Post-Newtonian effects in
                    <i>N</i>
                    -body dynamics: conserved quantities in hierarchical triple systems

Will, Clifford M.

doi:10.1088/0264-9381/31/24/244001

Cited by 26 publications

(20 citation statements)

References 22 publications

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“…The KL-oscillation timescale is also modified when the GR effect is taken into account [58]. Note that it has been pointed out [61,62] that it is imperative to take into account the "cross terms" between the Newtonian perturbation and the post-Newtonian precession. In our numerical evolution, we integrate the equations of motion (up to 1PN) directly.…”

Section: ð2:1þmentioning

confidence: 99%

Gravitational waves from hierarchical triple systems with Kozai-Lidov oscillation

et al. 2020

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We study gravitational waves from a hierarchical three-body system up to first-order post-Newtonian approximation. Under certain conditions, the existence of a nearby third body can cause periodic exchange between eccentricity of an inner binary and relative inclination, known as Kozai-Lidov oscillations. We analyze features of the waveform from the inner binary system undergoing such oscillations. We find that variation caused due to the tertiary companion can be observed in the gravitational waveforms and energy spectra, which should be compared with those from isolated binaries and coplanar three-body system. The detections from future space-based interferometers will make possible the investigation of gravitational wave spectrum in mHz range and may fetch signals by sources addressed.

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Section: ð2:1þmentioning

confidence: 99%

Gravitational waves from hierarchical triple systems with Kozai-Lidov oscillation

et al. 2020

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“…If arbitrarily small initial energy always evolves to have finite energy density somewhere, it is a clear sign of a runaway behavior due to gravitational attraction. 5 Finally, we should note that the truncated theory is already nonlinear and may be difficult to solve directly. If one invokes another approximation while solving the truncated theory, such as time-averaging, then the process becomes vulnerable to an additional form of breakdown, such as the oscillating singularity seen in [2].…”

Section: The Ads (In)stability Problemmentioning

confidence: 99%

“…We thank Luis Lehner for pointing out that some Post-Newtonian expansions to General Relativity also shows validity at this long time scale[5] 3. It is extremely likely that a capable mathematician can directly point to a textbook material to backup this claim.…”

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confidence: 95%

Conditionally extended validity of perturbation theory: Persistence of AdS stability islands

Dimitrakopoulos

Yang

2015

Phys. Rev. D

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Conditionally extended validity of perturbation theory: Persistence of AdS stability islands Dimitrakopoulos, F.; Yang, I.S. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Approximating nonlinear dynamics with a truncated perturbative expansion may be accurate for a while, but it, in general, breaks down at a long time scale that is one over the small expansion parameter. There are interesting cases in which such breakdown does not happen. We provide a mathematically general and precise definition of those cases, in which we prove that the validity of truncated theory trivially extends to the long time scale. This enables us to utilize numerical results, which are only obtainable within finite times, to legitimately predict the dynamics when the expansion parameter goes to zero, and thus the long time scale goes to infinity. In particular, this shows that existing noncollapsing solutions in the AdS (in)stability problem persist to the zero-amplitude limit, opposing the conjecture by Dias, Horowitz, Marolf, and Santos that predicts a shrinkage to measure zero [O. J. Dias et al., Classical Quantum Gravity 29, 235019 (2012)]. We also point out why the persistence of collapsing solutions is harder to prove, and how the recent interesting progress by Bizon, Maliborski, and Rostoworowski has not yet proven this [P. Bizon, M. Maliborski, and A. Rostworowski, arXiv:1506.03519].

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“…It is worth mentioning that in planetary systems, similar three-body dynamics have been extensively studied and many interesting behaviours have been discovered in the Newtonian and Post-Newtonian regimes For example, the well-known Kozai-Lidov (KL) mechanism [14,15] suggests that the inner binary could trade eccentricity for inclination angle under the influence of the quadrupole tidal field of the third body. In recent years, the KL mechanism has been further extended to include eccentric orbits [16], the octupole tidal field [17,18] and Post-Newtonian corrections [19,20]. As the inner binary transfers from the Newtonian regime to the relativistic regime, the degeneracy between radial and angular orbital frequencies breaks down, which in principle allows for a much richer phenomenology, as indicated by previous Post-Newtonian studies [20].…”

Section: Introductionmentioning

confidence: 99%

General relativistic dynamics of an extreme mass-ratio binary interacting with an external body

Yang

Casals

2017

Phys. Rev. D

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We study the dynamics of a hierarchical three-body system in the general-relativistic regime: an extreme mass-ratio inner binary under the tidal influence of an external body. The inner binary consists of a central Schwarzschild black hole and a test body moving around it. We discuss three types of tidal effects on the orbit of the test body. First, the angular momentum of the inner binary precesses around the angular momentum of the outer binary. Second, the tidal field drives a "transient resonance" when the radial and azimuthal frequencies are commensurable. In contrast with resonances driven by the gravitational self-force, this tidal-driven resonance may boost the orbital angular momentum and eccentricity (a relativistic version of the Kozai-Lidov effect). Finally, as an orbit-dynamical effect during the non-resonant phase, we calculate the correction to the Innermost Stable Circular (mean) Orbit due to the tidal interaction. Hierarchical three-body systems are potential sources for future space-based gravitational wave missions and the tidal effects that we find could contribute significantly to their waveform. * Electronic address: hyang@perimeterinstitute.ca † Electronic address: mcasals@cbpf.br

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Post-Newtonian effects in N -body dynamics: conserved quantities in hierarchical triple systems

Cited by 26 publications

References 22 publications

Gravitational waves from hierarchical triple systems with Kozai-Lidov oscillation

Gravitational waves from hierarchical triple systems with Kozai-Lidov oscillation

Conditionally extended validity of perturbation theory: Persistence of AdS stability islands

General relativistic dynamics of an extreme mass-ratio binary interacting with an external body

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