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Probing the Distribution and Nature of Dark Matter Around Supermassive Black Holes from EMRI and IMRI Gravitational Waves

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Pith's one-line read Relativistic dark-matter halos around supermassive black holes measurably alter the gravitational-wave phase, cycle count, signal-to-noise ratio, and mismatch of extreme- and intermediate-mass-ratio inspirals, with the effect dominated by…

desk verdict Genuinely new application of exact Einstein-cloud spacetimes to EMRI/IMRI observables with sound conservative-sector derivations, but the headline mismatch detectability times are not reproducible because the SNR and noise calibration are never specified. read the letter →

arxiv 2608.12540 v1 pith:II6OYIL7 submitted 2026-08-12 gr-qc

Jared Fier , Farah Abdelshahed , Lilly Kowalczyk , Zhengfei Lyu , Anzhong Wang This is my paper · ORCID
classification gr-qc PACS 04.30.-w04.70.-s95.35.+d
keywords EinsteincloudsdarkmatteraroundsupermassiveblackholesEMRI/IMRIgravitationalwavesgravitational-wavedephasingdynamicalfrictionwaveformmismatchLISAinnermoststablecircularorbit
topics Dark Matter
open problems Dark Matter
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

This paper tries to show that a collisionless dark-matter halo wrapped around a supermassive black hole leaves a measurable fingerprint in the gravitational waves of a compact-object inspiral, and that future space-based detectors like LISA could read it. Using an exact General-Relativity solution for the halo (an Einstein cloud of particles on circular orbits that vanishes inside $r=4M$), the authors compute the adiabatic inspiral and compare four diagnostics: accumulated gravitational-wave cycles, waveform phase, signal-to-noise ratio, and waveform mismatch. For a benchmark 10-solar-mass object spiraling into a $10^6$-solar-mass black hole with a 20 kpc halo at $ ho_0=0.3\,\mathrm{GeV\,cm^{-3}}$, the phase difference reaches one radian at about 2.02 years and the mismatch crosses the distinguishability threshold at about 3.6 years. The signal is almost entirely due to the conservative change in the spacetime geometry, with relativistic dynamical friction negligible for these models. If this is right, LISA-type observatories can probe the relativistic distribution of dark matter around black holes, not just its galactic-scale profile.

What carries the argument

The central object is the Einstein-cloud halo: a stationary, spherically symmetric ensemble of collisionless particles on circular timelike geodesics, whose coarse-grained stress-energy has only tangential pressure. The paper uses the exact Model I solution, with density $\rho(r)=\rho_0 a^4(r-4M)/[r^2(r+a)^3]$ for $r\ge 4M$, vanishing inside, and mass function $m(r)=M+M_h(r-4M)^2/(r+a)^2$. The machinery is the set of circular-geodesic quantities in this geometry—the generalized Kepler frequency $\Omega^2=f m/[r^2(r-2m)]$, the specific energy and angular momentum, and the ISCO equation $r^2m'(r)+rm(r)-6m^2(r)=0$—which feed an adiabatic energy-balance inspiral $\dot r=-(F_{\mathrm{GW}}+F_{\mathrm{DF}})/(dE_{\mathrm{orb}}/dr)$, using a quadrupole gravitational-wave flux and a relativistic collisionless dynamical-friction drag. Integrating these quantities over the inspiral yields the accumulated cycles and phase, while the same trajectories build frequency-domain waveforms whose noise-weighted overlap gives the mismatch. The mechanism that makes the halo visible is accumulation: over millions of orbits, tiny geometric shifts in the orbital frequency add coherently into measurable dephasing.

What would settle it

Compute the equilibrium collisionless phase-space distribution in the full Einstein-cloud metric without imposing the $H(r-4M)$ cutoff, and locate the actual radius below which no stable bound circular orbits exist; if stable orbits or nonvanishing density exist inside $4M$, the Model I predictions change and the claimed 2.02-year one-radian time and 3.6-year mismatch threshold would shift. Observationally, a LISA EMRI with $M=10^6\,M_\odot$, $m_*=10\,M_\odot$, and $a=20\,\mathrm{kpc}$ whose phase follows the vacuum template to better than one radian over two years would contradict the detectability claim for $\rho_0=0.3\,\mathrm{GeV\,cm^{-3}}$.

