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arxiv: 2606.06557 · v1 · pith:65ETIXEOnew · submitted 2026-06-04 · 🌀 gr-qc · astro-ph.CO· astro-ph.HE

Robustness of the relativistic intermediate-axis instability around dark-matter-dressed rotating black holes

Mohsen Fathi This is my paper

Pith reviewed 2026-06-28 00:36 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COastro-ph.HE
keywords dark matterrotating black holesintermediate-axis instabilityflip frequencyeffective response modelrelativistic effectsEinasto profileNavarro-Frenk-White profile
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The pith

Dark matter normalization decreases the flip frequency of relativistic intermediate-axis instability relative to Kerr.

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

The paper examines how dark matter profiles around rotating black holes influence the relativistic version of the intermediate-axis instability. It employs a controlled effective response model to scan variations in DM normalization, profile extent, and other parameters, tracking changes in the frequency at which a coherent matter element flips its orientation. The results establish a perturbative response where greater enclosed DM lowers this frequency compared with the pure Kerr case, while more extended profiles dampen the effect. This positions the flip frequency as a diagnostic timescale sensitive to the local DM environment.

Core claim

In the effective response model, increasing the enclosed dark matter normalization decreases the flip frequency relative to Kerr, while more extended profiles weaken the local response. This trend persists across Einasto and cored-NFW profiles (Hernquist as benchmark) in one- and two-dimensional parameter scans, profile-contrast maps, time-domain simulations, and timing-response diagnostics.

What carries the argument

The effective response model (ERM), which isolates the flip frequency as an orientation-modulation timescale responding to changes in the dark-matter environment.

If this is right

  • Flip frequency decreases monotonically with rising DM normalization.
  • More extended DM profiles produce weaker shifts in the local response.
  • The same perturbative ordering appears for both Einasto and cored-NFW distributions.
  • The flip frequency functions as a controlled DM-sensitive orientation clock.
  • Local projected-emissivity proxies track the same DM-induced changes.

Where Pith is reading between the lines

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

  • If the frequency shift survives in more complete dynamical models, it could serve as an indirect timing signature of DM in accreting systems.
  • Combining the frequency diagnostic with independent mass or spin measurements might help discriminate among DM density profiles.
  • The approach invites direct comparison against observed quasi-periodic signals once the model is embedded in radiative-transfer calculations.

Load-bearing premise

The effective response model captures the essential dynamics of the instability well enough that its frequency response to dark-matter variations can be treated as a reliable diagnostic without full accretion simulations.

What would settle it

A full general-relativistic magnetohydrodynamic simulation of a non-axisymmetric matter element in a dark-matter-dressed Kerr spacetime that shows no systematic drop in flip frequency as enclosed DM normalization is increased would falsify the reported trend.

read the original abstract

DARK-FLIP I introduced a semi-analytical and Python-based framework for studying a relativistic version of the intermediate-axis instability (IAI) of a coherent non-axisymmetric matter element around rotating black holes dressed by dark matter (DM). In this second paper I test the robustness of that idea. The main question is simple: if the local environment is changed by the DM profile, how does the flip frequency respond? To answer this, I use a controlled effective response model (ERM), not a full accretion or radiative-transfer simulation. The flip frequency is therefore treated as a diagnostic orientation-modulation timescale, not as a direct quasi-periodic oscillation (QPO) model. I vary the DM normalization, profile scale radius, intermediate principal moment of inertia, effective tidal coupling, initial perturbation, and initial orientation. Einasto and regularized cored Navarro--Frenk--White (cored-NFW) profiles are used as the main DM models, while Hernquist is kept as a control benchmark. The analysis includes one-dimensional scans, two-dimensional response maps, profile-contrast maps, time-domain flip simulations, a profile timing-response diagnostic, and a local projected-emissivity proxy. The results show a clear perturbative trend: increasing the enclosed DM normalization decreases the flip frequency relative to Kerr, while more extended profiles weaken the local response. DARK-FLIP II therefore strengthens the interpretation of the flip frequency as a controlled DM-sensitive orientation clock.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper extends DARK-FLIP I by introducing a controlled effective response model (ERM) to test robustness of the relativistic intermediate-axis instability flip frequency to dark-matter (DM) variations around rotating black holes. Using Einasto, cored-NFW, and Hernquist profiles, it performs one-dimensional parameter scans, two-dimensional response maps, profile-contrast maps, time-domain simulations, a profile timing-response diagnostic, and a local projected-emissivity proxy while varying DM normalization, scale radius, principal moments, tidal coupling, and initial conditions. The central result is a perturbative trend: increasing enclosed DM normalization decreases flip frequency relative to Kerr, while more extended profiles weaken the local response. The flip frequency is treated explicitly as a diagnostic orientation-modulation timescale rather than a direct QPO model.

