Pith. sign in

REVIEW 3 major objections 5 minor 79 references

Resonant interactions from dynamical perturbers on generic orbits around an extreme mass ratio inspiral

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A third body on a generic orbit around an EMRI can shift the gravitational-wave phase by 0.1 radian while leaving the inspiral's actions below 1% change.

desk verdict A genuinely useful extension of the EMRI third-body resonance formalism, but the survey's 'none exceeds 1%' bound is softer than advertised because of censored eccentric orbits and unverified mode truncation. read the letter →

arxiv 2507.22260 v2 pith:SE76WFSB submitted 2025-07-29 gr-qc astro-ph.HE

Makana Silva , Harrison G. Blake-Goszyk , Christopher M. Hirata This is my paper
classification gr-qcastro-ph.HE
keywords extrememass-ratioinspiraltidalresonancethird-bodyperturberKerrgeodesicsaction-anglevariablesTeukolskyequationgravitationalwaveformphaseLISA
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Extreme mass-ratio inspirals in galactic centers will not be isolated two-body systems: other compact objects orbiting the same supermassive black hole can pass through resonances with the inspiraling body. This paper claims that such third-body resonances are individually small in their effect on the inspiral's orbital actions, with none of the 141,130 resonant interactions surveyed across 180 simulated orbit systems changing any action variable by more than about 1%, but that they can still be audibly large in the gravitational-wave phase, with the strongest cases reaching roughly 0.1 radian. If true, visible phase shifts from third bodies are an environmental signal rather than a fundamental-physics anomaly, and EMRI waveform models for LISA will need to include them. The paper's contribution is a general pipeline that computes these resonance jumps for an outer perturber on an arbitrary eccentric, inclined Kerr orbit, not just circular equatorial ones.

What carries the argument

The load-bearing object is Eq. (18), the stationary-phase resonance jump formula $$\$\Delta$ \tilde{J}_{\mathrm{inner},i} = \sum_{\mathrm{res}} \tilde{G}_{\vec{N}_{\mathrm{inner}},\vec{N}_{\mathrm{outer}},td,i} $e^{{i\Theta_{\mathrm{res}}$}} $e^{{i\pi\,\mathrm{sgn}}$(\Gamma)/4} \sqrt{\frac{2\pi}{|\Gamma|}},$$ with $\Gamma$ from Eq. (17) giving the rate at which the two bodies' resonant frequency difference is swept by self-force evolution. The tidal coefficient $\tilde{G}$ is built from the Weyl scalar $\psi_4$ through the Teukolsky amplitudes $Z^{\mathrm{out}}, Z^{\mathrm{down}}$ of both bodies, so each resonance strength is computed without evolving the two bodies together; selection rules $m_{\mathrm{inner}}=m_{\mathrm{outer}}$ and $k_{\mathrm{inner}}-k_{\mathrm{outer}}=\mathrm{even}$ filter which integer six-tuples are physical. This machinery converts a six-frequency resonance search into a concrete action jump and, via Eq. (20) and the frequency-action derivative matrix of Appendix A, into an extrapolated waveform phase shift.

What would settle it

A self-consistent evolution of one resonant configuration, with the two bodies' mutual tidal force active during the crossing or with overlapping resonances, that produces a relative action change at or above 1%, or a phase shift meaningfully different from the Eq. (20) extrapolation for the same initial data, would show that the post-processing Born approximation misses the effect.

Watch

Extended reading notes

Core claim

The central claim is that a dynamical third body orbiting a supermassive black hole on a generic eccentric, inclined trajectory can resonantly perturb an EMRI in a way that is always perturbative in the actions, with the survey's largest relative action changes around the $10^{-5}$ level and far below the 1% threshold where the linear calculation would break down, yet the cumulative phase of the emitted gravitational wave can shift by up to roughly 0.1 radian, at the edge of what LISA-like detectors can resolve. The paper states this as a separation of scales: resonant encounters look dangerous but are dynamically gentle one by one, and they are still not negligible for waveform modeling. It further claims that the stationary-phase jump formula, fed by each body's Teukolsky amplitudes and self-force evolution, is robust enough to catalog resonances across a wide parameter space, including resonances with no Newtonian analogue, such as nodal-precession resonances driven by the black hole's spin.

Load-bearing premise

The paper computes resonance jumps after the fact from two trajectories that were evolved separately under each body's own self-force, so the central assumption is that the mutual pull between the two bodies during a resonance crossing is too weak to bend the trajectories while the crossing happens; if the mutual tidal torque is not negligible then, or if overlapping resonances occur, the computed jumps and the sub-1% conclusion do not follow.