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Extended reading notes

Core claim

The paper's central claim is that a collisionless dark-matter halo built as an Einstein cloud around a Schwarzschild black hole changes the inspiral of a small compact object enough for a future space-based detector to notice, even when the halo is tenuous. Working with the exact Model I solution, the authors find that for $M=10^6\,M_\odot$, $m_*=10\,M_\odot$, $a=20\,\mathrm{kpc}$, and $\rho_0=0.3\,\mathrm{GeV\,cm^{-3}}$, the accumulated phase difference between the halo and vacuum inspirals reaches one radian at $t\simeq2.02\,\mathrm{yr}$, and the waveform mismatch crosses the fixed-parameter distinguishability threshold $M\gtrsim 1/(2\,\mathrm{SNR}^2)$ at $t\simeq3.6\,\mathrm{yr}$. All four diagnostics—cycle count, phase, signal-to-noise ratio, and mismatch—point the same way. The effect is dominated by the conservative modification of the orbital geometry: the contribution of relativistic dynamical friction to the phase and mismatch is many orders of magnitude smaller for the halos considered. The paper therefore claims that LISA-type observations of EMRIs and IMRIs can probe the relativistic distribution of dark matter immediately outside the innermost stable circular orbit.

Load-bearing premise

The detectability numbers assume the dark-matter density vanishes for $r<4M$, a boundary transplanted from phase-space analyses of vacuum Schwarzschild spacetime; if the true stable-orbit boundary or the halo density inside that radius differs, the predicted dephasing and distinguishability times shift.

Editorial extensions

If this is right

  • For the benchmark system ($M=10^6\,M_\odot$, $m_*=10\,M_\odot$, $a=20\,\mathrm{kpc}$, $\rho_0=0.3\,\mathrm{GeV\,cm^{-3}}$), the halo-vs-vacuum phase difference reaches one radian at about 2.02 years and the waveform mismatch crosses $1/(2\,\mathrm{SNR}^2)$ at about 3.6 years, so a four-year LISA observation can distinguish the halo from vacuum.
  • Denser halos become distinguishable sooner: at $\rho_0=10\,\mathrm{GeV\,cm^{-3}}$ the mismatch threshold is crossed at about 1.5 years, while at $\rho_0=0.1\,\mathrm{GeV\,cm^{-3}}$ the halo is not distinguishable within four years.
  • Dynamical friction contributes negligibly to all four diagnostics; the observable signal is carried by the conservative modification of the spacetime geometry, so waveform templates must include the halo's metric, not only a drag force.
  • One-cycle dephasing requires about 0.20 years around a $10^5\,M_\odot$ black hole, 2.57 years around $10^6\,M_\odot$, and 35.9 years around $10^7\,M_\odot$, making lighter supermassive black holes the most promising targets.
  • The consistency across accumulated cycles, phase, signal-to-noise ratio, and waveform mismatch means the detectability conclusion does not rest on any single diagnostic.
  • If the claims hold, future space-based gravitational-wave observatories can constrain the density normalization and inner structure of dark-matter halos in the strong-field region, complementing electromagnetic probes such as black-hole shadows and stellar orbits.

Reading between the lines

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

  • Because the conservative geometry dominates, halo density may be partially degenerate with the black-hole mass in an actual parameter-estimation analysis: both alter the orbital frequency. A joint measurement of the frequency at several radii, or of the inspiral rate, would be needed to break that degeneracy.
  • The quoted detectability times depend on the inner cutoff at $r=4M$; if a self-consistent solution of the collisionless phase-space distribution in the Einstein-cloud metric places the boundary elsewhere, the one-radian and mismatch times will shift. The framework thus turns the detectability time into a potential measurement of the inner halo boundary, not just of the density normalization.
  • The inspiral is evolved with a leading-order quadrupole flux; replacing it with gravitational self-force waveforms, as the paper lists for future work, will alter the vacuum baseline at a level that could matter for the small phase differences considered here, so the final LISA data-analysis statements will need self-force-accurate templates.
  • The same Einstein-cloud spacetime also predicts shifts in black-hole shadow size and photon-ring features, so combining LISA dephasing measurements with horizon-scale imaging could jointly constrain both the halo density profile and its inner cutoff.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper develops a general relativistic framework for computing gravitational-wave observables from EMRIs/IMRIs embedded in spherically symmetric Einstein-cloud dark-matter halos around supermassive black holes. Building on exact solutions constructed in prior work, the authors derive circular geodesics, the ISCO condition, adiabatic inspiral equations with gravitational-wave and dynamical-friction dissipation, accumulated phase, SNR, and waveform mismatch. The formalism is then applied to a specific cuspy model (Model I) with a 20 kpc halo scale radius and densities 0.1--10 GeV/cm^3 around a 10^6 M_sun black hole. The central claim is that relativistic halos produce measurable dephasing, SNR changes, and waveform mismatch, with the conservative geometric modification dominating over dynamical friction.