Significance. If the ERM faithfully reproduces the essential relativistic dynamics, the controlled parameter study would supply a semi-analytical route to DM-sensitive diagnostics near galactic-center black holes. The systematic use of multiple diagnostics and profile contrasts constitutes a clear methodological strength. At present, however, the absence of any validation that the ERM recovers the pure-Kerr limit or follows from the geodesic/Euler equations in the DM-dressed metric confines the significance to an internal exploration of one particular effective model.

major comments (3)
  1. [Section introducing and defining the effective response model (ERM)] The manuscript states that the ERM is employed 'not [as] a full accretion or radiative-transfer simulation' and that the flip frequency is only a 'diagnostic orientation-modulation timescale.' No derivation is supplied showing that the ERM equations follow from the geodesic or Euler equations in the DM-dressed metric, and no explicit check is reported that the ERM recovers the pure-Kerr IAI frequency from DARK-FLIP I when the DM component is switched off. Because every reported trend (including the decrease in flip frequency with increasing DM normalization) is generated inside this unvalidated model, the central claim that the trends are robust DM-induced effects rests on an untested assumption.
  2. [Sections presenting the one-dimensional scans, two-dimensional response maps, and profile timing-response diagnostic] The one-dimensional scans and two-dimensional response maps that underpin the main perturbative trend contain no error bars, convergence tests with respect to numerical resolution or time-stepping, or sensitivity analysis to the free parameters of the ERM itself. Without these, it is impossible to determine whether the reported decrease in flip frequency with DM normalization is numerically stable or an artifact of the particular discretization or initial-condition choices.
  3. [Sections describing the time-domain flip simulations and local projected-emissivity proxy] The time-domain flip simulations and local projected-emissivity proxy are offered as supporting diagnostics, yet the manuscript does not quantify how orientation-dependent back-reaction or metric perturbations induced by the non-axisymmetric element (omitted by construction in the ERM) would propagate into the reported flip-frequency shifts. This omission directly affects the load-bearing claim that extended profiles weaken the local response.
minor comments (1)
  1. The distinction between the ERM and a full simulation is stated once but could be reiterated in the figure captions of the response maps to prevent readers from over-interpreting the trends as direct predictions.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments correctly identify areas where the scope and numerical robustness of the effective response model (ERM) require clearer presentation. We address each major comment below and indicate the revisions that will be made.

read point-by-point responses

  1. Referee: [Section introducing and defining the effective response model (ERM)] The manuscript states that the ERM is employed 'not [as] a full accretion or radiative-transfer simulation' and that the flip frequency is only a 'diagnostic orientation-modulation timescale.' No derivation is supplied showing that the ERM equations follow from the geodesic or Euler equations in the DM-dressed metric, and no explicit check is reported that the ERM recovers the pure-Kerr IAI frequency from DARK-FLIP I when the DM component is switched off. Because every reported trend (including the decrease in flip frequency with increasing DM normalization) is generated inside this unvalidated model, the central claim that the trends are robust DM-induced effects rests on an untested assumption.

