Pith. sign in

REVIEW 4 minor 69 references

The paper argues that tidal transitions between saturated Kerr boson-cloud states are suppressed by up to 21.67% relative to hydrogenic estimates, with most of the effect coming from the radial profile of the Kerr quasibound modes.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-02 01:32 UTC pith:WAITWA6Q

load-bearing objection First relativistic quasibound-to-quasibound tidal matrix elements on saturated Kerr cloud branches; solid numerics, but the headline 21.67% sits outside the paper's own strict sample and the bilinear normalization deserves independent scrutiny.

arxiv 2607.14627 v1 pith:WAITWA6Q submitted 2026-07-16 astro-ph.GA gr-qchep-ph

Relativistic Tidal Transitions of Saturated Kerr Boson Clouds

Yi-kun Li This is my paper
classification astro-ph.GA gr-qchep-ph
keywords Kerr black holessuperradianceboson cloudsgravitational atomsquasibound modestidal resonancesLandau-Zenermatrix elements
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Rotating black holes can grow macroscopic clouds of ultralight bosons, and a binary companion sweeping through the cloud's level spacings drives resonant transitions between its quantum states. Most calculations model these clouds as hydrogenic atoms, but the paper argues that the Kerr geometry deforms the cloud's bound states enough to change the transition amplitudes by as much as 21.67% on the saturated |211⟩, |322⟩, and |433⟩ branches. Most of that change comes from the radial shape of the cloud modes, not from relativistic corrections to the tidal field itself. If the calculation is right, binary-history models that use hydrogenic amplitudes are off at the ten-percent level, and the predicted depletion of a cloud at an intermediate-speed resonance crossing changes by up to 13.7%.

Core claim

The central claim is that hydrogenic wave functions are not accurate enough for tidal transitions between superradiantly saturated Kerr boson clouds. Using exact Kerr quasibound modes normalized by the conserved bilinear form and an adiabatic quadrupolar Kerr tidal field, the paper finds that the relativistic matrix element is smaller than the hydrogenic value across all five Δm = -2 channels, with the largest suppression 21.67% for |322⟩→|320⟩. A component-resolved decomposition attributes 78.7–82.5% of the logarithmic suppression to the radial mode profile and 13.3–16.2% to the bilinear normalization, while the Kerr tidal geometry contributes only 0.031–0.207%. The result survives exact Ne

What carries the argument

The load-bearing object is the conserved bilinear form ⟨⟨Φp,Φq⟩⟩, built from the t–φ reflection and defined by analytic continuation of the radial coordinate through the near-horizon region; it supplies the orthogonality and normalization for Kerr quasibound modes that the usual L² inner product cannot. Around this sit the massive-scalar continued-fraction solutions for the quasibound frequencies and wave functions, the adiabatic Kerr quadrupole perturbation in ingoing radiation gauge, and the two-level Landau–Zener formula that converts the matrix element into a depletion probability.

Load-bearing premise

The load-bearing premise is that the way the paper defines the size of a transition—using a special conserved inner product that requires analytic continuation through the region near the black hole's horizon—is the right one; if that definition is subtly wrong, every reported percentage shifts.

What would settle it

Run a time-domain numerical evolution of the massive scalar field in a tidally perturbed Kerr spacetime and extract the |322⟩→|320⟩ transition amplitude at α = 0.35, where the paper predicts a -13.24% correction relative to hydrogenic; agreement within the quoted numerical and multipole uncertainties would support the claim, and disagreement beyond them would falsify it.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The hydrogenic approximation understates the suppression of the five corotating Δm = -2 transitions, by up to 21.67% for |322⟩→|320⟩.
  • The correction is not a small tidal-geometry effect: the radial Kerr mode profile drives 78.7–82.5% of the logarithmic change, and the relativistic tidal metric contributes under 0.21%.
  • Corrections above 10% survive conservative cuts (99% of the cloud within 7% of the orbital separation), so they are not an artifact of pushing the cloud to the edge of the tidal region.
  • For intermediate Landau–Zener crossings, the corrected matrix elements change cloud depletion by up to 13.7%; the largest effect occurs where depletion is neither negligible nor saturated.
  • Resonance calculations for saturated clouds should therefore use relativistic Kerr quasibound modes rather than hydrogenic wave functions when aiming for ten-percent-level accuracy.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Extension: the same machinery could be applied to higher-n clouds or to Proca (vector) clouds, whose near-horizon boundary conditions are even stronger; the radial-profile dominance suggests the corrections may be at least as large there.
  • Extension: a fully self-consistent binary evolution that tracks the surviving cloud level through a sequence of resonances could turn the 13.7% depletion shift into a measurable change in gravitational-wave dephasing, which this paper's fixed-inspiral illustration does not attempt.
  • Extension: the absolute normalization rests on the near-horizon analytic continuation; an independent time-domain evolution of the massive scalar on a tidally perturbed Kerr background would provide a direct check of that normalization.
  • Extension: since the radial profile dominates and higher multipoles are sub-percent, the practical path to improved binary-cloud models is better bound-state wave functions rather than higher-order tidal multipoles.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 4 minor