Significance. If correct, the paper would provide a useful, fully relativistic end-to-end pipeline for environmental dephasing in EMRIs, with clean analytic geodesic and ISCO results and a transparent separation of conservative and dissipative effects. The framework is not fitted to data, and the exact-geodesic derivations in Sections III.A--III.D are internally consistent. However, the numerical application contains a serious error in the metric expansion used for all integrations, and the reported detectability epochs are not reproducible from the stated equations. As it stands, the quantitative conclusions cannot be trusted.

major comments (4)
  1. [Appendix A, Eq. (A.20)] The Taylor expansion f(x)=C_+ x(1+alpha_1 x+alpha_2 x^2) is not the correct solution of Eq. (A.19) in the black-hole spacetime. In the vacuum limit m(r)=M, Eq. (A.19) integrates exactly to f=C(1-2M/r)=C(1-2mu/x), which has a Laurent 1/x term and is not analytic at x=0 with a simple zero. The expansion in Eq. (A.20) instead describes a regular center with m(0)=0. Since the text states that all numerical integrations use the expanded solution, the metric function actually used in the code is not the Model I spacetime. This invalidates the numerical results in Figs. 2--8 unless the exact f is used or the expansion is corrected.
  2. [Sec. IV, Eqs. (48)--(50); Figs. 4--5] Even taking Model I at face value, the reported dephasing is inconsistent with the enclosed halo mass by many orders of magnitude. For M=10^6 M_sun, a=20 kpc, and rho0=0.3 GeV cm^-3, Eq. (50) gives M_h/M ~ 4x10^5. The 4-year vacuum inspiral for m_*=10 M_sun starts near r~11M, and Eq. (49) gives (m(r)-M)/M ~ (M_h/M)(r/a)^2 ~ 10^-16 in the relevant band. The fractional orbital-frequency shift is of the same order, so over ~10^5 gravitational-wave cycles the accumulated phase difference is ~10^-10 rad, not 1 rad as reported for t ~ 2.02 yr. The authors need to provide the numerical evaluation of Eq. (39) for this benchmark case or identify the missing factor that produces the plotted 10-order-of-magnitude discrepancy.
  3. [Sec. IV.B, Eq. (67); Figs. 5--7] The accumulated SNR and the distinguishability threshold M_th=1/(2 SNR^2(t)) are not reproducible from the manuscript. Equation (67) requires a detector noise power spectral density S_n(f), and Eq. (68) requires a luminosity distance and an explicit waveform amplitude A(t); none of these is specified in Sec. IV. Consequently the SNR=8, 20, 29, 38 vertical lines and the quoted 3.6-yr mismatch-crossing time for rho0=0.3 GeV cm^-3 cannot be checked, and the claim that all four diagnostics lead to consistent detectability conclusions is underdetermined by the presented analysis.
  4. [Sec. II, Eqs. (6)--(8)] The inner cutoff rho(r<4M)=0 is imported from the Schwarzschild phase-space analyses of Refs. [11,12] and imposed on the Einstein-cloud spacetime. Because m(r)>M for r>4M in the halo, the stable-bound-orbit boundary of the actual spacetime differs from 4M, so the Heaviside cutoff is an additional assumption rather than a consequence of the phase-space construction for this geometry. Since the dominant conservative dephasing accumulates in the strong-field region just outside the ISCO, the quoted detectability epochs depend on this structural assumption; a self-consistent derivation or at least a sensitivity test is needed.
minor comments (4)
  1. [Abstract and Sec. III.C.1, Eq. (27)] The paper calls the framework 'fully relativistic' while the gravitational-wave luminosity is the flat-space quadrupole formula evaluated with halo-modified quantities. The wording should be tempered to 'relativistic conservative dynamics with leading-order quadrupole dissipation' or the flux should be upgraded to a black-hole perturbation theory or self-force result.
  2. [Sec. IV.C, Eq. (72)] The numerical mismatch calculation is not fully specified: the tapering window, sampling rate, frequency grid, and noise curve are mentioned but their explicit choices are not given, so the reader cannot reproduce the mismatch curves in Figs. 7 and 8.
  3. [Fig. 5 caption] The caption contains an apparent typo: 'SNR = 380' should read 'SNR = 38', and the density labels are typeset as '0 = 0.1 GeV cm^-3' rather than rho_0.
  4. [Appendix A, Eq. (A.28)] With a corrected expansion for f, the matching condition should give C_in = 1 in the vacuum limit; the current expression C_in = a C_+/(2M)(...) does not reduce to 1 when M_h = 0 and C_+ is fixed by f(4M)=1/2. This indicates an internal inconsistency in the matching calculation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the gravitational-wave observables are derived from an externally checkable exact solution and standard GR formulas, with no fitted parameter relabeled as a prediction.

