Pith. sign in

REVIEW 3 major objections 4 minor 2 cited by

On Equation of State of Dark Matter around Massive Black Holes

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read The paper argues that static dark matter around massive black holes must have negative pressure, and it maps the allowed parameter windows for two simple equations of state.

desk verdict A clean toy-model TOV scan whose 'negative pressure is necessary' claim rests on an unproven boundary condition at the horizon; worth reviewing, but the conclusion needs qualification. read the letter →

arxiv 2501.12574 v1 pith:KIHIVWCK submitted 2025-01-22 gr-qc astro-ph.GAhep-ph

Zhong-Ming Xie , Yong Tang This is my paper · ORCID
classification gr-qcastro-ph.GAhep-ph
keywords darkmatterequationofstateTolman-Oppenheimer-VolkoffequationsSchwarzschildblackholenegativepressureSagittariusA*densityprofileperfectfluidgalacticcenter
topics 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

The paper tries to establish that dark matter can sit in static, quasi-equilibrium profiles around massive black holes only if its equation of state allows negative pressure. Working in a spherically symmetric Schwarzschild background and integrating the Tolman–Oppenheimer–Volkoff equations outward from an NFW boundary far from Sgr A*, the paper shows that positive-pressure power-law equations of state are nonviable: they would require negative total mass inside the horizon region or violate the assumed vanishing density at the horizon. For the power-law $p=\omega\rho_B^{1-\gamma}\rho^{\gamma}$ only $\omega\in(-1,0)$ and $\gamma\ge 1$ work; for the radius-dependent $p=\zeta(r/r_{\rm BH})\rho$ only a narrow negative band of coefficients works. If true, that would mean dark-matter models must allow negative pressure in the strong-gravity regime.

What carries the argument

The central object is the Tolman–Oppenheimer–Volkoff system for a static, spherically symmetric perfect fluid, together with the two boundary criteria $M_{\rm encl}\lesssim 10^{-3}\,M_\odot$ and $\rho(r_{\rm BH})=0$. The argument runs on a sign analysis of the density gradient $\rho'$: the sign of $\rho'$ is controlled by $E(r)=M(r)+4\pi r^3 p(r)$, and for positive pressure $E$ must turn negative to make the density vanish at the horizon, which forces the enclosed mass $M(r)$ to become negative somewhere; negative pressure avoids that failure. The same sign analysis shows that for power-law EoS with $0<\gamma<1$ the density becomes constant at a nonzero value before reaching the horizon, violating $\rho(r_{\rm BH})=0$, so only $\gamma\ge 1$ and $\omega\in(-1,0)$ survive.

What would settle it

Replace the boundary condition $\rho(r_{\rm BH})=0$ with the conservative condition $M(r_{\rm BH})=m_{\rm BH}$ and integrate the TOV equations for $p=\omega\rho$ with $\omega>0$: if a solution exists with nonnegative total mass everywhere and $M_{\rm encl}\lesssim 10^{-3}\,M_\odot$, the paper's negative-pressure conclusion would be falsified.

Watch

Extended reading notes

Core claim

The paper's central claim is that dark matter around a massive black hole can be described as a static, spherically symmetric perfect fluid in quasi-equilibrium, but only if its pressure is negative. Solving the Tolman–Oppenheimer–Volkoff equations with outer boundary data set by the NFW profile and the Sgr A* parameters, the paper finds that all positive-pressure power-law equations of state either produce negative total mass in the inner region or violate the requirement that density vanish at the horizon; negative-pressure equations of state with $|p|<\rho$ produce static profiles that are shallower than the NFW profile. For the power-law EoS the viable parameter space is $\omega\in(-1,0)$, $\gamma\ge 1$, and for the radius-dependent EoS it is $-10^{-5}<\zeta\lesssim -10^{-10}/2$. The paper takes this as evidence that dark-matter model-building in the relativistic regime should incorporate the possibility of negative pressure.

Load-bearing premise

The load-bearing premise is that the dark-matter density must be zero at the event horizon, an expectation the paper imposes as a boundary criterion; every positive-pressure equation of state is judged against that condition.