Editorial extensions

If this is right

  • If these results hold, LISA-era EMRI templates must include third-body tidal resonances, because unmodeled phase shifts near 0.1 radian could otherwise be misread as deviations from general relativity.
  • Each detected resonant phase jump is a positive detection of a nearby body carrying partial information about its mass and orbit, so the catalog opens a population-survey channel for galactic center environments.
  • Because the pipeline accepts arbitrary eccentric and inclined outer orbits, the same machinery covers mean-motion resonances and Kerr-specific precession resonances, and the largest phase shifts cluster at high black-hole spin with inner pericenters of order $8$-$15M$.
  • The survey's bound of no resonance above 1% action change legitimizes a perturbative treatment for these configurations, meaning waveforms can be built by linearly superposing individual resonance kicks rather than by evolving the full three-body system.
  • Resonance crossings in the studied systems occur on timescales of tens of days with widths near $1/\sqrt{|\Gamma|}$, placing the effect inside LISA's observational band as a transient feature of the event.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: the 0.1-radian tail may matter even though most crossings are tiny, because an inspiral can cross many resonances; whether the small phase contributions add coherently is not settled here and is the natural next test.
  • Beyond the paper: since the largest dephasings cluster at high black-hole spin and close inner pericenters, spin bias in the EMRI population could make third-body phase shifts preferentially common, complicating parameter estimation for exactly the sources most prized for strong-field tests.
  • A testable extension would be running the same survey with retrograde inner orbits and eccentricities above 0.8; if the action-change distribution shifts upward there, the 'always perturbative' conclusion may be specific to the prograde, low-eccentricity corner of parameter space.
  • One could also integrate a single resonant configuration with the mutual tidal force active during the crossing and compare the resulting phase shift with the paper's linear extrapolation; agreement would validate the post-processing pipeline, while disagreement would show where feedback between the bodies matters.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper extends the Silva–Hirata resonant-interaction formalism for extreme-mass-ratio inspirals (EMRIs) from a circular, equatorial perturber to a generic eccentric and inclined outer body, and uses the extended pipeline to survey resonant interactions across 180 Monte-Carlo-generated orbital systems (12 parameter combinations of inner/outer semi-major axes and black-hole spin, 15 realizations each). The pipeline generates initial actions, evolves both bodies adiabatically under the self-force, identifies resonances using the selection rules of Eq. (13), and computes the tidal change in the inner body's actions via the stationary-phase formula (Eq. 18) with Teukolsky amplitudes. The paper reports approximately 141,130 resonant interactions after excluding events with eccentricity above 0.8, and finds that none produce action changes larger than 1%; however, some produce extrapolated waveform phase shifts of order 0.1 radian, which the authors argue could be relevant for LISA parameter estimation. The paper also highlights four representative resonances, including one with a strong-field inner pericenter of about 8–10M, and discusses the corresponding Keplerian resonant angles.

Significance. If the central survey claim is correct, this is a valuable step toward understanding whether third-body resonances can be treated perturbatively in EMRI waveform models: individually small action jumps with phase shifts of order 0.1 radian would matter for LISA data analysis, and a pipeline that handles generic outer-body orbits is a useful tool for the community. The paper is honest about several of its limitations: it states in Sec. III C that trajectories are not changed during a resonance crossing, it declares the e>0.8 exclusion in footnote 6, and it publicly lists the truncation parameters s=5 and n_l=4. The formalism itself is not new, but its application to generic eccentric and inclined perturbers and the resulting catalog are the main contributions. The phase-shift estimate (Eq. 20) is clearly labeled as a linear extrapolation, which is appropriate for a first survey. The paper would be strengthened by quantitative convergence and robustness checks for the quantities that underpin the 'no resonance exceeds 1%' claim.

major comments (3)
  1. [Sec. IV, Eq. (18) and Table II] The central claim that no resonant interaction changes the actions by more than 1% is an upper-bound statement, so it depends on the completeness of the computed Delta-J values. The overtone index is truncated at s=5 and the multipole sum in Eq. (14) at n_l=4, with no convergence test reported; the strong-field events in Table II have pericenters of 8.7-15M, where high-l multipoles can be significant. I request either a convergence study in s and n_l for a representative subset (including the strong-field events), or an analytic/empirical bound showing that the omitted terms cannot change any Delta-J by more than a small factor. Without this, the claim 'none exceed 1%' is not yet established for the surveyed population.
  2. [Footnote 6 and Sec. III A] The survey excludes 21,530 resonances occurring when the eccentricity exceeds 0.8, which is 13% of the 162,660 nominal total, and these are precisely the events for which resonance strengths are typically largest. The paper justifies e<0.8 as a numerical-resolution constraint, but it does not quantify the effect of the exclusion on the headline upper bound. I ask for either an analysis of a sample of the excluded high-eccentricity events with better radial resolution, or an argument based on analytic scalings that the excluded events cannot produce Delta-J/J > 1%; otherwise the conclusion 'none of the ~142,000 interactions exceed 1%' applies only to a censored subset.
  3. [Sec. III C, Eqs. (17)-(18)] The resonance-jump calculation assumes the two trajectories evolve independently under the self-force alone, so Gamma in Eq. (17) contains no tidal contribution from the outer body and the trajectories are not modified during crossing. This is explicitly stated, and for the small computed jumps an order-unity correction is unlikely, but the claim is still conditional on the tidal torque not significantly altering the crossing time. I recommend adding a quantitative estimate of the fractional change in Gamma from the tidal interaction, or an explicit statement of the regime in which that correction is negligible, so that the 1% upper bound is not only a statement about the model but also about the physical system.
minor comments (5)
  1. [Throughout] There are several typographical and formatting issues: 'Schwarzchild' should be 'Schwarzschild' (Sec. II), 'back hole spacetimes' in the Introduction should be 'black hole spacetimes', and the phrase 'W eyl scalar' contains an unnecessary spacing.
  2. [Eq. (14)] The notation for the Teukolsky amplitudes is inconsistent: the text uses Z with a tilde, Z with a bar, and a script eZ form. Please define all symbols in one place and use them consistently.
  3. [Appendix A, Eq. (A6)] In the radial-action subsection, Eq. (A6) writes the second derivative as partial^2 J_theta / partial B partial D, but the context requires partial^2 J_r / partial B partial D.
  4. [Table I and footnote 6] The sum of the entries in Table I is 162,658, while the text reports 162,660; also the sentence in footnote 6 is grammatically incomplete. Please reconcile the numbers and rewrite the footnote.
  5. [Sec. IV, Figs. 2-3] The histograms use a logarithmic binning but the axis labels do not fully specify the binning convention or whether the y-axis is number of resonances per system normalized by bin width; clarifying this would make the figures easier to interpret.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the 1% action bound and 0.1-rad phase estimates are computed outputs of the authors' previously derived, externally benchmarked resonance-strength formalism, not fitted or definitionally forced; disclosed truncations and exclusions are correctness risks, not circularity.