full rationale

This paper is a forward-model calculation, not an inversion or fit. The inputs are the Einstein-cloud spacetime constructed in the authors' prior work [14] (an exact, externally checkable solution of Einstein's equations), the prescribed halo density profile in Eq. (6), the geodesic equations, the standard quadrupole flux in Eq. (27), a Chandrasekhar-type dynamical-friction prescription in Eq. (30), and the standard matched-filter mismatch definitions in Eqs. (44)-(46). The outputs—accumulated cycles, phase shift, SNR, and mismatch—are all computed from these inputs via the derived orbital equations (Eqs. (17)-(20), (35), (39), (54)-(56), (64), (67), (72)). No halo parameter is fitted to the predicted dephasing or mismatch; the density normalizations ρ0 are chosen independently. The r=4M inner cutoff is imported from the independent phase-space analyses of Refs. [11,12], not derived from the gravitational-wave observables, and the paper explicitly states that this is an adopted input. The self-citations to [14-16] are load-bearing for the background spacetime, but those are exact analytical solutions whose consistency can be verified independently, so under the review rules they count as real evidence rather than circular support. The relation N_GW = Φ/(2π) makes the cycle and phase diagnostics partially consistent by definition, but the central detectability claim rests on the independently computed dephasing and mismatch, not on that identity. The unspecified detector noise model and source distance affect the reproducibility of the SNR thresholds, but that is a completeness issue, not a circularity. No step was found in which a prediction reduces by construction to an input parameter or to an unverified self-citation.

Assumptions & free parameters 7 free parameters · 8 assumptions · 0 invented entities

The calculations rest on standard general relativity plus several modeling choices. The key free parameters are the halo density normalization, scale radius, and benchmark binary parameters, all chosen by hand rather than fitted to data. The Einstein-cloud stress-energy tensor and the inner density cutoff are domain assumptions taken from previous work. No new particles, forces, or conserved quantities are introduced.