    Authors: The ERM is constructed as a controlled effective model to isolate the response of the flip frequency to variations in DM profiles, building directly on the Kerr results of DARK-FLIP I. We agree that an explicit recovery check is necessary to substantiate the perturbative interpretation. In the revised manuscript we will add a dedicated validation subsection demonstrating that, in the limit of vanishing DM normalization, the ERM reproduces the intermediate-axis instability flip frequency reported in DARK-FLIP I. We will also expand the discussion of the model's assumptions and its phenomenological construction. A first-principles derivation from the geodesic or Euler equations in the DM-dressed metric is not claimed and lies outside the intended scope of this effective approach. revision: partial

  2. Referee: [Sections presenting the one-dimensional scans, two-dimensional response maps, and profile timing-response diagnostic] The one-dimensional scans and two-dimensional response maps that underpin the main perturbative trend contain no error bars, convergence tests with respect to numerical resolution or time-stepping, or sensitivity analysis to the free parameters of the ERM itself. Without these, it is impossible to determine whether the reported decrease in flip frequency with DM normalization is numerically stable or an artifact of the particular discretization or initial-condition choices.

    Authors: We accept the referee's point on numerical robustness. The revised manuscript will incorporate error bars obtained from ensembles of runs with varied initial conditions, convergence tests with respect to time-step size and spatial resolution, and a sensitivity analysis varying the principal moments and tidal-coupling parameter of the ERM. These additions will allow quantitative assessment of the stability of the reported trends. revision: yes

  3. Referee: [Sections describing the time-domain flip simulations and local projected-emissivity proxy] The time-domain flip simulations and local projected-emissivity proxy are offered as supporting diagnostics, yet the manuscript does not quantify how orientation-dependent back-reaction or metric perturbations induced by the non-axisymmetric element (omitted by construction in the ERM) would propagate into the reported flip-frequency shifts. This omission directly affects the load-bearing claim that extended profiles weaken the local response.

    Authors: The ERM is formulated, by design, to examine the local response within a fixed background metric and therefore omits orientation-dependent back-reaction and non-axisymmetric metric perturbations. A quantitative propagation analysis of these effects would require a self-consistent dynamical simulation that exceeds the scope of the present effective model, as already stated in the manuscript. We will revise the text to include an explicit discussion of this limitation and its implications for interpreting the weakening of the local response in extended profiles, thereby clarifying the domain of applicability of the reported trends. revision: partial

Circularity Check

2 steps flagged

Flip-frequency DM trends are internal outputs of the ERM from DARK-FLIP I

specific steps
  1. self citation load bearing [Abstract]
    "DARK-FLIP I introduced a semi-analytical and Python-based framework for studying a relativistic version of the intermediate-axis instability (IAI) of a coherent non-axisymmetric matter element around rotating black holes dressed by dark matter (DM). In this second paper I test the robustness of that idea. ... To answer this, I use a controlled effective response model (ERM), not a full accretion or radiative-transfer simulation. The flip frequency is therefore treated as a diagnostic orientation-modulation timescale"

    The robustness test and all DM-response trends rest on the ERM framework from the author's own prior paper; the central claim reduces to outputs of that self-cited construction without independent derivation or external validation shown here.

  2. fitted input called prediction [Abstract]
    "The results show a clear perturbative trend: increasing the enclosed DM normalization decreases the flip frequency relative to Kerr, while more extended profiles weaken the local response."

    The flip frequency is defined as a diagnostic inside the ERM; the reported decrease with DM normalization is produced by directly varying those same DM parameters inside the model, so the trend is a built-in output rather than an independent prediction.

full rationale

The paper's central result (DM normalization decreases flip frequency relative to Kerr; extended profiles weaken response) is generated by varying parameters inside the effective response model (ERM) introduced in the author's prior DARK-FLIP I work. The abstract explicitly frames the ERM as a controlled diagnostic tool rather than a derivation from geodesics or Euler equations, and no recovery of the pure-Kerr IAI frequency is reported. This reduces the reported sensitivity to a direct consequence of the model's internal structure and self-cited construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the validity of the effective response model introduced in the prior paper and on the assumption that flip frequency remains a faithful orientation-modulation diagnostic when DM is added; no new free parameters are introduced in this work but the model inherits any fitted quantities from DARK-FLIP I.