Editorial extensions

If this is right

  • If the conclusion holds, positive-pressure dark-matter equations of state cannot describe static halos around non-rotating black holes, so the usual pressureless $p\simeq 0$ treatment fails in the strong-gravity region.
  • The viable power-law window $\omega\in(-1,0)$, $\gamma\ge 1$ gives static profiles that are shallower than the NFW profile, which could be tested against observed central density slopes.
  • The radius-dependent window $-10^{-5}<\zeta\lesssim -10^{-10}/2$ predicts a density maximum whose radius is tied to $\zeta$, a concrete feature for future horizon-scale probes.
  • The enclosed dark-matter mass inside about $10^{-2}$ pc is $\lesssim 10^{-3}\,M_\odot$, well below current observational limits, so the predicted halos evade existing mass constraints.
  • Gravitational waves from extreme-mass-ratio inspirals could probe the environmental density around the black hole and distinguish these negative-pressure profiles from collisionless spike models.

Reading between the lines

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

  • The negative-pressure requirement is a direct consequence of adopting $\rho(r_{\rm BH})=0$ as a boundary condition; if staticity or the vanishing-density condition is relaxed, for example by allowing steady accretion, positive-pressure dark matter could still surround the black hole.
  • The two equations of state studied are phenomenological, so a natural next step is to identify a microphysical dark-matter model that realizes the allowed negative-pressure windows, such as a scalar field or an effective superfluid regime.
  • Applying the same sign-analysis method to rotating black holes or to anisotropic pressure could widen or shift the viable parameter windows, providing a test of how robust the negative-pressure requirement actually is.
  • Tighter stellar-orbit constraints on the extended mass around Sgr A* would either shrink the negative-pressure parameter space or strengthen the case for it, depending on where the measured enclosed mass lands.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper models dark matter near a Schwarzschild black hole (Sgr A*) as a static, spherically symmetric perfect fluid, integrating the Tolman–Oppenheimer–Volkoff equations with outer boundary conditions taken from the NFW profile at r_B = 10^5 r_BH. Two equation-of-state families are studied: p = ωρ_B^{1-γ}ρ^γ and p = ζ(r/r_BH)ρ. Using the criteria of small enclosed mass (Eq. 10) and vanishing density at the horizon (Eq. 11), the authors conclude that static DM profiles require negative pressure, with viable parameters ω ∈ (−1, 0), γ ≥ 1 for the power-law case and −10^-5 < ζ ≲ −10^-10/2 for the radius-dependent case.

Significance. If the conclusion were established, it would be an interesting strong-gravity constraint on DM models. The paper's analytic sign arguments are clean and are checked against numerical integrations; the weak energy condition is tracked, and the sensitivity to the outer mass boundary condition is tested. The main limitation is that the central criterion ρ(r_BH)=0 is assumed rather than derived, and the equation-of-state choices are not tied to microphysics; hence the advertised conclusion is broader than what the calculation actually supports.

major comments (3)
  1. [II, Eq. (11)] The criterion ρ(r_BH)=0 is an extra modeling assumption, not a consequence of the TOV equations. The justification that time-like and null geodesics only go inward concerns test particles; a static perfect fluid is not well-defined at the horizon because u^μ = e^{-Φ}(1,0,0,0) diverges as e^Φ → 0 and Eq. (7) is singular at 1−2M/r=0. The rejection of ω>0 in Sec. III A relies on Eq. (11): without it, the positive-pressure profiles simply have density increasing toward the horizon and do not produce negative M(r). The paper should either derive Eq. (11) from a matched or regularized fluid description or explicitly restrict its conclusion to solutions satisfying this boundary condition.
  2. [II, Eq. (10)] The statement that Eq. (10) follows from the GRAVITY constraint is not supported: the quoted observational bound is about 1200 M⊙ of extended mass at ~10^-2 pc, whereas Eq. (10) imposes Mencl ≲ 10^-3 M⊙, six orders of magnitude smaller. Since Eq. (10) is one of the two viability criteria used to reject positive-pressure solutions, this assumed bound needs its own justification, for example an estimate of the stellar contribution and a translation into a DM-only upper limit.
  3. [III, A and B] The two equations of state are introduced ad hoc and no microphysical origin is offered, so the conclusion that DM pressure 'should be negative' overreaches. The calculations show that within these two isotropic perfect-fluid families the imposed criteria select negative-pressure parameters; they do not rule out positive-pressure profiles with anisotropic stress, non-perfect-fluid terms, or a different closure. A concrete minimal test would be to repeat the analysis with p_r ≠ p_t, or to match the static solution to a steady inflow inside some r_c > r_BH, and to check whether positive-pressure profiles satisfying Eqs. (10) and (11) exist.
minor comments (4)
  1. [III, Eq. (17)] The numerical value in Eq. (17) appears incorrect: 4πr_B^3ρ_B/3 ≈ 0.94 M⊙, not 10^-1 M⊙; additionally, this bound is only valid for profiles with ρ(r) ≤ ρ_B everywhere, which is not the case for the radius-dependent solutions shown in Fig. 5.
  2. [Footnote 1] Footnote 1 concedes that the curves inside the event horizon are not physically reliable; since Eq. (11) is imposed at r_BH, which lies in that region, the paper should state whether the boundary condition is meant as a regularizing condition and whether the solutions are continuous limits from r > r_BH.
  3. [References] Reference [41] is cited with an incomplete author list ('T. G. Collaboration, K. A. E. Dayem, and et al.'); this should be corrected.
  4. [II, after Eq. (8)] The phrase 'upper or conservative value 1200 M⊙' is ambiguous; please specify whether 1200 M⊙ is an upper limit or a conservative central estimate.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the TOV derivation is self-contained and the negative-pressure conclusion is a conditional consequence of stated criteria, not an input.