free parameters (7)
  • Halo characteristic density rho0 = 0.1, 0.3, 1, 3, 10 GeV cm^-3
    Controls the halo mass M_h through Eq. (50) and therefore the magnitude of dephasing; chosen by hand as representative values, not measured.
  • Halo scale radius a = 20 kpc
    Sets the length scale of the halo and enters M_h and the small-x expansion; chosen as a typical galactic halo scale.
  • Primary black hole mass M = 10^6 M_sun
    Benchmark SMBH mass; Figure 4 shows the detectability time depends strongly on M.
  • Secondary compact object mass m_* = 10 M_sun
    Sets the gravitational-wave luminosity and SNR; chosen as a representative stellar-mass companion for an EMRI.
  • Coulomb logarithm ln Lambda = 3
    Order-of-magnitude choice for the dynamical-friction prescription; since DF is negligible, this parameter has little impact on the results.
  • Observation time T_obs = 4 yr
    Assumed LISA mission duration; all detectability times are compared against this interval.
  • Model I shape parameters (alpha,beta,gamma,n) = (1,1,5,1)
    Defines the specific halo density profile in Eq. (48); other models would produce different dephasing estimates.
assumptions (8)
  • standard math Einstein field equations with a static, spherically symmetric metric ansatz (Eq. 1) and stress-energy diag[-rho,0,P,P] (Eq. 2).
    Used throughout Sections II and III; standard general-relativistic formalism.
  • domain assumption Model I density and mass profile with H(r-4M) cutoff (Eqs. 6, 48, 49).
    A halo model imported from the authors' prior exact solutions [14]; not derived from observations in this paper.
  • domain assumption Inner boundary condition rho(r<4M)=0, transposed from Schwarzschild phase-space analyses [11,12].
    This cutoff defines where the halo begins and shapes the strong-field contribution to the dephasing.
  • domain assumption Adiabatic, quasicircular inspiral with energy balance dE_orb/dt = -(F_GW + F_DF) (Eq. 26).
    Standard EMRI approximation assuming radiation-reaction is slow compared with the orbital period.
  • domain assumption Leading-order quadrupole gravitational-wave flux F_GW = (32/5) m_*^2 r^4 Omega^6 evaluated with halo-modified Omega (Eq. 27).
    A flat-space quadrupole formula applied in the curved halo spacetime; not a self-force or black-hole perturbation theory flux.
  • domain assumption Chandrasekhar-type dynamical friction with relativistic correction factor xi(v) (Eqs. 30 and 31).
    Local drag prescription taken from [12]; neglects the global response of the halo to the inspiraling body.
  • standard math Stationary-phase approximation for frequency-domain waveforms and fixed-parameter mismatch criterion M >= 1/(2 SNR^2) (Eqs. 44-46 and 74).
    Standard matched-filtering formalism; the paper explicitly notes that full parameter estimation is not performed.
  • domain assumption Existence and use of a LISA noise power spectral density for SNR and mismatch evaluation (Eqs. 67 and 76).
    The noise curve and waveform amplitude/distance are not fully specified, yet the figures quote specific SNR thresholds.

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Pith. "Pith review of Probing the Distribution and Nature of Dark Matter Around Supermassive Black Holes from EMRI and IMRI Gravitational Waves." pith.science (2026). https://pith.science/paper/II6OYIL7

@misc{pith2026260812540,
  author       = {Pith},
  title        = {Pith review of: Probing the Distribution and Nature of Dark Matter Around Supermassive Black Holes from EMRI and IMRI Gravitational Waves},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/II6OYIL7}},
  note         = {Machine review of arXiv:2608.12540}
}
read the original abstract

The distribution of dark matter in the immediate vicinity of supermassive black holes remains poorly understood despite its importance for galaxy evolution and precision tests of gravity. Future space-based gravitational-wave observatories offer a unique opportunity to probe this relativistic regime through the inspiral of compact objects into supermassive black holes. Building upon our previously constructed exact Einstein-cloud solutions within General Relativity, we develop a fully relativistic framework to investigate the gravitational-wave signatures of collisionless dark-matter halos surrounding supermassive black holes. The framework provides a unified treatment of orbital dynamics, adiabatic inspiral, accumulated gravitational-wave cycles, waveform phase evolution, signal-to-noise ratio, and waveform mismatch for extreme- and intermediate-mass-ratio inspirals (EMRIs/IMRIs). As a representative application, we specialize the formalism to Model I. We show that relativistic dark-matter halos can produce measurable modifications to the accumulated gravitational-wave cycles, waveform phase, signal-to-noise ratio, and waveform mismatch, leading to consistent conclusions regarding detectability. By separating conservative modifications of the spacetime geometry from dissipative effects due to relativistic dynamical friction, we find that the observable signatures are dominated by the former, while the latter remains negligible for the halo models considered. These results demonstrate that future gravitational-wave observations by LISA and similar missions may provide a powerful probe of the relativistic distribution and physical nature of dark matter around supermassive black holes.

Figures

Figures reproduced from arXiv: 2608.12540 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Accumulated gravitational-wave cycle shifts [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Observation time required for the total Model [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figures from the paper (3 more)
Figure 6
Figure 6. Figure 6: FIG. 6. Decomposition of the accumulated [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Evolution of the total waveform mismatch, [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Decomposition of the waveform mismatch for the representative halo density [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

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Reference graph

Works this paper leans on

32 extracted references · 11 canonical work pages

  1. [14]

    Speeney, A

    N. Speeney, A. Antonelli, V. Baibhav, and E. Berti,Impact of relativistic corrections on the detectability of dark-matter spikes with gravita- tional waves, Phys. Rev. D106, 044027 (2022) [arXiv:2204.12508]

    arXiv 2022

  2. [1]