axioms (1)
  • domain assumption The effective response model accurately reproduces the orientation dynamics of the relativistic IAI without requiring full hydrodynamical or radiative simulations.
    Stated explicitly in the abstract as the methodological choice for the robustness test.

pith-pipeline@v0.9.1-grok · 5793 in / 1245 out tokens · 29499 ms · 2026-06-28T00:36:23.553299+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

105 extracted references · 75 canonical work pages · 1 internal anchor

  1. [1]

    Kerr, Phys

    R.P. Kerr, Phys. Rev. Lett.11, 237 (1963). DOI 10. 1103/PhysRevLett.11.237

    1963

  2. [2]

    Carter, Phys

    B. Carter, Phys. Rev.174, 1559 (1968). DOI 10.1103/ PhysRev.174.1559

    1968

  3. [3]

    M., Press, W

    J.M. Bardeen, W.H. Press, S.A. Teukolsky, Astrophys. J.178, 347 (1972). DOI 10.1086/151796

    work page doi:10.1086/151796 1972

  4. [4]

    Bardeen, inBlack Holes, ed

    J.M. Bardeen, inBlack Holes, ed. by C. DeWitt, B.S. DeWitt (Gordon and Breach, New York, 1973), pp. 215–239

    1973

  5. [5]

    Wilkins, Phys

    D.C. Wilkins, Phys. Rev. D5, 814 (1972). DOI 10. 1103/PhysRevD.5.814 Robustness of the relativistic intermediate-axis instability around dark-matter-dressed rotating black holes 13

    1972

  6. [6]

    Teukolsky, Astrophys

    S.A. Teukolsky, Astrophys. J.185, 635 (1973). DOI 10.1086/152444

    work page doi:10.1086/152444 1973

  7. [7]

    Chandrasekhar,The Mathematical Theory of Black Holes(Oxford University Press, Oxford, 1983)

    S. Chandrasekhar,The Mathematical Theory of Black Holes(Oxford University Press, Oxford, 1983)

    1983

  8. [8]

    Wald,General Relativity(University of Chicago Press, Chicago, 1984)

    R.M. Wald,General Relativity(University of Chicago Press, Chicago, 1984)

    1984

  9. [9]

    Misner, K.S

    C.W. Misner, K.S. Thorne, J.A. Wheeler,Gravitation (W. H. Freeman, San Francisco, 1973)

    1973

  10. [10]

    Synge, Mon

    J.L. Synge, Mon. Not. Roy. Astron. Soc.131, 463 (1966). DOI 10.1093/mnras/131.3.463

    work page doi:10.1093/mnras/131.3.463 1966

  11. [11]

    Luminet, Astron

    J.P. Luminet, Astron. Astrophys.75, 228 (1979)

    1979

  12. [12]

    Falcke, F

    H. Falcke, F. Melia, E. Agol, Astrophys. J. Lett.528, L13 (2000). DOI 10.1086/312423

    work page doi:10.1086/312423 2000

  13. [13]

    Bozza, Phys

    V . Bozza, Phys. Rev. D66, 103001 (2002). DOI 10. 1103/PhysRevD.66.103001

    2002

  14. [14]

    Perlick, Living Rev

    V . Perlick, Living Rev. Rel.7, 9 (2004). DOI 10.12942/ lrr-2004-9

    2004

  15. [15]

    Hioki, K.i

    K. Hioki, K.i. Maeda, Phys. Rev. D80, 024042 (2009). DOI 10.1103/PhysRevD.80.024042

    work page doi:10.1103/physrevd.80.024042 2009

  16. [16]

    Johannsen, D

    T. Johannsen, D. Psaltis, Astrophys. J.718, 446 (2010). DOI 10.1088/0004-637X/718/1/446

    work page doi:10.1088/0004-637x/718/1/446 2010

  17. [17]

    Bambi,Black Holes: A Laboratory for Testing Strong Gravity(Springer, Singapore, 2017)