Summary. This paper computes relativistic quadrupole tidal transition matrix elements for five Δm = −2 channels among saturated Kerr scalar boson clouds (|211⟩, |322⟩, |433⟩ saturation branches). The calculation combines finite-α Kerr quasibound modes from Leaver's continued fraction, the conserved bilinear normalization of Ref. [41], and an adiabatic Kerr quadrupole perturbation in ingoing radiation gauge. The central result is a systematic comparison with the usual hydrogenic gravitational-atom matrix element: the relativistic amplitude is suppressed by up to 21.67%, corrections above 10% survive in a conservative r99/b ≤ 0.07 sample, a component-resolved decomposition attributes most of the effect to the radial mode profile, and the corrected Landau–Zener depletion differs by up to 13.7% at intermediate adiabaticity. Robustness is addressed with exact Newtonian multipoles through l = 10, an independent complex-contour radial construction, resolution studies, and a Schwarzschild-limit comparison with Ref. [41].

Significance. If the numbers are correct, this is a useful and timely correction to the gravitational-atom literature: it shows that hydrogenic wavefunctions misestimate saturated-cloud transition amplitudes at the 10–20% level in observationally relevant regimes, and it provides a clean hierarchy (radial profile, then bilinear normalization, with tidal geometry subdominant) that can guide future approximations. The paper is unusually well cross-checked: the code and numerical data are released, the independent contour construction and exact Newtonian multipole sum bound different classes of error, and the hydrogenic and Schwarzschild limits provide external anchors. The stress-test concern about a common-mode error in the bilinear normalization is a legitimate epistemic caveat, but on reading the paper it does not land as a demonstrated defect: the two numerical constructions differ in radial representation, and the hydrogenic-limit and Schwarzschild comparisons supply independent limits. The remaining risk is the generic one that any calculation built on a single normalization framework carries, not a specific internal inconsistency in this manuscript.

minor comments (4)
  1. [Sec. V.B vs. Appendix E] Please reconcile the quoted agreement between the central and independent radial constructions. Sec. V.B states the five Kerr matrix elements agree in amplitude to at worst 3.24e-06, while Appendix E says these same elements agree with the central values within 5e-3 in magnitude and phase. If the 5e-3 number includes the contour-deformation envelope (2e-3) or other variations, this should be stated explicitly; as written, the two numbers appear inconsistent.
  2. [Eq. (11)] The Ward-identity expression K_fi[L_ξ g] = (ω_i − ω_f − (m_i − m_f)Ω) B_fi[ξ] introduces the boundary functional B_fi without a definition. A one-sentence definition in Appendix C (e.g., the boundary integral produced by integration by parts before compact support is invoked) would make the identity checkable.
  3. [Eq. (12)] Please specify precisely what the 'hydrogenic' benchmark KH contains. The sentence 'The same exact frequencies and saturation spin are used in the last two layers' leaves open whether KH uses hydrogenic frequencies and no saturation spin, or exact frequencies applied to hydrogenic modes. This matters for interpreting the component-resolved 'frequency' contribution in Eq. (13).
  4. [Abstract and Table II] The abstract's 'as much as 21.67%' and the later statement that corrections above 10% persist at r99/b ≤ 0.07 should be connected explicitly. The 21.67% maximum occurs in the r99/b ≤ 0.10 domain; under the stricter r99/b ≤ 0.07 criterion in Table II the largest suppression is 15.15% (|322⟩→|320⟩, α = 0.375). This is not an error, but stating it directly would avoid an over-reading of the headline number.