    The corresponding lumi- nosityF GW is the orbital energy carried by gravi- tational waves per unit coordinate time

    Gravitational Wave Luminosity The accelerated compact object generates spacetime perturbations that propagate away as gravitational radiation. The corresponding lumi- nosityF GW is the orbital energy carried by gravi- tational waves per unit coordinate time. At lead- ing, quadrupolar order, the luminosity of a quasi- circular binary is [27–29] FGW = 32 5 ...

    work page

  3. [2]

    The gravitational attraction of this wake opposes the motion of the compact ob- ject and removes orbital energy

    Dynamical Friction Luminosity As the compact object moves through the dark- matter distribution, its gravitational field focuses the surrounding particles and creates an overdense wake behind it. The gravitational attraction of this wake opposes the motion of the compact ob- ject and removes orbital energy. In a collisionless medium, the standard Chandras...

    work page 2026

  4. [3]

    Aghanim, et al

    N. Aghanim, et al. (Planck Collaboration),Planck 2018 results VI. Cosmological parameters, A&A 641, A6 (2020) [arXiv:1807.06209]

    arXiv 2020

  5. [4]

    Bertone, D

    G. Bertone, D. Hooper and J. Silk,Particle dark matter: Evidence, candidates and constraints, Phys. Rept.405(2005) 279 [hep-ph/0404175]

    arXiv 2005

  6. [5]

    J. L. Feng,Dark Matter Candidates from Particle Physics and Methods of Detection, Ann. Rev. As- tron. Astrophys.48(2010) 495 [arXiv:1003.0904]

    arXiv 2010

  7. [6]

    Kormendy and L

    J. Kormendy and L. C. Ho,Coevolution (Or Not) of Supermassive Black Holes and Host Galax- ies, Ann. Rev. Astron. Astrophys.51(2013) 511 [arXiv:1304.7762]

    arXiv 2013

  8. [7]

    V. C. Rubin, N. Thonnard and W. K. Ford,Ro- tational properties of 21 Sc galaxies with a large range of luminosities and radii, from NGC 4605 (R = 4 kpc) to UGC 2885 (R = 122 kpc), Astro- phys. J.238(1980) 471

    work page 1980

Show all 32 references
  1. [8]

    Clowe, et al.,A direct empirical proof of the existence of dark matter, Astrophys

    D. Clowe, et al.,A direct empirical proof of the existence of dark matter, Astrophys. J.648, L109 (2006) [arXiv:astro-ph/0608407]

    2006 arXiv

  2. [9]

    Abuteret al.(GRAVITY Collaboration),De- tection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole, Astron

    R. Abuteret al.(GRAVITY Collaboration),De- tection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole, Astron. Astrophys.615(2018) L15 [arXiv:1807.09409]

    2018 arXiv

  3. [10]

    Abuteret al.(GRAVITY Collaboration),De- tection of the Schwarzschild precession in the orbit of the star S2, Astron

    R. Abuteret al.(GRAVITY Collaboration),De- tection of the Schwarzschild precession in the orbit of the star S2, Astron. Astrophys.636(2020) L5 [arXiv:2004.07187]

    2020 arXiv

  4. [11]

    Akiyamaet al.(Event Horizon Telescope Collaboration),First M87 Event Horizon Tele- scope Results

    K. Akiyamaet al.(Event Horizon Telescope Collaboration),First M87 Event Horizon Tele- scope Results. I. The Shadow of the Supermas- sive Black Hole, Astrophys. J. Lett.875(2019) L1 [arXiv:1906.11238]

    2019 arXiv

  5. [12]

    Akiyamaet al.(Event Horizon Telescope Col- laboration),First Sagittarius A* Event Hori- zon Telescope Results

    K. Akiyamaet al.(Event Horizon Telescope Col- laboration),First Sagittarius A* Event Hori- zon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way, Astrophys. J. Lett.930(2022) L12 [arXiv:2311.09484]

    2022 arXiv

  6. [13]

    Sadeghian, F

    L. Sadeghian, F. Ferrer, and C. M. Will,Dark- matter distributions around massive black holes: A general relativistic analysis, Phys. Rev. D88, 063522 (2013) [arXiv:1305.2619]

    2013 arXiv

  7. [15]