    C. Bambi,Black Holes: A Laboratory for Testing Strong Gravity(Springer, Singapore, 2017). DOI 10.1007/978-981-10-4524-0

    work page doi:10.1007/978-981-10-4524-0 2017

  18. [18]

    Event Horizon Telescope Collaboration, Astrophys. J. Lett.875, L1 (2019). DOI 10.3847/2041-8213/ab0ec7

    work page doi:10.3847/2041-8213/ab0ec7 2019

  19. [19]

    Event Horizon Telescope Collaboration, Astrophys. J. Lett.875, L6 (2019). DOI 10.3847/2041-8213/ab1141

    work page doi:10.3847/2041-8213/ab1141 2019

  20. [20]

    Event Horizon Telescope Collaboration, Astrophys. J. Lett.930, L12 (2022). DOI 10.3847/2041-8213/ac6674

    work page doi:10.3847/2041-8213/ac6674 2022

  21. [21]

    Event Horizon Telescope Collaboration, Astrophys. J. Lett.930, L17 (2022). DOI 10.3847/2041-8213/ac6756

    work page doi:10.3847/2041-8213/ac6756 2022

  22. [22]

    Z. Xu, X. Hou, X. Gong, J. Wang, JCAP09, 038 (2018). DOI 10.1088/1475-7516/2018/09/038

    work page doi:10.1088/1475-7516/2018/09/038 2018

  23. [23]

    Z. Xu, X. Gong, S.N. Zhang, Phys. Rev. D101(2), 024029 (2020). DOI 10.1103/PhysRevD.101.024029

    work page doi:10.1103/physrevd.101.024029 2020

  24. [24]

    Jusufi, M

    K. Jusufi, M. Jamil, P. Salucci, T. Zhu, S. Haroon, Phys. Rev. D100(4), 044012 (2019). DOI 10.1103/ PhysRevD.100.044012

    2019

  25. [25]

    Cardoso, K

    V . Cardoso, K. Destounis, F. Duque, R.P. Macedo, A. Maselli, Phys. Rev. D105(6), L061501 (2022). DOI 10.1103/PhysRevD.105.L061501

    work page doi:10.1103/physrevd.105.l061501 2022

  26. [26]

    Adhikary et al

    E. Figueiredo, A. Maselli, V . Cardoso, Phys. Rev. D 107(10), 104033 (2023). DOI 10.1103/PhysRevD.107. 104033

    work page doi:10.1103/physrevd.107 2023

  27. [27]

    Konoplya, A

    R.A. Konoplya, A. Zhidenko, Astrophys. J.933(2), 166 (2022). DOI 10.3847/1538-4357/ac75b0

    work page doi:10.3847/1538-4357/ac75b0 2022

  28. [28]

    ‘Solar neutrino measurements using the full data period of Super- Kamiokande-IV’

    N. Speeney, E. Berti, V . Cardoso, A. Maselli, Phys. Rev. D109, 084068 (2024). DOI 10.1103/PhysRevD.109. 084068

    work page doi:10.1103/physrevd.109 2024

  29. [29]

    D. Liu, Y . Yang, Z. Xu, Z.W. Long, Eur. Phys. J. C84, 136 (2024). DOI 10.1140/epjc/s10052-024-12492-4

    work page doi:10.1140/epjc/s10052-024-12492-4 2024

  30. [30]

    Y . Yang, D. Liu, A. Övgün, G. Lambiase, Z.W. Long, Eur. Phys. J. C84, 63 (2024). DOI 10.1140/epjc/ s10052-024-12363-4

    work page doi:10.1140/epjc/ 2024

  31. [31]

    S.R. Wu, B.Q. Wang, Z.W. Long, H. Chen, Phys. Dark Univ.44, 101455 (2024). DOI 10.1016/j.dark.2024. 101455

    work page doi:10.1016/j.dark.2024 2024

  32. [32]

    Zeng, C.Y

    X.X. Zeng, C.Y . Yang, M. Israr Aslam, R. Saleem, S. Aslam, Journal of Cosmology and Astroparticle Physics2025(08), 066 (2025). DOI 10.1088/1475-7516/2025/08/066. URL https://iopscience.iop.org/article/10. 1088/1475-7516/2025/08/066

    work page doi:10.1088/1475-7516/2025/08/066 2025

  33. [33]

