al. 2017

Class. Quantum Grav.

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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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Section: Frequency Shift Of Innermost Stable Spherical Orbitssupporting

confidence: 74%

“…It is also supported by a variety of calculations comparing self-force, post-Newtonian and numericalrelativity predictions [78,94,132]. In particular, the recent results of Ref.…”

mentioning

confidence: 56%

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

Fujita

Isoyama

Tiec

et al. 2017

Class. Quantum Grav.

Self Cite

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show abstract

“…II D. We hope that the radiation-gauge formalism developed by Friedman, Shah and collaborators [47] may be extended to compute highly accurate results in the Kerr case (see, e.g., Ref. [69] for recent progress).…”

Section: Discussionmentioning

confidence: 99%

Tidal invariants for compact binaries on quasicircular orbits

et al. 2015

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We extend the gravitational self-force approach to encompass "self-interaction" tidal effects for a compact body of mass μ on a quasicircular orbit around a black hole of mass M ≫ μ. Specifically, we define and calculate at OðμÞ (conservative) shifts in the eigenvalues of the electric-and magnetic-type tidal tensors, and a (dissipative) shift in a scalar product between their eigenbases. This approach yields four gauge-invariant functions, from which one may construct other tidal quantities such as the curvature scalars and the speciality index. First, we analyze the general case of a geodesic in a regular perturbed vacuum spacetime admitting a helical Killing vector and a reflection symmetry. Next, we specialize to focus on circular orbits in the equatorial plane of Kerr spacetime at OðμÞ. We present accurate numerical results for the Schwarzschild case for orbital radii up to the light ring, calculated via independent implementations in Lorenz and Regge-Wheeler gauges. We show that our results are consistent with leading-order postNewtonian expansions, and demonstrate the existence of additional structure in the strong-field regime. We anticipate that our strong-field results will inform (e.g.) effective one-body models for the gravitational two-body problem that are invaluable in the ongoing search for gravitational waves.

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“…Barack and Sago [244] combined the conservative pieces of the GSF and metric perturbations to calculate the frequency shift in the innermost, stable circular orbit that originates from the GSF of the small body in Schwarzschild spacetime (see [257] for the extension to the Kerr spacetime). In [258] a similar shift was computed in the rate of periastron advance for eccentric orbits.…”

Section: Perturbation Theory and Gravitational Self Forcementioning

confidence: 99%