    Cardoso, K

    V. Cardoso, K. Destounis, F. Duque, R. P. Macedo, A. Maselli,Black holes in galaxies: en- vironmental impact on gravitational-wave genera- tion and propagation, Phys. Rev. D105, L061501 18 (2022) [arXiv:2109.00005]

    2022 arXiv

  8. [17]

    Z. Shen, A. Wang, S. Yin,Inner radius and en- ergy conditions of dark matter halos surround- ing Schwarzschild black holes, Phys. Lett. B862 (2025) 139300, arXiv:2311.12259

    2025 arXiv

  9. [18]

    Maeda, V

    K.-i. Maeda, V. Cardoso, A. Wang,Einstein Cluster as Central Spiky Distribution of Galactic Dark Matter, Phys. Rev. D111, 044060 (2025), arXiv:2410.04175

    2025 arXiv

  10. [19]

    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 Klein,Science with the space-based interferometer LISA. V. Extreme mass-ratio inspirals, Phys. Rev. D95, 103012 (2017) [arXiv:1703.09722]

    2017 arXiv

  11. [20]

    C. P. L. Berryet al.,The unique potential of ex- treme mass-ratio inspirals for gravitational-wave astronomy, Astron. Astrophys. Rev.31(2023) 2 [arXiv:2206.15035]

    2023 arXiv

  12. [21]

    Gondolo and J

    P. Gondolo and J. Silk,Dark Matter Annihilation at the Galactic Center, Phys. Rev. Lett.83, 1719 (1999)

    1999

  13. [22]

    Hernquist,An Analytical Model for Spheri- cal Galaxies and Bulges, Astrophys

    L. Hernquist,An Analytical Model for Spheri- cal Galaxies and Bulges, Astrophys. J.356, 359 (1990)

    1990

  14. [23]

    Zhao,Analytical models for galactic nu- clei, Mon

    H.S. Zhao,Analytical models for galactic nu- clei, Mon. Not. R. Astron. Soc.278, 488 (1996) [arXiv:astro-ph/9509122]

    1996 arXiv

  15. [24]

    Bertone, D

    G. Bertone, D. Hooper, and J. Silk,Particle Dark Matter: Evidence, Candidates and Con- straints, Phys. Rep.405, 279 (2005) [arXiv:hep- ph/0404175]

    2005

  16. [25]

    Freese,Review of Observational Evidence for Dark Matter in the Universe and in upcoming searches for Dark Stars, EAS Publ

    K. Freese,Review of Observational Evidence for Dark Matter in the Universe and in upcoming searches for Dark Stars, EAS Publ. Ser.36, 113 (2009) [arXiv:0812.4005]

    2009 arXiv

  17. [26]

    J. G. de Swart, G. Bertone, and J. van Dongen, How dark matter came to matter, Nature Astron. 1, 0059 (2017) [arXiv:1703.00013]

    2017 arXiv

  18. [27]

    Arbey, F

    A. Arbey, F. Mahmoudi,Dark matter and the early Universe: a review, Prog. Part. Nucl. Phys. 119(2021) 103865 [arXiv:2104.11488]

    2021 arXiv

  19. [28]

    Navarro, C.F

    J.F. Navarro, C.F. Frenk, S.D.M. White,a uni- versal density profile from hierarchical cluster- ing, Astrophys. J.490, 493 (1997) [arXiv:astro- ph/9611107]

    1997

  20. [29]

    Einstein, ¨Uber Gravitationswellen, Sitzungs- ber

    A. Einstein, ¨Uber Gravitationswellen, Sitzungs- ber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 1918, 154 (1918)

    1918

  21. [30]

    L. D. Landau and E. M. Lifshitz,The Classical Theory of Fields, 4th ed., (Pergamon Press, Ox- ford, 1975)

    1975

  22. [31]

    Maggiore,Gravitational Waves

    M. Maggiore,Gravitational Waves. Vol. 1: The- ory and Experiments, (Oxford University Press, Oxford, 2008)

    2008

  23. [32]

    Zhang, Y.-G

    B.-K. Zhang, Y.-G. Gong, and A. Wang,Self- forces as nonlocal probes of gravastar interiors, arXiv:2608.xxxx

  24. [33]

    Chandrasekhar,Dynamical Friction

    S. Chandrasekhar,Dynamical Friction. I. Gen- eral Considerations: the Coefficient of Dynamical Friction, Astrophys. J.97, 255 (1943)

    1943

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