    Z. Ma, Z. Xu, M. Tang, Eur. Phys. J. C85, 780 (2025). DOI 10.1140/epjc/s10052-025-14480-8

    work page doi:10.1140/epjc/s10052-025-14480-8 2025

  34. [34]

    Barausse, V

    E. Barausse, V . Cardoso, P. Pani, Phys. Rev. D89(10), 104059 (2014). DOI 10.1103/PhysRevD.89.104059

    work page doi:10.1103/physrevd.89.104059 2014

  35. [35]

    Goldstein, C.P

    H. Goldstein, C.P. Poole, J.L. Safko,Classical Mechan- ics, 3rd edn. (Addison-Wesley, San Francisco, 2002)

    2002

  36. [36]

    Landau, E.M

    L.D. Landau, E.M. Lifshitz,Mechanics, 3rd edn. (Butterworth-Heinemann, Oxford, 1976)

    1976

  37. [37]

    Arnold,Mathematical Methods of Classical Me- chanics, 2nd edn

    V .I. Arnold,Mathematical Methods of Classical Me- chanics, 2nd edn. (Springer, New York, 1989). DOI 10.1007/978-1-4757-2063-1

    work page doi:10.1007/978-1-4757-2063-1 1989

  38. [38]

    Borisov, I.S

    A.V . Borisov, I.S. Mamaev,Rigid Body Dynamics(De Gruyter, Berlin, 2001)

    2001

  39. [39]

    Shakura, R.A

    N.I. Shakura, R.A. Sunyaev, Astron. Astrophys.24, 337 (1973)

    1973

  40. [40]

    Novikov, K.S

    I.D. Novikov, K.S. Thorne, inBlack Holes, ed. by C. DeWitt, B.S. DeWitt (Gordon and Breach, New York, 1973), pp. 343–450

    1973

  41. [41]

    Thorne, Astrophys

    K.S. Thorne, Astrophys. J.191, 507 (1974). DOI 10.1086/152991

    work page doi:10.1086/152991 1974

  42. [42]

    Advection-dominated Accretion: A Self-similar Solution.Astrophys

    R. Narayan, I. Yi, Astrophys. J. Lett.428, L13 (1994). DOI 10.1086/187381

    work page doi:10.1086/187381 1994

  43. [43]

    D., & Znajek, R

    R.D. Blandford, R.L. Znajek, Mon. Not. Roy. Astron. Soc.179, 433 (1977). DOI 10.1093/mnras/179.3.433

    work page doi:10.1093/mnras/179.3.433 1977

  44. [44]

    Bardeen, J.A

    J.M. Bardeen, J.A. Petterson, Astrophys. J. Lett.195, L65 (1975). DOI 10.1086/181711

    work page doi:10.1086/181711 1975

  45. [45]

    Okazaki, S

    A.T. Okazaki, S. Kato, J. Fukue, Publ. Astron. Soc. Japan39, 457 (1987)

    1987

  46. [46]

    1365-2966.2003.07017.x

    A. Merloni, M. Vietri, L. Stella, D. Bini, Mon. Not. Roy. Astron. Soc.304, 155 (1999). DOI 10.1046/j. 1365-8711.1999.02291.x

    work page doi:10.1046/j 1999

  47. [47]

    M., White, S

    L. Rezzolla, S. Yoshida, T.J. Maccarone, O. Zanotti, Mon. Not. Roy. Astron. Soc.344, L37 (2003). DOI 10.1046/j.1365-8711.2003.07018.x

    work page doi:10.1046/j.1365-8711.2003.07018.x 2003

  48. [48]

    Schnittman, L

    J.D. Schnittman, L. Rezzolla, Astrophys. J.637, L113 (2006). DOI 10.1086/500722

    work page doi:10.1086/500722 2006

  49. [49]

    Fathi, DARK-FLIP I: Relativistic intermediate-axis instability around dark-matter-dressed rotating black holes (2026)