full rationale

The derivation chain is not circular. The survey output (|ΔJ_i/J_i| ≲ 1%, ΔΦ up to ~0.1 rad) is computed from Eq. (18) using the tidal Fourier amplitudes G̃ of Eq. (14) and the stationary-phase width Γ of Eq. (17); Γ itself is built only from the self-force secular rates and the Appendix A frequency-action matrix. No parameter is fitted to the surveyed result: initial actions are Monte Carlo drawn, Θ_res is randomly sampled, and s=5, n_ℓ=4 are truncations rather than tuned values, so the claimed upper bound is a property of the computed distribution, not an input. The citations to the authors' prior work [14,37] supply the resonance-strength formula and Teukolsky solver; this is real evidence by the reviewer's criteria, since the cited result is a parameter-free linearized-GR derivation whose stated assumptions (small μ_outer, unchanged trajectories) do not include the headline conclusion, and the paper cross-checks the machinery against external weak-field results (Newtonian 6:1 mean-motion resonance with semi-major ratio 6^(2/3) ≈ 3.302 versus the computed ≈3.292, and the Lense-Thirring nodal precession in Eq. 23). No uniqueness theorem is invoked, and the selection rules of Eq. (13) are justified in-text from Kerr symmetries rather than smuggled in by citation. The genuine limitations (post-processing with trajectories not altered during crossing per Sec. III C; the footnote-6 removal of 21,530 e>0.8 resonances from the ΔJ calculation; the untested s=5, n_ℓ=4 mode-sum truncation) are completeness and accuracy risks that could conceal larger jumps, but they are not circular steps: no equation in the paper reduces its prediction to its own input by construction.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The paper's central numbers rest on the prior resonance formalism of Silva and Hirata and Hirata, plus several hand-chosen truncations and sampling restrictions. There are no fitted parameters in the usual sense, but the overtone cutoff s=5, multipole cutoff n_l=4, mode scan bounds, and e<0.8 cut all shape the catalog. No new physical entities are introduced.

free parameters (4)
  • Overtone truncation index s = 5
    Chosen by hand to truncate the sum over integer multiples of fundamental resonances in Eq. 18; no convergence study is reported, so the computed Delta-J and Delta-Phi_lin could change if s is increased.
  • Multipole truncation n_l = 4
    Number of angular multipoles kept in the tidal strength sum in Eq. 14; no convergence check is shown.
  • Resonance-mode scan bounds = [-5,5] per component
    The resonance search sweeps each of the six integer mode numbers over [-5,5]; resonances with larger mode numbers are not scanned, so the catalog is restricted by this cutoff.
  • Inspiral-time prefactor in phase extrapolation = 1/8
    Eq. 20 approximates the integrated phase shift as Delta-Phi_lin using t_inspiral approximately (1/8) sum J_i / sum Jdot_sf,i; this prefactor and the linear extrapolation are hand-chosen and are not the full integral of the post-resonance frequency difference.
assumptions (7)
  • standard math Bound orbits in Kerr can be described by three action-angle variables with fundamental frequencies Omega_i = dH/dJ_i.
    Standard Hamiltonian action-angle theory for integrable geodesic motion; used throughout Section II A.
  • domain assumption The Teukolsky equation and Weyl scalar psi_4 encode both radiation and non-radiative parts of the first-order metric perturbation.
    Invoked in Section II B to compute resonance amplitudes Z from a Teukolsky solver; assumes first-order black hole perturbation theory in the small masses.
  • domain assumption Adiabatic self-force evolution in Eq. 11 gives the secular change of actions for both bodies.
    Taken from prior literature; neglects conservative self-force and assumes flux-balance dissipation suffices for the inspiral timescale.
  • domain assumption The stationary phase and Born approximation in Eq. 18 gives the total action jump at each resonance crossing.
    Central formula from the authors' prior work, valid only for isolated resonances with nonzero Gamma and small perturbing mass; used throughout Section III D.
  • domain assumption Selection rules m_inner = m_outer and k_inner minus k_outer even capture all physical resonances.
    Derived from Kerr azimuthal and reflection symmetries in the prior paper; adopted without re-derivation in Section III C.
  • ad hoc to paper Uniform random generation of the parameters in Eq. 9 adequately represents possible EMRI and perturber configurations.
    The initial actions are drawn from uniform distributions independent of any EMRI formation model; no astrophysical weighting is attempted.
  • ad hoc to paper The pericenter and apocenter condition r_p,outer / r_a,inner < 2 and eccentricity e < 0.8 define the safe, numerically resolvable regime.
    Stated in Section III A as numerical and stability constraints; resonances outside this regime, especially e > 0.8, are excluded from the strength calculation.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Resonant interactions from dynamical perturbers on generic orbits around an extreme mass ratio inspiral." pith.science (2026). https://pith.science/paper/SE76WFSB

@misc{pith2026250722260,
  author       = {Pith},
  title        = {Pith review of: Resonant interactions from dynamical perturbers on generic orbits around an extreme mass ratio inspiral},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SE76WFSB}},
  note         = {Machine review of arXiv:2507.22260}
}
read the original abstract