full rationale

The paper's central chain is a forward integration of the standard TOV equations (Eqs. 6-7) with explicit boundary conditions (Eq. 8), explicit EoS forms, and two stated viability criteria (Eqs. 10-11). The EoS parameters ω, γ, and ζ are inputs; the paper does not fit them to the target conclusion. The result that positive-pressure EoS fail the criteria is derived by sign analysis of Eqs. 12-13 and Eq. 18, not by construction. The boundary condition ρ(r_BH)=0 (Eq. 11) is an unproved modeling assumption, and its justification via geodesics is physically questionable, but imposing an assumption and drawing a logical consequence is not circular; the conclusion is conditional on that criterion, and the paper's own footnote that curves inside the EH are not physically reliable underscores the modeling choice. Self-citations [10,12,14,15] are used only as examples of prior gravitational-wave and environment work and are not load-bearing for the TOV analysis or the parameter-space exclusion. No step exhibits a quantity that is defined in terms of the claimed output, and no fitted parameter is renamed as a prediction. Hence no significant circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central conclusion rests on the assumed EoS forms, the NFW boundary, the WEC, and the ad hoc horizon condition ρ(r_BH)=0. No new particle or force is introduced. The EoS parameters are scanned inputs, not fitted outputs.

free parameters (4)
  • ω (power-law EoS coefficient) = scanned in (-1,0) for viable cases
    Dimensionless coefficient in p = ωρ_B^{1-γ}ρ^γ; chosen by hand, not derived; viable range selected by the paper's criteria.
  • γ (power-law EoS exponent) = γ ≥ 1 for viable cases
    Exponent in the power-law EoS; chosen by hand; 0<γ<1 rejected for violating ρ(r_BH)=0.
  • ζ (radius-dependent EoS coefficient) = -10^-5 < ζ ≤ -10^-10/2
    Dimensionless coefficient in p = ζ(r/r_BH)ρ; chosen by hand; viable range from the maximum condition and WEC.
  • ρ_* (RD pivot density) = ρ_B
    Pivot density introduced to nondimensionalize the RD equation; set equal to the boundary density, so it is not an independent fit.
assumptions (5)
  • domain assumption Static, spherically symmetric spacetime with a perfect-fluid energy-momentum tensor (Eq. 3)
    DM is assumed to be a static perfect fluid in quasi-equilibrium; motivated by self-interacting DM but not derived. A static fluid cannot be static at the horizon.
  • domain assumption Outer boundary density follows the NFW profile at r_B = 10^5 r_BH (Eqs. 8-9)
    NFW is observationally supported for cold DM, but extrapolating to 10^-2 pc is an assumption.
  • ad hoc to paper Density vanishes at the horizon, ρ(r_BH)=0 (Eq. 11)
    A criterion imposed without derivation; it is load-bearing for the negative-pressure conclusion.
  • standard math Weak energy condition p/ρ > -1 holds
    Standard energy condition used throughout to restrict parameter space.
  • domain assumption Negative total mass M(r)<0 is unphysical and rules out ω>0 solutions
    An interpretive judgment; the paper treats negative M(r) as nonviable rather than deriving an inconsistency.

how reviews work

0 comments
Cite this review

Pith. "Pith review of On Equation of State of Dark Matter around Massive Black Holes." pith.science (2026). https://pith.science/paper/KIHIVWCK

@misc{pith2026250112574,
  author       = {Pith},
  title        = {Pith review of: On Equation of State of Dark Matter around Massive Black Holes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KIHIVWCK}},
  note         = {Machine review of arXiv:2501.12574}
}
abstract