    M. Fathi, DARK-FLIP I: Relativistic intermediate-axis instability around dark-matter-dressed rotating black holes (2026). Submitted for publication

    2026

  50. [50]

    Stella, M

    L. Stella, M. Vietri, Phys. Rev. Lett.82, 17 (1999). DOI 10.1103/PhysRevLett.82.17 14 Mohsen Fathi

    work page doi:10.1103/physrevlett.82.17 1999

  51. [51]

    Nowak, J

    M.A. Nowak, J. Wilms, J.B. Dove, Astrophys. J.517, 355 (1999). DOI 10.1086/307184

    work page doi:10.1086/307184 1999

  52. [52]

    Abramowicz, W

    M.A. Abramowicz, W. Kluzniak, Astron. Astrophys. 374, L19 (2001). DOI 10.1051/0004-6361:20010791

    work page doi:10.1051/0004-6361:20010791 2001

  53. [53]

    Abramowicz, W

    M.A. Abramowicz, W. Kluzniak, Z. Stuchlik, G. Torok, Class. Quant. Grav.21, S595 (2004). DOI 10.1088/ 0264-9381/21/5/037

    2004

  54. [54]

    doi:10.1086/431174 , eprint =

    P. Casella, T. Belloni, L. Stella, Astrophys. J.629, 403 (2005). DOI 10.1086/431174

    work page doi:10.1086/431174 2005

  55. [55]

    Török, M.A

    G. Török, M.A. Abramowicz, W. Klu´ zniak, Z. Stuch- lík, Astron. Astrophys.436, 1 (2005). DOI 10.1051/ 0004-6361:20047115

    2005

  56. [56]

    Broadband reflection spectroscopy of MAXI J1535-571 using AstroSat: Estimation of black hole mass and spin

    R.A. Remillard, J.E. McClintock, Ann. Rev. Astron. Astrophys.44, 49 (2006). DOI 10.1146/annurev.astro. 44.051905.092532

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1146/annurev.astro 2006

  57. [57]

    van der Klis,Rapid X-ray variability(Cambridge University Press, 2006)

    M. van der Klis,Rapid X-ray variability(Cambridge University Press, 2006)

    2006

  58. [58]

    S. Kato, J. Fukue, S. Mineshige,Black-Hole Accretion Disks: Towards a New Paradigm(Kyoto University Press, Kyoto, 2008)

    2008

  59. [59]

    Ingram, C

    A. Ingram, C. Done, P.C. Fragile, Mon. Not. Roy. As- tron. Soc.397, L101 (2009). DOI 10.1111/j.1745-3933. 2009.00693.x

    work page doi:10.1111/j.1745-3933 2009

  60. [60]

    Belloni, L

    T. Belloni, L. Stella, Space Sci. Rev.183, 43 (2014). DOI 10.1007/s11214-014-0076-0

    work page doi:10.1007/s11214-014-0076-0 2014

  61. [61]

    Motta, T.M

    S.E. Motta, T.M. Belloni, L. Stella, T. Muñoz Darias, R. Fender, Mon. Not. Roy. Astron. Soc.437, 2554 (2014). DOI 10.1093/mnras/stt2068

    work page doi:10.1093/mnras/stt2068 2014

  62. [62]

    Pasham, T.E

    D.R. Pasham, T.E. Strohmayer, R.F. Mushotzky, Nature 513, 74 (2014). DOI 10.1038/nature13710

    work page doi:10.1038/nature13710 2014

  63. [63]

    Stuchlík, M

    Z. Stuchlík, M. Kološ, Mon. Not. Roy. Astron. Soc. 451, 2575 (2015). DOI 10.1093/mnras/stv1120

    work page doi:10.1093/mnras/stv1120 2015

  64. [64]

    Kaaret, H

    P. Kaaret, H. Feng, T.P. Roberts, Ann. Rev. As- tron. Astrophys.55, 303 (2017). DOI 10.1146/ annurev-astro-091916-055259

    2017

  65. [65]