Circularity Check

0 steps flagged

No significant circularity: corrections computed forward from independent inputs and checked externally.

full rationale

The paper's central claim is a forward comparison of transition matrix elements computed with Kerr quasibound modes versus hydrogenic modes (Eqs. 9 and 12). The 21.67% suppression is not fitted or defined by the hydrogenic result: frequencies come from the massive-scalar continued fraction (Appendix A), the normalization is fixed by the conserved bilinear form (Eq. 5, Appendix B), and the tidal operator is the independently published adiabatic Kerr quadrupole (Eq. 8, Ref. [47]). The component decomposition in Eq. (13) is explicitly an explanatory accounting whose contributions sum to the total by construction, not a separate fitted prediction. The Landau-Zener depletion change in Eq. (17) is a mathematical consequence of z proportional to |K|^2, not a circular reuse of the correction. Internal consistency checks and the Schwarzschild comparison to Ref. [41], an external work, provide independent support. The only self-reference is the data record [69], which carries no load. The skeptic's common-mode-error concern is a correctness risk, not circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 6 axioms · 0 invented entities

No new entities and no fitted physical constants. The computation scans physical parameters (α, q) and solves for χ_sat from Eq. (2); the only hand-chosen inputs are convergence thresholds and validity-window criteria, which do not enter the integrals. Six axioms carry the calculation; the bilinear-normalization axiom is the most consequential and is the chosen weakest assumption.

free parameters (1)
  • tidal-validity thresholds (r99/b ≤ 0.10 survey, ≤ 0.07 strict; MΩ_res ≤ 1e-2)
    Hand-chosen inclusion criteria defining which α–q points are presented as robust (Tables I-II, Fig. 5). They do not enter the matrix-element integrals but set the validity domain of the headline numbers: 21.67% is the maximum inside the looser window, while the strict window peaks at 15.15%.
axioms (6)
  • domain assumption Quasibound modes are orthonormalized with the conserved symplectic bilinear form ⟨⟨Φp,Φq⟩⟩, evaluated by analytic continuation of the radial coordinate through the near-horizon region (Eq. 5, Appendix B).
    Adopted from Refs. [41,42]; every matrix element in the paper is defined through it. The paper validates it internally and against the Schwarzschild limit, but it is the least familiar premise and the most consequential.
  • domain assumption The cloud is a single scalar mode evaluated on its saturation branch, Re ω_i(α, χ_sat) = m_i Ω_H(χ_sat) (Eq. 2).
    Scoping stated in the title; selects the evaluation point on each branch. A cloud encountered before or after saturation would have different mode profiles and possibly different corrections.
  • domain assumption The companion's tide is an adiabatic quadrupolar perturbation in ingoing radiation gauge with helical phase e^{−2i(φ−Ωv)} (Eq. 8), valid for r99/b ≤ 0.10 and MΩ_res ≤ 1e-2.
    Tidal geometry taken from Ref. [47]; higher Newtonian multipoles through l=10 are checked (Fig. 5b) and shift results by ≤0.085%; the paper restricts its claims to this window.
  • domain assumption Resonant depletion is described by the two-level Landau–Zener formula with a prescribed Newtonian or 1PN chirp (Eqs. 15-16).
    Standard in the gravitational-atom literature [29,51-53]; the paper explicitly calls it a 'local use' and disclaims self-consistent orbit, backreaction, and multi-level effects.
  • standard math Leaver's continued fraction converges for massive scalar quasibound modes, and the spheroidal eigenvalue branch is followed continuously (Eq. A4, Appendix A).
    Background numerical method from Refs. [7,49,50]; convergence is validated internally by increasing series order.
  • standard math The on-resonance matrix element is invariant under compact-support gauge transformations (Ward identity, Eqs. 10-11, Appendix C).
    Derived in the paper from scalar covariance; it justifies the helical-phase prescription and the gauge choice of the tidal metric.

pith-pipeline@v1.3.0-alltime-deepseek · 15711 in / 20221 out tokens · 200640 ms · 2026-08-02T01:32:22.186377+00:00 · methodology