Extreme mass-ratio inspirals (EMRIs) are binary systems where a compact object slowly inspirals into its much larger compact partner. Since we anticipate such systems to exist within and be dynamically influenced by the galactic center environment, we expect them to be instrumental in studying these environments and testing our theories of gravity in the strong field regime. The gravitational waves associated with the EMRI motion fall within the mHz regime, making them target sources for future space-based detectors. However, because of the crowded nature of these galactic centers, these EMRIs could be perturbed by other nearby orbiting bodies. In this work, we analyze potential perturbations in EMRIs due to a third-body perturber near resonance. We use the formalism and code tools developed in the previous paper in this series [Silva \& Hirata, {\slshape Phys. Rev. D} {\bfseries 106}:084508 (2022)] and expand them to account for a general outer body orbit, allowing for multiple resonant interactions within an orbit and across a variety of SMBH spins. We find that, after investigating nearly 142,000 resonant interactions across a restricted set of 180 different simulated orbit systems, none cause changes to the EMRI dynamics beyond a perturbative correction, but could lead to potentially large changes in the phase of the waveform of order 0.1 radian. Detectable phase changes in the waveform induced by third-body perturbers could be a common occurrence and will require careful consideration for developing accurate EMRI waveform models. This analysis suggests that our formalism and pipeline are robust enough to handle a wide variety of resonances from various perturbing orbit configurations around the EMRI, which will aid in developing more accurate waveform models to better probe galactic center environments and test theories of gravity using gravitational wave observations of EMRIs.

Figures

Figures reproduced from arXiv: 2507.22260 by the authors.

Figure 1
Figure 1. FIG. 1. This flowchart depicts the process which we used to complete our analysis. First, we would generate two sets of three [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Histograms of resonance strengths (∆ [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Histograms of phase change crossing a resonance (∆Φ [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Evolution of the frequencies of both bodies for the system described in Resonance 2 in Table (II). The upper panel [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The path of integration used in Eq. (A2). The branch points [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The path of integration used in Eq. (A6). The branch points [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

79 extracted references · 40 canonical work pages

  1. [1]

    The longitude direction: ˜Jϕ This action is trivial: ˜Jϕ = ˜L, so the second derivatives are zero:∂ 2 ˜Jϕ/∂B ∂D= 0

    work page

  2. [2]

    +2𝑓𝜒2𝜒𝜒=𝑎

    The latitude direction: ˜Jθ This time, we need to use the integral form of the action, and differentiate it twice. From the defining relation for the vertical action: 16 Re z Imz +1–1 Key:removable singularitybranch pointbranch cutintegration path Re uz>0Re uz<0–z––z+ z+z– 𝑧±=1+𝜒±1+𝜒"+2𝑓𝜒2𝜒𝜒=𝑎"(1−,ℰ"),ℒ"+0𝒬𝑓=,ℒ"−0𝒬,ℒ"+0𝒬 FIG. 5. The path of integration us...

    work page

  3. [3]

    ((r2 +a 2)2 −a 2∆)P(r)−([(r 2 +a 2) ˜E−a ˜L](r2 +a 2) +a∆( ˜L−a ˜E))2 ∆P(r) # drp P(r) , ∂2 ˜Jr ∂L 2 = 1 2π I

    The radial direction: ˜Jr A similar argument can be made for the radial direction. This time, we find ˜Jr = 1 2π I ur dr⇒ ∂ ˜Jr ∂D = 1 2π I 1 2ur ∂(ur)2 ∂D dr⇒ ∂2 ˜Jθ ∂B∂D = 1 2π I 1 2ur ∂2(ur)2 ∂B ∂D − 1 2(ur)2 ∂(ur)2 ∂B ∂(ur)2 ∂D dr. (A6) The second derivatives are ∂2(ur)2 ∂B ∂D =   2(r2+a2)2 ∆2 − 2a2 ∆ 0− 2a(r2+a2) ∆2 + 2a ∆ 0 0 0 − 2a(r2+a2) ∆2 + 2...

    work page

  4. [4]

    The LIGO Scientific collaboration, Gravitational wave astronomy with LIGO and similar detectors in the next decade, arXiv e-prints , arXiv:1904.03187 (2019), arXiv:1904.03187 [gr-qc]

    work page Pith review arXiv 2019

  5. [5]

    Akutsu, M

    T. Akutsu, M. Ando, K. Arai, Y. Arai, S. Araki, A. Araya, N. Aritomi, H. Asada, Y. Aso, S. Bae, Y. Bae, L. Baiotti, R. Bajpai, M. A. Barton, K. Cannon, Z. Cao, E. Capocasa, M. Chan, C. Chen, K. Chen, Y. Chen, C. Y. Chiang, H. Chu, Y. K. Chu, S. Eguchi, Y. Enomoto, R. Flaminio, Y. Fujii, F. Fujikawa, M. Fukunaga, M. Fukushima, D. Gao, G. Ge, S. Ha, A. Hagi...

    work page 2021

  6. [6]

    Abbott, B. P.et al., LIGO Scientific Collaboration, and Virgo Collaboration, A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo, ApJ909, 218 (2021), arXiv:1908.06060 [astro-ph.CO]

    arXiv 2021

  7. [7]

    S. Ando, B. Baret, I. Bartos, B. Bouhou, E. Chassande-Mottin, A. Corsi, I. Di Palma, A. Dietz, C. Donzaud, D. Eichler, C. Finley, D. Guetta, F. Halzen, G. Jones, S. Kandhasamy, K. Kotake, A. Kouchner, V. Mandic, S. M´ arka, Z. M´ arka, L. Moscoso, M. A. Papa, T. Piran, T. Pradier, G. E. Romero, P. Sutton, E. Thrane, V. Van Elewyck, and E. Waxman, Colloqui...