    Strohmayer, R.F

    T.E. Strohmayer, R.F. Mushotzky, Astrophys. J. Lett. 586, L61 (2003). DOI 10.1086/374732

    work page doi:10.1086/374732 2003

  66. [66]

    2005, MNRAS, 364, 1105, doi:10.1111/j.1365-2966.2005.09655.x —

    P. Mucciarelli, P. Casella, T. Belloni, L. Zampieri, P. Ranalli, Mon. Not. Roy. Astron. Soc.365, 1123 (2006). DOI 10.1111/j.1365-2966.2005.09805.x

    work page doi:10.1111/j.1365-2966.2005.09805.x 2006

  67. [67]

    McClintock, R

    J.E. McClintock, R. Narayan, J.F. Steiner, Space Sci. Rev.183, 295 (2014). DOI 10.1007/ s11214-013-0003-9

    2014

  68. [68]

    , volume =

    J.F. Navarro, C.S. Frenk, S.D.M. White, Astrophys. J. 462, 563 (1996). DOI 10.1086/177173

    work page doi:10.1086/177173 1996

  69. [69]

    Navarro, C.S

    J.F. Navarro, C.S. Frenk, S.D.M. White, Astrophys. J. 490, 493 (1997). DOI 10.1086/304888

    work page doi:10.1086/304888 1997

  70. [70]

    Einasto, Trudy Astrofizicheskogo Instituta Alma-Ata 5, 87 (1965)

    J. Einasto, Trudy Astrofizicheskogo Instituta Alma-Ata 5, 87 (1965)

    1965

  71. [71]

    1990, ApJ, 356, 359, doi: 10.1086/168845

    L. Hernquist, Astrophys. J.356, 359 (1990). DOI 10.1086/168845

    work page doi:10.1086/168845 1990

  72. [72]

    Burkert, Astrophys

    A. Burkert, Astrophys. J. Lett.447, L25 (1995). DOI 10.1086/309560

    work page doi:10.1086/309560 1995

  73. [73]

    Gondolo, J

    P. Gondolo, J. Silk, Phys. Rev. Lett.83, 1719 (1999). DOI 10.1103/PhysRevLett.83.1719

    work page doi:10.1103/physrevlett.83.1719 1999

  74. [74]

    Ullio, H

    P. Ullio, H. Zhao, M. Kamionkowski, Phys. Rev. D64, 043504 (2001). DOI 10.1103/PhysRevD.64.043504

    work page doi:10.1103/physrevd.64.043504 2001

  75. [75]

    Sadeghian, F

    L. Sadeghian, F. Ferrer, C.M. Will, Phys. Rev. D88(6), 063522 (2013). DOI 10.1103/PhysRevD.88.063522

    work page doi:10.1103/physrevd.88.063522 2013

  76. [76]

    K. Eda, Y . Itoh, S. Kuroyanagi, J. Silk, Phys. Rev. Lett. 110, 221101 (2013). DOI 10.1103/PhysRevLett.110. 221101

    work page doi:10.1103/physrevlett.110 2013

  77. [77]

    Lacroix, Astron

    T. Lacroix, Astron. Astrophys.619, A46 (2018). DOI 10.1051/0004-6361/201832652

    work page doi:10.1051/0004-6361/201832652 2018

  78. [78]

    Kavanagh, D.A

    B.J. Kavanagh, D.A. Nichols, G. Bertone, D. Gaggero, Phys. Rev. D102(8), 083006 (2020). DOI 10.1103/ PhysRevD.102.083006

    2020

  79. [79]

    Ghez, et al., Astrophys

    A.M. Ghez, et al., Astrophys. J.689, 1044 (2008). DOI 10.1086/592738

    work page doi:10.1086/592738 2008

  80. [80]

    Gillessen, F

    S. Gillessen, F. Eisenhauer, S. Trippe, T. Alexander, R. Genzel, F. Martins, T. Ott, Astrophys. J.692, 1075 (2009). DOI 10.1088/0004-637X/692/2/1075

    work page doi:10.1088/0004-637x/692/2/1075 2009

Showing first 80 references.