0 comments
read the original abstract

Rotating black holes can bind ultralight bosons in macroscopic clouds whose level structure is swept by the tidal field of a binary companion. Existing estimates of the resulting resonant transitions have largely used hydrogenic wave functions, even where the cloud grows most efficiently and the Kerr geometry appreciably deforms its quasibound states. I compute tidal transition matrix elements on the numerically determined saturation branches of the $|211\rangle$, $|322\rangle$, and $|433\rangle$ clouds. The calculation combines Kerr quasibound modes, their relativistic bilinear normalization, and an adiabatic uadrupolar perturbation of the Kerr metric. Across five $\Delta m=-2$ channels, the relativistic matrix element differs from its hydrogenic value by as much as $21.67\%$. Corrections above $10\%$ persist when $99\%$ of the cloud lies within $7\%$ of the orbital separation. A component-resolved comparison attributes $78.7-82.5\%$ of the logarithmic change to the radial mode profile and $13.3-16.2\%$ to the bilinear normalization; the relativistic tidal geometry supplies a smaller additional correction. Exact Newtonian multipoles and an independent complex-contour construction confirm the quadrupole matrix elements. For resonances with intermediate Landau--Zener adiabaticity, the corrected matrix elements change the predicted cloud depletion by up to $13.7\%$. Relativistic cloud structure is therefore quantitatively important for binary histories that cross saturated-cloud resonances.

Figures

Figures reproduced from arXiv: 2607.14627 by Yi-kun Li.

Figure 1
Figure 1. Figure 1: FIG. 1. Physical setting and selected transitions. (a) A saturated Kerr black hole is surrounded by a scalar cloud and perturbed [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Saturation and resonance scales. (a) Numerically determined saturation spins for the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Relativistic transition spectrum. (a) Fractional change of the Kerr-tide matrix element relative to the hydrogenic [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Physical origin of the relativistic correction at eight selected samples. (a) Order-averaged contributions of the radial [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Spatial validity and higher tidal multipoles. (a) Range of [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Absolute change in Landau–Zener depletion produced by the relativistic matrix element. Filled circles lie within [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

69 extracted references · 54 linked inside Pith

  1. [1]

    Y. B. Zel’dovich, Generation of waves by a rotating body, JETP Lett.14, 180 (1971)

    1971

  2. [2]

    W. H. Press and S. A. Teukolsky, Floating orbits, super- radiant scattering and the black-hole bomb, Nature238, 211 (1972)

    1972

  3. [3]

    S. A. Teukolsky, Rotating black holes - separable wave equations for gravitational and electromagnetic perturba- tions, Phys. Rev. Lett.29, 1114 (1972)

    1972

  4. [4]

    S. A. Teukolsky, Perturbations of a rotating black hole. 1. Fundamental equations for gravitational electromagnetic and neutrino field perturbations, Astrophys. J.185, 635 (1973)

    1973

  5. [5]

    S. A. Teukolsky and W. H. Press, Perturbations of a rotating black hole. III - Interaction of the hole with gravitational and electromagnet ic radiation, Astrophys. J.193, 443 (1974)

    1974

  6. [6]

    S. L. Detweiler, Klein-Gordon equation and rotating black holes, Phys. Rev. D22, 2323 (1980)

    1980

  7. [7]

    S. R. Dolan, Instability of the massive Klein-Gordon field on the Kerr spacetime, Phys.Rev.D76, 084001 (2007), arXiv:0705.2880 [gr-qc]

    Pith/arXiv arXiv 2007

  8. [8]

    Arvanitaki, S

    A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, and J. March-Russell, String Axiverse, Phys. Rev.D81, 123530 (2010), arXiv:0905.4720 [hep-th]

    Pith/arXiv arXiv 2010

  9. [9]

    Arvanitaki and S

    A. Arvanitaki and S. Dubovsky, Exploring the String Axiverse with Precision Black Hole Physics, Phys.Rev. D83, 044026 (2011), arXiv:1004.3558 [hep-th]

    Pith/arXiv arXiv 2011

  10. [10]

    Brito, V

    R. Brito, V. Cardoso, and P. Pani,Superradiance: New Frontiers in Black Hole Physics, Vol. 906 (Springer, 2015) arXiv:1501.06570 [gr-qc]

    Pith/arXiv arXiv 2015

  11. [11]

    Brito, V

    R. Brito, V. Cardoso, and P. Pani, Black holes as particle detectors: evolution of superradiant instabilities, Class. Quant. Grav.32, 134001 (2015), arXiv:1411.0686 [gr-qc]

    Pith/arXiv arXiv 2015

  12. [12]

    Cardoso, O

    V. Cardoso, O. J. Dias, G. S. Hartnett, M. Middleton, P. Pani, and J. E. Santos, Constraining the mass of dark photons and axion-like particles through black-hole super- radiance, JCAP03(03), 043, arXiv:1801.01420 [gr-qc]

    Pith/arXiv arXiv

  13. [13]