    work page Pith review arXiv 2013

  8. [8]

    Branchesi, Multi-messenger astronomy: gravitational waves, neutrinos, photons, and cosmic rays, inJournal of Physics Conference Series, Journal of Physics Conference Series, Vol

    M. Branchesi, Multi-messenger astronomy: gravitational waves, neutrinos, photons, and cosmic rays, inJournal of Physics Conference Series, Journal of Physics Conference Series, Vol. 718 (IOP, 2016) p. 022004

    work page 2016

Show all 79 references
  1. [9]

    Glampedakis and S

    K. Glampedakis and S. Babak, Mapping spacetimes with LISA: inspiral of a test body in a ’quasi-Kerr’ field, Classical and Quantum Gravity23, 4167 (2006), arXiv:gr-qc/0510057 [gr-qc]

    2006 arXiv

  2. [10]

    Amaro Seoane, S

    eLISA Consortium, P. Amaro Seoane, S. Aoudia, H. Audley, G. Auger, S. Babak, J. Baker, E. Barausse, S. Barke, M. Bassan, V. Beckmann, M. Benacquista, P. L. Bender, E. Berti, P. Bin´ etruy, J. Bogenstahl, C. Bonvin, D. Bortoluzzi, N. C. Brause, J. Brossard, S. Buchman, I. Bykov...

    2013 arXiv

  3. [11]

    C ¸ alı¸ skan, L

    M. C ¸ alı¸ skan, L. Ji, R. Cotesta, E. Berti, M. Kamionkowski, and S. Marsat, Observability of lensing of gravitational waves from massive black hole binaries with LISA, Phys. Rev. D107, 043029 (2023), arXiv:2206.02803 [astro-ph.CO]

    2023 arXiv

  4. [12]

    Zhang and Y

    C. Zhang and Y. Gong, Probing new fundamental fields with extreme mass ratio inspirals, Phys. Rev. D110, 104052 (2024), arXiv:2407.07449 [gr-qc]

    2024 arXiv

  5. [13]

    Drasco and S

    S. Drasco and S. A. Hughes, Gravitational wave snapshots of generic extreme mass ratio inspirals, Phys. Rev. D73, 024027 (2006), arXiv:gr-qc/0509101 [gr-qc]

    2006 arXiv

  6. [14]

    Merritt, The Distribution of Stars and Stellar Remnants at the Galactic Center, ApJ718, 739 (2010), arXiv:0909.1318 [astro-ph.GA]

    D. Merritt, The Distribution of Stars and Stellar Remnants at the Galactic Center, ApJ718, 739 (2010), arXiv:0909.1318 [astro-ph.GA]

    2010 arXiv

  7. [15]

    Gourgoulhon, A

    E. Gourgoulhon, A. Le Tiec, F. H. Vincent, and N. Warburton, Gravitational waves from bodies orbiting the Galactic center black hole and their detectability by LISA, AAP627, A92 (2019), arXiv:1903.02049 [gr-qc]

    2019 arXiv

  8. [16]

    Bonga, H

    B. Bonga, H. Yang, and S. A. Hughes, Tidal Resonance in Extreme Mass-Ratio Inspirals, Phys. Rev. Lett.123, 101103 (2019), arXiv:1905.00030 [gr-qc]. 20

    2019 arXiv

  9. [17]

    Silva and C

    M. Silva and C. Hirata, Dynamical perturbations around an extreme mass ratio inspiral near resonance, Physical Review D106, 10.1103/physrevd.106.084058 (2022)

    2022 doi

  10. [18]

    Berti, E

    E. Berti, E. Barausse, V. Cardoso, L. Gualtieri, P. Pani, U. Sperhake, L. C. Stein, N. Wex, K. Yagi, T. Baker, C. P. Burgess, F. S. Coelho, D. Doneva, A. D. Felice, P. G. Ferreira, P. C. C. Freire, J. Healy, C. Herdeiro, M. Horbatsch, B. Kleihaus, A. Klein, K. Kokkotas, J. Kun...

    2015

  11. [19]

    Barack and C

    L. Barack and C. Cutler, Using LISA extreme-mass-ratio inspiral sources to test off-Kerr deviations in the geometry of massive black holes, Phys. Rev. D75, 042003 (2007), arXiv:gr-qc/0612029 [gr-qc]

    2007 arXiv

  12. [20]

    Levati, A

    E. Levati, A. C´ ardenas-Avenda˜ no, K. Destounis, and P. Pani, Cumulative effect of orbital resonances in extreme-mass-ratio inspirals, Phys. Rev. D111, 104006 (2025), arXiv:2502.20457 [gr-qc]

    2025 arXiv

  13. [21]

    Lukes-Gerakopoulos, T

    G. Lukes-Gerakopoulos, T. A. Apostolatos, and G. Contopoulos, Observable signature of a background deviating from the Kerr metric, Phys. Rev. D81, 124005 (2010), arXiv:1003.3120 [gr-qc]

    2010 arXiv

  14. [22]

    Destounis, A

    K. Destounis, A. G. Suvorov, and K. D. Kokkotas, Gravitational-wave glitches in chaotic extreme-mass-ratio inspirals, Phys. Rev. Lett.126, 141102 (2021), arXiv:2103.05643 [gr-qc]

    2021 arXiv

  15. [23]