The nature of Dark Matter (DM) remains mysterious despite the substantial evidence from astrophysical and cosmological observations. While the majority of DM in our universe is non-relativistic, collisionless and its equation of state (EoS) is approximately pressureless $p\simeq 0$, DM becomes relativistic near the massive black holes in galactic center. Yet its EoS is seldom discussed in the relativistic regime. Here we initially explore the possible equation of state for DM in the vicinity of Schwarzschild black holes. We work in a spherical and quasi-static background spacetime, and describe DM as a perfect fluid in equilibrium. Through numerically solving the TOV equations with physical boundary conditions, we show that DM can have static profiles near black holes and its pressure should be negative in order to support the viable density profiles $\rho$. We illustrate with two simple general equations of state, namely the power law $p \propto \rho^\gamma$ and the radius-dependent $p \propto r\cdot \rho$, and compare them with the observations of the Milky Way. Our findings provide insights into the model-building of DM, which should incorporate the possibility of negative pressure in the relativistic regime around black holes.

Figures

Figures reproduced from arXiv: 2501.12574 by the authors.

Figure 1
Figure 1. FIG. 1. Density profiles for [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Mass function [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Verification of Eq [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Comparison between the profiles with [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Density profiles for [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Mass functions for [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Probing Dark Matter Spike with Gravitational Waves from Early EMRIs in the Milky Way Center

    astro-ph.GA 2025-06 conditional novelty 5.0 of 10

    Dark matter's drag on black holes spiraling into the Milky Way's central black hole would weaken low-frequency and strengthen high-frequency gravitational waves, a signal LISA or Taiji could potentially detect.

  2. Probing Self-Interacting Dark Matter via Gravitational-Wave Background from Eccentric Supermassive Black Hole Mergers

    astro-ph.GA 2025-05 conditional novelty 5.0 of 10

    Eccentric supermassive black hole binaries embedded in self-interacting dark matter produce a suppressed nanohertz gravitational-wave background, and current PTA data bound the cross section at sigma/mchi less than ab...

Reference graph

Works this paper leans on

43 extracted references · 15 canonical work pages · cited by 2 Pith papers

  1. [1]

    We expect that the curve ρ to smoothly change as ω varies for a given γ

    And there is always a solution with no matter distribu- tion when ω = 0. We expect that the curve ρ to smoothly change as ω varies for a given γ. As a conclusion for the cases with γ >0, scenarios with p >0 are not viable, as they at least violate one criterion of Eq. 10 and Eq. 11. And for p <0, to satisfy the WEC we only consider ω ∈ (−1, 0), where we f...

    work page

  2. [2]

    Cirelli, A

    M. Cirelli, A. Strumia, and J. Zupan, Dark matter (2024), arXiv:2406.01705 [hep-ph]

    arXiv 2024

  3. [3]

    Bertone, D

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

    arXiv 2005

  4. [4]

    L. B. et al., Black holes, gravitational waves and fun- damental physics: a roadmap, Classical and Quantum Gravity 36, 143001 (2019)

    work page 2019

  5. [5]

    Bertone et al., Gravitational wave probes of dark mat- ter: challenges and opportunities, SciPost Phys

    G. Bertone et al., Gravitational wave probes of dark mat- ter: challenges and opportunities, SciPost Phys. Core 3, 007 (2020), arXiv:1907.10610 [astro-ph.CO]

    arXiv 2020

  6. [6]

    K. Eda, Y. Itoh, S. Kuroyanagi, and J. Silk, New Probe of Dark-Matter Properties: Gravitational Waves from an Intermediate-Mass Black Hole Embedded in a Dark- Matter Minispike, Phys. Rev. Lett. 110, 221101 (2013), arXiv:1301.5971 [gr-qc]

    arXiv 2013

  7. [7]

    Lacroix, C

    T. Lacroix, C. Boehm, and J. Silk, Probing a dark matter density spike at the Galactic Center, Phys. Rev. D 89, 063534 (2014), arXiv:1311.0139 [astro-ph.HE]

    arXiv 2014

  8. [8]

    Yue, W.-B

    X.-J. Yue, W.-B. Han, and X. Chen, Dark matter: an effi- cient catalyst for intermediate-mass-ratio-inspiral events, Astrophys. J. 874, 34 (2019), arXiv:1802.03739 [gr-qc]

    arXiv 2019

Show all 43 references
  1. [9]