    Baryakhtar, R

    M. Baryakhtar, R. Lasenby, and M. Teo, Black Hole Superradiance Signatures of Ultralight Vectors, Phys. Rev. D96, 035019 (2017), arXiv:1704.05081 [hep-ph]

    Pith/arXiv arXiv 2017

  14. [14]

    Brito, S

    R. Brito, S. Ghosh, E. Barausse, E. Berti, V. Cardoso, I. Dvorkin, A. Klein, and P. Pani, Stochastic and resolv- able gravitational waves from ultralight bosons, Phys. Rev. Lett.119, 131101 (2017), arXiv:1706.05097 [gr-qc]

    Pith/arXiv arXiv 2017

  15. [15]

    Brito, S

    R. Brito, S. Ghosh, E. Barausse, E. Berti, V. Cardoso, I. Dvorkin, A. Klein, and P. Pani, Gravitational wave searches for ultralight bosons with LIGO and LISA, Phys. Rev. D96, 064050 (2017), arXiv:1706.06311 [gr-qc]

    Pith/arXiv arXiv 2017

  16. [16]

    O. A. Hannuksela, K. W. K. Wong, R. Brito, E. Berti, and T. G. F. Li, Probing the existence of ultralight bosons with a single gravitational-wave measurement, Nature As- tron. 10.1038/s41550-019-0712-4 (2019), arXiv:1804.09659 [astro-ph.HE]

    Pith/arXiv arXiv 2019

  17. [17]

    M. Isi, L. Sun, R. Brito, and A. Melatos, Directed searches for gravitational waves from ultralight bosons, Phys. Rev. D99, 084042 (2019), [Erratum: Phys.Rev.D 102, 049901 (2020)], arXiv:1810.03812 [gr-qc]

    Pith/arXiv arXiv 2019

  18. [18]

    Siemonsen and W

    N. Siemonsen and W. E. East, Gravitational wave signa- tures of ultralight vector bosons from black hole superradi- ance, Phys. Rev. D101, 024019 (2020), arXiv:1910.09476 [gr-qc]

    Pith/arXiv arXiv 2020

  19. [19]

    Siemonsen, T

    N. Siemonsen, T. May, and W. E. East, Modeling the black hole superradiance gravitational waveform, Phys. Rev. D107, 104003 (2023), arXiv:2211.03845 [gr-qc]

    Pith/arXiv arXiv 2023

  20. [20]

    Tsukada, R

    L. Tsukada, R. Brito, W. E. East, and N. Siemonsen, Modeling and searching for a stochastic gravitational-wave background from ultralight vector bosons, Phys. Rev. D 103, 083005 (2021), arXiv:2011.06995 [astro-ph.HE]

    Pith/arXiv arXiv 2021

  21. [21]

    Yoshino and H

    H. Yoshino and H. Kodama, Bosenova collapse of axion cloud around a rotating black hole, Prog. Theor. Phys. 128, 153 (2012), arXiv:1203.5070 [gr-qc]

    Pith/arXiv arXiv 2012

  22. [22]

    Witek, V

    H. Witek, V. Cardoso, A. Ishibashi, and U. Sperhake, Superradiant instabilities in astrophysical systems, Phys. Rev. D87, 043513 (2013), arXiv:1212.0551 [gr-qc]

    Pith/arXiv arXiv 2013

  23. [23]

    S. R. Dolan, Superradiant instabilities of rotating black holes in the time domain, Phys.Rev.D87, 124026 (2013), arXiv:1212.1477 [gr-qc]

    Pith/arXiv arXiv 2013

  24. [24]

    P. Pani, V. Cardoso, L. Gualtieri, E. Berti, and A. Ishibashi, Black hole bombs and photon mass bounds, Phys. Rev. Lett.109, 131102 (2012), arXiv:1209.0465 [gr-qc]

    Pith/arXiv arXiv 2012

  25. [25]

    S. R. Dolan, Instability of the Proca field on Kerr space- time, Phys. Rev.D98, 104006 (2018), arXiv:1806.01604 [gr-qc]. 12

    Pith/arXiv arXiv 2018

  26. [26]

    Percival and S

    J. Percival and S. R. Dolan, Quasinormal modes of massive vector fields on the Kerr spacetime, Phys. Rev. D102, 104055 (2020), arXiv:2008.10621 [gr-qc]

    Pith/arXiv arXiv 2020

  27. [27]

    Baryakhtar, M

    M. Baryakhtar, M. Galanis, R. Lasenby, and O. Simon, Black hole superradiance of self-interacting scalar fields, Phys. Rev. D103, 095019 (2021), arXiv:2011.11646 [hep- ph]