    Destounis and K

    K. Destounis and K. D. Kokkotas, Gravitational-wave glitches: Resonant islands and frequency jumps in nonintegrable extreme-mass-ratio inspirals, Phys. Rev. D104, 064023 (2021), arXiv:2108.02782 [gr-qc]

    2021 arXiv

  16. [24]

    Destounis, G

    K. Destounis, G. Huez, and K. D. Kokkotas, Geodesics and gravitational waves in chaotic extreme-mass-ratio inspirals: the curious case of Zipoy-Voorhees black-hole mimickers, Gen. Rel. Grav.55, 71 (2023), arXiv:2301.11483 [gr-qc]

    2023 arXiv

  17. [25]

    Destounis, F

    K. Destounis, F. Angeloni, M. Vaglio, and P. Pani, Extreme-mass-ratio inspirals into rotating boson stars: Nonintegrability, chaos, and transient resonances, Phys. Rev. D108, 084062 (2023), arXiv:2305.05691 [gr-qc]

    2023 arXiv

  18. [26]

    A. M. Ghez, S. Salim, N. N. Weinberg, J. R. Lu, T. Do, J. K. Dunn, K. Matthews, M. R. Morris, S. Yelda, E. E. Becklin, T. Kremenek, M. Milosavljevic, and J. Naiman, Measuring Distance and Properties of the Milky Way’s Central Supermassive Black Hole with Stellar Orbits, ApJ689...

    2008 arXiv

  19. [27]

    Gillessen, F

    S. Gillessen, F. Eisenhauer, S. Trippe, T. Alexander, R. Genzel, F. Martins, and T. Ott, Monitoring Stellar Orbits Around the Massive Black Hole in the Galactic Center, ApJ692, 1075 (2009), arXiv:0810.4674 [astro-ph]

    2009 arXiv

  20. [28]

    Sch¨ odel, T

    R. Sch¨ odel, T. Ott, R. Genzel, R. Hofmann, M. Lehnert, A. Eckart, N. Mouawad, T. Alexander, M. J. Reid, R. Lenzen, M. Hartung, F. Lacombe, D. Rouan, E. Gendron, G. Rousset, A. M. Lagrange, W. Brandner, N. Ageorges, C. Lidman, A. F. M. Moorwood, J. Spyromilio, N. Hubin, and K...

    2002 arXiv

  21. [29]

    A. M. Ghez, G. Duchˆ ene, K. Matthews, S. D. Hornstein, A. Tanner, J. Larkin, M. Morris, E. E. Becklin, S. Salim, T. Kremenek, D. Thompson, B. T. Soifer, G. Neugebauer, and I. McLean, The First Measurement of Spectral Lines in a Short-Period Star Bound to the Galaxy’s Central ...

    2003

  22. [30]

    Emami and A

    R. Emami and A. Loeb, Detectability of gravitational waves from a population of inspiralling black holes in Milky Way-mass galaxies, MNRAS502, 3932 (2021), arXiv:1903.02579 [astro-ph.HE]

    2021

  23. [32]

    ´E. ´E. Flanagan and T. Hinderer, Transient Resonances in the Inspirals of Point Particles into Black Holes, Phys. Rev. Lett.109, 071102 (2012), arXiv:1009.4923 [gr-qc]

    2012 arXiv

  24. [33]

    Colpi, K

    M. Colpi, K. Danzmann, M. Hewitson, K. Holley-Bockelmann, P. Jetzer, G. Nelemans, A. Petiteau, D. Shoemaker, C. Sopuerta, R. Stebbins, N. Tanvir, H. Ward, W. J. Weber, I. Thorpe, A. Daurskikh, A. Deep, I. F. N´ u˜ nez, C. G. Marirrodriga, M. Gehler, J.-P. Halain, O. Jennrich, ...

    2024 arXiv

  25. [34]

    M. L. Katz, N. Karnesis, N. Korsakova, J. R. Gair, and N. Stergioulas, Efficient GPU-accelerated multisource global fit pipeline for LISA data analysis, Phys. Rev. D111, 024060 (2025), arXiv:2405.04690 [gr-qc]

    2025 arXiv

  26. [35]

    J. R. Gair, Probing black holes at low redshift using lisa emri observations, Classical and Quantum Gravity26, 10.1088/0264-9381/26/9/094034 (2009)

    2009 doi

  27. [36]

    J. K. Hoormann, B. Beheshtipour, and H. Krawczynski, Testing general relativity’s no-hair theorem with x-ray observations of black holes, Physical Review D93, 10.1103/physrevd.93.044020 (2016)

    2016 doi

  28. [37]

    Johannsen and D

    T. Johannsen and D. Psaltis, Metric for rapidly spinning black holes suitable for strong-field tests of the no-hair theorem, Physical Review D83, 10.1103/physrevd.83.124015 (2011). 21

    2011 doi

  29. [38]

    Hinderer and ´E

    T. Hinderer and ´E. ´E. Flanagan, Two-timescale analysis of extreme mass ratio inspirals in Kerr spacetime: Orbital motion, Phys. Rev. D78, 064028 (2008), arXiv:0805.3337 [gr-qc]

    2008 arXiv

  30. [39]

    C. M. Hirata, Lindblad resonance torques in relativistic discs - I. Basic equations, MNRAS414, 3198 (2011), arXiv:1010.0758 [astro-ph.HE]

    2011 arXiv

  31. [40]

    C. M. Hirata, Lindblad resonance torques in relativistic discs - II. Computation of resonance strengths, MNRAS414, 3212 (2011), arXiv:1010.0759 [astro-ph.HE]