    Pith/arXiv arXiv 2021

  28. [28]

    Baumann, H

    D. Baumann, H. S. Chia, and R. A. Porto, Probing Ul- tralight Bosons with Binary Black Holes, Phys. Rev. D 99, 044001 (2019), arXiv:1804.03208 [gr-qc]

    Pith/arXiv arXiv 2019

  29. [29]

    Baumann, H

    D. Baumann, H. S. Chia, R. A. Porto, and J. Stout, Gravitational Collider Physics, Phys. Rev. D101, 083019 (2020), arXiv:1912.04932 [gr-qc]

    Pith/arXiv arXiv 2020

  30. [30]

    Baumann, G

    D. Baumann, G. Bertone, J. Stout, and G. M. Tomaselli, Ionization of gravitational atoms, Phys. Rev. D105, 115036 (2022), arXiv:2112.14777 [gr-qc]

    Pith/arXiv arXiv 2022

  31. [31]

    Baumann, G

    D. Baumann, G. Bertone, J. Stout, and G. M. Tomaselli, Sharp Signals of Boson Clouds in Black Hole Bi- nary Inspirals, Phys. Rev. Lett.128, 221102 (2022), arXiv:2206.01212 [gr-qc]

    Pith/arXiv arXiv 2022

  32. [32]

    Baumann, H

    D. Baumann, H. S. Chia, J. Stout, and L. ter Haar, The Spectra of Gravitational Atoms, JCAP1912(12), 006, arXiv:1908.10370 [gr-qc]

    Pith/arXiv arXiv 1908

  33. [33]

    Berti, R

    E. Berti, R. Brito, C. F. B. Macedo, G. Raposo, and J. L. Rosa, Ultralight boson cloud depletion in binary systems, Phys. Rev. D99, 104039 (2019), arXiv:1904.03131 [gr-qc]

    Pith/arXiv arXiv 2019

  34. [34]

    Cardoso, F

    V. Cardoso, F. Duque, and T. Ikeda, Tidal effects and disruption in superradiant clouds: a numerical investiga- tion, Phys. Rev. D101, 064054 (2020), arXiv:2001.01729 [gr-qc]

    Pith/arXiv arXiv 2020

  35. [35]

    X. Tong, Y. Wang, and H.-Y. Zhu, Termination of super- radiance from a binary companion, Phys. Rev. D106, 043002 (2022), arXiv:2205.10527 [gr-qc]

    Pith/arXiv arXiv 2022

  36. [36]

    Takahashi, H

    T. Takahashi, H. Omiya, and T. Tanaka, Evolution of binary systems accompanying axion clouds in extreme mass ratio inspirals, Phys. Rev. D107, 103020 (2023), arXiv:2301.13213

    Pith/arXiv arXiv 2023

  37. [37]

    G. M. Tomaselli, T. F. M. Spieksma, and G. Bertone, Dynamical friction in gravitational atoms, JCAP07(07), 070, arXiv:2305.15460 [gr-qc]

    Pith/arXiv arXiv

  38. [38]

    G. M. Tomaselli, T. F. M. Spieksma, and G. Bertone, Res- onant history of gravitational atoms in black hole binaries, Phys. Rev. D110, 064048 (2024), arXiv:2403.03147 [gr- qc]

    Pith/arXiv arXiv 2024

  39. [39]

    G. M. Tomaselli, Smooth binary evolution from wide resonances in boson clouds, Phys. Rev. D112, 063033 (2025), arXiv:2507.15110 [gr-qc]

    arXiv 2025

  40. [40]

    Boˇ skovi´ c, R

    M. Boˇ skovi´ c, R. A. Porto, and M. Koschnitzke, Trails of clouds in binary black holes, Phys. Rev. D113, 124053 (2026), arXiv:2512.17887 [gr-qc]

    arXiv 2026

  41. [41]

    Cannizzaro, L

    E. Cannizzaro, L. Sberna, S. R. Green, and S. Hol- lands, Relativistic Perturbation Theory for Black-Hole Boson Clouds, Phys. Rev. Lett.132, 051401 (2024), arXiv:2309.10021 [gr-qc]

    Pith/arXiv arXiv 2024

  42. [42]

    S. R. Green, S. Hollands, L. Sberna, V. Toomani, and P. Zimmerman, Conserved currents for a Kerr black hole and orthogonality of quasinormal modes, Phys. Rev. D 107, 064030 (2023), arXiv:2210.15935 [gr-qc]

    Pith/arXiv arXiv 2023

  43. [43]

    Cannizzaro, M

    E. Cannizzaro, M. Palleschi, L. Sberna, R. Brito, and S. R. Green, Excitation of scalar quasi-normal modes from boson clouds, Phys. Rev. D113, 083039 (2026), arXiv:2512.15878 [gr-qc]

    arXiv 2026

  44. [44]

    Yunes and J

    N. Yunes and J. A. Gonzalez, Metric of a tidally perturbed spinning black hole, Phys. Rev. D73, 024010 (2006), arXiv:gr-qc/0510076

    Pith/arXiv arXiv 2006

  45. [45]

    Poisson, Tidal deformation of a slowly rotating black hole, Phys

    E. Poisson, Tidal deformation of a slowly rotating black hole, Phys. Rev.D91, 044004 (2015), arXiv:1411.4711 [gr-qc]

    Pith/arXiv arXiv 2015

  46. [46]

    Landry and E

    P. Landry and E. Poisson, Tidal deformation of a slowly rotating material body. External metric, Phys. Rev.D91, 104018 (2015), arXiv:1503.07366 [gr-qc]

    Pith/arXiv arXiv 2015

  47. [47]

    Katagiri and V

    T. Katagiri and V. Cardoso, The relativistic restricted three-body problem: geometry and motion around tidally perturbed black holes, Phys. Rev. D113, 104036 (2026), arXiv:2601.14979 [gr-qc]

    Pith/arXiv arXiv 2026

  48. [48]

    Cocco, G

    M. Cocco, G. Grignani, T. Harmark, M. Orselli, D. Pere˜ niguez, and M. van de Meent, Tidal perturbations of an extreme mass ratio inspiral around a kerr black hole, Class. Quantum Grav. 10.1088/1361-6382/ae80b6 (2026), arXiv:2601.00954 [gr-qc]

    Pith/arXiv arXiv 2026

  49. [49]

    E. W. Leaver, An Analytic representation for the quasi normal modes of Kerr black holes, Proc. Roy. Soc. Lond. A402, 285 (1985)

    1985

  50. [50]

    Berti, V

    E. Berti, V. Cardoso, and M. Casals, Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions, Phys.Rev.D73, 024013 (2006), erratum: Phys. Rev. D 73, 109902 (2006), arXiv:gr- qc/0511111 [gr-qc]

    arXiv 2006

  51. [51]

    L. D. Landau, On the theory of transfer of energy at collisions ii, Phys. Z. Sowjetunion2, 46 (1932)

    1932

  52. [52]

    Zener, Non-adiabatic crossing of energy levels, Proc

    C. Zener, Non-adiabatic crossing of energy levels, Proc. R. Soc. A137, 696 (1932)

    1932

  53. [53]

    Blanchet, Gravitational Radiation from Post- Newtonian Sources and Inspiralling Compact Binaries, Living Rev

    L. Blanchet, Gravitational Radiation from Post- Newtonian Sources and Inspiralling Compact Binaries, Living Rev. Rel.17, 2 (2014), arXiv:1310.1528 [gr-qc]

    Pith/arXiv arXiv 2014

  54. [54]

    Cardoso, S

    V. Cardoso, S. Chakrabarti, P. Pani, E. Berti, and L. Gualtieri, Floating and sinking: The Imprint of mas- sive scalars around rotating black holes, Phys. Rev. Lett. 107, 241101 (2011), arXiv:1109.6021 [gr-qc]

    Pith/arXiv arXiv 2011

  55. [55]

    M. C. Ferreira, C. F. B. Macedo, and V. Cardoso, Orbital fingerprints of ultralight scalar fields around black holes, Phys. Rev.D96, 083017 (2017), arXiv:1710.00830 [gr-qc]

    Pith/arXiv arXiv 2017

  56. [56]

    Zhang and H

    J. Zhang and H. Yang, Dynamic Signatures of Black Hole Binaries with Superradiant Clouds, Phys. Rev. D101, 043020 (2020), arXiv:1907.13582 [gr-qc]

    Pith/arXiv arXiv 2020

  57. [57]

    Cardoso, K

    V. Cardoso, K. Destounis, F. Duque, R. Panosso Macedo, and A. Maselli, Gravitational Waves from Extreme-Mass- Ratio Systems in Astrophysical Environments, Phys. Rev. Lett.129, 241103 (2022), arXiv:2210.01133 [gr-qc]