    2011 arXiv

  32. [41]

    Gupta, B

    P. Gupta, B. Bonga, A. J. K. Chua, and T. Tanaka, Importance of tidal resonances in extreme-mass-ratio inspirals, Phys. Rev. D104, 044056 (2021), arXiv:2104.03422 [gr-qc]

    2021 arXiv

  33. [42]

    Gupta, L

    P. Gupta, L. Speri, B. Bonga, A. J. K. Chua, and T. Tanaka, Modeling transient resonances in extreme-mass-ratio inspirals, Phys. Rev. D106, 104001 (2022), arXiv:2205.04808 [gr-qc]

    2022 arXiv

  34. [43]

    Gupta, T

    P. Gupta, T. Kakehi, and T. Tanaka, Resonant jumps induced by stationary tidal perturbation: a two-for-one deal, Classical and Quantum Gravity39, 245005 (2022), arXiv:2207.13369 [gr-qc]

    2022 arXiv

  35. [44]

    Mukherjee, O

    S. Mukherjee, O. Kop´ aˇ cek, and G. Lukes-Gerakopoulos, Resonance crossing of a charged body in a magnetized Kerr background: An analog of extreme mass ratio inspiral, Phys. Rev. D107, 064005 (2023), arXiv:2206.10302 [gr-qc]

    2023 arXiv

  36. [45]

    Bronicki, A

    D. Bronicki, A. C´ ardenas-Avenda˜ no, and L. C. Stein, Tidally-induced nonlinear resonances in EMRIs with an analogue model, Classical and Quantum Gravity40, 215015 (2023), arXiv:2203.08841 [gr-qc]

    2023 arXiv

  37. [46]

    Z. Pan, H. Yang, L. Bernard, and B. Bonga, Resonant dynamics of extreme mass-ratio inspirals in a perturbed Kerr spacetime, Phys. Rev. D108, 104026 (2023), arXiv:2306.06576 [gr-qc]

    2023 arXiv

  38. [47]

    Kuntz, Precession resonances in hierarchical triple systems, Phys

    A. Kuntz, Precession resonances in hierarchical triple systems, Phys. Rev. D105, 024017 (2022), arXiv:2112.05167 [gr-qc]

    2022 arXiv

  39. [48]

    N. Sago, T. Tanaka, W. Hikida, and H. Nakano, Adiabatic Radiation Reaction to Orbits in Kerr Spacetime, Progress of Theoretical Physics114, 509 (2005), arXiv:gr-qc/0506092 [gr-qc]

    2005 arXiv

  40. [49]

    C. M. Hirata, Resonant recoil in extreme mass ratio binary black hole mergers, Phys. Rev. D83, 104024 (2011), arXiv:1011.4987 [gr-qc]

    2011 arXiv

  41. [50]

    R. H. Boyer and R. W. Lindquist, Maximal Analytic Extension of the Kerr Metric, Journal of Mathematical Physics8, 265 (1967)

    1967

  42. [51]

    Mino, Perturbative approach to an orbital evolution around a supermassive black hole, Phys

    Y. Mino, Perturbative approach to an orbital evolution around a supermassive black hole, Phys. Rev. D67, 084027 (2003), arXiv:gr-qc/0302075 [gr-qc]

    2003 arXiv

  43. [52]

    Fujita and W

    R. Fujita and W. Hikida, Analytical solutions of bound timelike geodesic orbits in Kerr spacetime, Classical and Quantum Gravity26, 135002 (2009), arXiv:0906.1420 [gr-qc]

    2009 arXiv

  44. [53]

    Carter, Global Structure of the Kerr Family of Gravitational Fields, Physical Review174, 1559 (1968)

    B. Carter, Global Structure of the Kerr Family of Gravitational Fields, Physical Review174, 1559 (1968)

    1968

  45. [54]

    Newman and R

    E. Newman and R. Penrose, An Approach to Gravitational Radiation by a Method of Spin Coefficients, Journal of Mathematical Physics3, 566 (1962)

    1962

  46. [55]

    S. A. Teukolsky, Perturbations of a Rotating Black Hole. I. Fundamental Equations for Gravitational, Electromagnetic, and Neutrino-Field Perturbations, ApJ185, 635 (1973)

    1973

  47. [56]

    S. A. Teukolsky and W. H. Press, Perturbations of a rotating black hole. III. Interaction of the hole with gravitational and electromagnetic radiation., ApJ193, 443 (1974)

    1974

  48. [57]

    P. L. Chrzanowski, Vector potential and metric perturbations of a rotating black hole, Phys. Rev. D11, 2042 (1975)

    1975

  49. [58]

    R. M. Wald, Construction of Solutions of Gravitational, Electromagnetic, or Other Perturbation Equations from Solutions of Decoupled Equations, Phys. Rev. Lett.41, 203 (1978)

    1978

  50. [59]

    S. A. Hughes, Evolution of circular, nonequatorial orbits of Kerr black holes due to gravitational-wave emission, Phys. Rev. D61, 084004 (2000), arXiv:gr-qc/9910091 [gr-qc]

    2000 arXiv

  51. [60]

    Panamarev, A

    T. Panamarev, A. Just, R. Spurzem, P. Berczik, L. Wang, and M. Arca Sedda, Direct n-body simulation of the galactic centre, Monthly Notices of the Royal Astronomical Society484, 3279 (2019), https://academic.oup.com/mnras/article- pdf/484/3/3279/27711897/stz208.pdf

    2019

  52. [61]