    Pith/arXiv arXiv 2022

  58. [58]

    Brito and S

    R. Brito and S. Shah, Extreme mass-ratio inspirals into black holes surrounded by scalar clouds, Phys. Rev. D 108, 084019 (2023), [Erratum: Phys.Rev.D 110, 109902 (2024)], arXiv:2307.16093 [gr-qc]

    Pith/arXiv arXiv 2023

  59. [59]

    Duque, C

    F. Duque, C. F. B. Macedo, R. Vicente, and V. Cardoso, Extreme-Mass-Ratio Inspirals in Ultralight Dark Matter, Phys. Rev. Lett.133, 121404 (2024), arXiv:2312.06767 [gr-qc]

    Pith/arXiv arXiv 2024

  60. [60]

    Dyson, T

    C. Dyson, T. F. M. Spieksma, R. Brito, M. van de Meent, and S. Dolan, Environmental Effects in Extreme-Mass- Ratio Inspirals: Perturbations to the Environment in Kerr Spacetimes, Phys. Rev. Lett.134, 211403 (2025), arXiv:2501.09806 [gr-qc]

    Pith/arXiv arXiv 2025

  61. [61]

    D. Li, C. Weller, P. Bourg, M. LaHaye, N. Yunes, and H. Yang, Extreme mass-ratio inspiral within an ultralight scalar cloud: Scalar radiation, Phys. Rev. D112, 084057 (2025), arXiv:2507.02045 [gr-qc]

    Pith/arXiv arXiv 2025

  62. [62]

    Della Monica and R

    R. Della Monica and R. Brito, Detectability of gravita- tional atoms in black hole binaries with the Einstein Tele- 13 scope, Phys. Rev. D112, 024074 (2025), arXiv:2503.23419 [gr-qc]

    Pith/arXiv arXiv 2025

  63. [63]

    Audley, S

    H. Audley, S. Babak, J. Baker, E. Barausse, P. Bender, E. Berti, P. Binetruy, M. Born, D. Bortoluzzi, J. Camp, C. Caprini, V. Cardoso, M. Colpi, J. Conklin, N. Cornish, C. Cutler,et al., Laser Interferometer Space Antenna, ArXiv e-prints (2017), arXiv:1702.00786 [astro-ph.IM]

    Pith/arXiv arXiv 2017

  64. [64]

    Babak, J

    S. Babak, J. Gair, A. Sesana, E. Barausse, C. F. Sopuerta, C. P. L. Berry, E. Berti, P. Amaro-Seoane, A. Petiteau, and A. Klein, Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals, Phys. Rev.D95, 103012 (2017), arXiv:1703.09722 [gr-qc]

    Pith/arXiv arXiv 2017

  65. [65]

    Kocsis, N

    B. Kocsis, N. Yunes, and A. Loeb, Observable Signatures of EMRI Black Hole Binaries Embedded in Thin Accretion Disks, Phys. Rev. D84, 024032 (2011), arXiv:1104.2322 [astro-ph.GA]

    Pith/arXiv arXiv 2011

  66. [66]

    Yunes, B

    N. Yunes, B. Kocsis, A. Loeb, and Z. Haiman, Imprint of Accretion Disk-Induced Migration on Gravitational Waves from Extreme Mass Ratio Inspirals, Phys. Rev. Lett.107, 171103 (2011), arXiv:1103.4609 [astro-ph.CO]

    Pith/arXiv arXiv 2011

  67. [67]

    Speri, A

    L. Speri, A. Antonelli, L. Sberna, S. Babak, E. Barausse, J. R. Gair, and M. L. Katz, Probing Accretion Physics with Gravitational Waves, Phys. Rev. X13, 021035 (2023), arXiv:2207.10086 [gr-qc]

    Pith/arXiv arXiv 2023

  68. [68]

    P. S. Cole, G. Bertone, A. Coogan, D. Gaggero, T. Kary- das, B. J. Kavanagh, T. F. M. Spieksma, and G. M. Tomaselli, Distinguishing environmental effects on binary black hole gravitational waveforms, Nature Astron.7, 943 (2023), arXiv:2211.01362 [gr-qc]

    arXiv 2023

  69. [69]

    Li, Kerr boson-cloud tidal transitions: code and numerical data, Zenodo (2026)

    Y.-k. Li, Kerr boson-cloud tidal transitions: code and numerical data, Zenodo (2026)

    2026