    C. D. Murray and S. F. Dermott,Solar System Dynamics(Cambridge University Press, 1999)

    1999

  53. [62]

    Casadio and G

    R. Casadio and G. Venturi, Black holes and the adiabatic phase, Classical and Quantum Gravity12, 1267 (1995), arXiv:gr- qc/9511054 [gr-qc]

    1995

  54. [63]

    S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, and W. H. Press,Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, 2007)

    2007

  55. [64]

    Lense and H

    J. Lense and H. Thirring, Phys. Z.19, 156 (1918)

    1918

  56. [65]

    P. A. Rosen and J. J. Lissauer, The Titan -1:0 Nodal Bending Wave in Saturn’s Ring C, Science241, 690 (1988)

    1988

  57. [66]

    M. S. Tiscareno, M. M. Hedman, J. A. Burns, J. W. Weiss, and C. C. Porco, Probing the inner boundaries of Saturn’s A ring with the Iapetus -1:0 nodal bending wave, ICARUS224, 201 (2013), arXiv:1302.5712 [astro-ph.EP]

    2013 arXiv

  58. [67]

    J. R. Gair, S. Babak, A. Sesana, P. Amaro-Seoane, E. Barausse, C. P. L. Berry, E. Berti, and C. Sopuerta, Prospects for observing extreme-mass-ratio inspirals with LISA, inJournal of Physics Conference Series, Journal of Physics Conference Series, Vol. 840 (IOP, 2017) p. 01202...

    2017 arXiv

  59. [68]

    Speri and J

    L. Speri and J. R. Gair, Assessing the impact of transient orbital resonances, Phys. Rev. D103, 124032 (2021)

    2021

  60. [69]

    E. A. Huerta, J. R. Gair, and D. A. Brown, Importance of including small body spin effects in the modelling of intermediate mass-ratio inspirals. ii. accurate parameter extraction of strong sources using higher-order spin effects, Physical Review D 85, 10.1103/physrevd.85.0640...

    2012 doi

  61. [70]

    M. L. Katz, A. J. Chua, L. Speri, N. Warburton, and S. A. Hughes, Fast extreme-mass-ratio-inspiral waveforms: New tools for millihertz gravitational-wave data analysis, Physical Review D104, 10.1103/physrevd.104.064047 (2021)

    2021 doi

  62. [71]

    Chakraborty, R

    J. Chakraborty, R. Arcodia, E. Kara, G. Miniutti, M. Giustini, A. J. Tetarenko, L. Rhodes, A. Franchini, M. Bonetti, K. B. Burdge, A. J. Goodwin, T. J. Maccarone, A. Merloni, G. Ponti, R. A. Remillard, and R. D. Saxton, Testing EMRI 22 Models for Quasi-periodic Eruptions with ...

    2024 arXiv

  63. [72]

    Franchini, M

    A. Franchini, M. Bonetti, A. Lupi, G. Miniutti, E. Bortolas, M. Giustini, M. Dotti, A. Sesana, R. Arcodia, and T. Ryu, Quasi-periodic eruptions from impacts between the secondary and a rigidly precessing accretion disc in an extreme mass- ratio inspiral system, Astronomy & Ast...

    2023

  64. [73]

    B. D. Metzger, N. C. Stone, and S. Gilbaum, Interacting Stellar EMRIs as Sources of Quasi-periodic Eruptions in Galactic Nuclei, ApJ926, 101 (2022), arXiv:2107.13015 [astro-ph.HE]

    2022 arXiv

  65. [74]

    Z. Pan, Z. Lyu, and H. Yang, Wet extreme mass ratio inspirals may be more common for spaceborne gravitational wave detection, Physical Review D104, 10.1103/physrevd.104.063007 (2021)

    2021 doi

  66. [75]

    W. H. Press and S. A. Teukolsky, On formation of close binaries by two-body tidal capture., ApJ213, 183 (1977)

    1977

  67. [76]

    Yu and D

    F. Yu and D. Lai, Binary Stars Approaching Supermassive Black Holes: Tidal Breakup, Double Stellar Disruptions, and Stellar Collision, Astrophys. J.977, 268 (2024), arXiv:2409.09597 [astro-ph.HE]

    2024 arXiv

  68. [77]

    Mannerkoski, A

    M. Mannerkoski, A. Rawlings, P. H. Johansson, T. Naab, A. Rantala, V. Springel, D. Irodotou, and S. Liao, KETJU - resolving small-scale supermassive black hole dynamics in GADGET-4, MNRAS524, 4062 (2023), arXiv:2306.04963 [astro-ph.IM]

    2023 arXiv

  69. [78]

    Guo and S

    B. Guo and S. D. Mathur, Are there echoes of gravitational waves?, International Journal of Modern Physics D31, 2242009 (2022), arXiv:2205.10921 [gr-qc]

    2022 arXiv

  70. [79]

    Uchikata, T

    N. Uchikata, T. Narikawa, H. Nakano, N. Sago, H. Tagoshi, and T. Tanaka, Searching for gravitational wave echoes from black hole binary events in the third observing run of ligo, virgo, and kagra collaborations, Phys. Rev. D108, 104040 (2023)

    2023

  71. [80]

    Komossa, Tidal disruption of stars by supermassive black holes: Status of observations, Journal of High Energy Astro- physics7, 148 (2015), arXiv:1505.01093 [astro-ph.HE]

    S. Komossa, Tidal disruption of stars by supermassive black holes: Status of observations, Journal of High Energy Astro- physics7, 148 (2015), arXiv:1505.01093 [astro-ph.HE]

    2015 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.