    Yue and Z

    X.-J. Yue and Z. Cao, Dark matter minispike: A sig- nificant enhancement of eccentricity for intermediate- mass-ratio inspirals, Phys. Rev. D 100, 043013 (2019), arXiv:1908.10241 [astro-ph.HE]

    2019 arXiv

  2. [10]

    B. J. Kavanagh, D. A. Nichols, G. Bertone, and D. Gag- gero, Detecting dark matter around black holes with gravitational waves: Effects of dark-matter dynamics on the gravitational waveform, Phys. Rev. D 102, 083006 (2020), arXiv:2002.12811 [gr-qc]

    2020 arXiv

  3. [11]

    G.-L. Li, Y. Tang, and Y.-L. Wu, Probing dark mat- ter spikes via gravitational waves of extreme-mass-ratio inspirals, Sci. China Phys. Mech. Astron. 65, 100412 (2022), arXiv:2112.14041 [astro-ph.CO]. 7

    2022 arXiv

  4. [12]

    Kadota, J

    K. Kadota, J. H. Kim, P. Ko, and X.-Y. Yang, Gravi- tational wave probes on self-interacting dark matter sur- rounding an intermediate mass black hole, Phys. Rev. D 109, 015022 (2024), arXiv:2306.10828 [hep-ph]

    2024 arXiv

  5. [13]

    Zhang and Y

    Z.-C. Zhang and Y. Tang, Velocity distribution of dark matter in spikes around Schwarzschild black holes and effects on gravitational waves from extreme-mass- ratio inspirals, Phys. Rev. D 110, 103008 (2024), arXiv:2403.18529 [astro-ph.GA]

    2024 arXiv

  6. [14]

    Y. Zhao, N. Dai, and Y. Gong, Distinguishing dark mat- ter halos with Extreme mass ratio inspirals, (2024), arXiv:2410.06882 [gr-qc]

    2024

  7. [15]

    Cheng, Y

    Y.-Z. Cheng, Y. Cao, and Y. Tang, Effects of black hole environments on extreme mass-ratio hyperbolic encoun- ters, (2024), arXiv:2411.03095 [gr-qc]

    2024 arXiv

  8. [16]

    Cao, Y.-Z

    Y. Cao, Y.-Z. Cheng, G.-L. Li, and Y. Tang, Probing vec- tor gravitational atom with eccentric intermediate mass- ratio inspirals, (2024), arXiv:2411.17247 [gr-qc]

    2024 arXiv

  9. [17]

    Liang, R

    D. Liang, R. Xu, Z.-F. Mai, and L. Shao, Probing vec- tor hair of black holes with extreme-mass-ratio inspirals, Phys. Rev. D 107, 044053 (2023), arXiv:2212.09346 [gr- qc]

    2023 arXiv

  10. [18]

    Gondolo and J

    P. Gondolo and J. Silk, Dark matter annihilation at the galactic center, Phys. Rev. Lett. 83, 1719 (1999)

    1999

  11. [19]

    Sadeghian, F

    L. Sadeghian, F. Ferrer, and C. M. Will, Dark-matter distributions around massive black holes: A general rel- ativistic analysis, Phys. Rev. D 88, 063522 (2013)

    2013

  12. [20]

    Matos and D

    T. Matos and D. Nunez, The general relativistic geome- try of the navarro-frenk-white model (2003), arXiv:astro- ph/0303594 [astro-ph]

    2003

  13. [21]

    Z. Xu, X. Hou, X. Gong, and J. Wang, Black hole space- time in dark matter halo, Journal of Cosmology and As- troparticle Physics 2018 (09), 038

    2018

  14. [22]

    E. T. Newman and A. I. Janis, Note on the Kerr spinning particle metric, J. Math. Phys. 6, 915 (1965)

    1965

  15. [23]

    Al-Badawi, S

    A. Al-Badawi, S. Shaymatov, and Y. Sekhmani, Schwarzschild black hole in galaxies surrounded by a dark matter halo (2024), arXiv:2411.01145 [gr-qc]

    2024 arXiv

  16. [24]

    F. S. Guzm´ an and F. D. Lora-Clavijo, Exploring the ef- fects of pressure on the radial accretion of dark matter by a Schwarzschild supermassive black hole, Monthly No- tices of the Royal Astronomical Society 415, 225 (2011)

    2011

  17. [25]

    F. S. Guzm´ an and F. D. Lora-Clavijo, Collisional density profiles of dark matter around supermassive black holes, Monthly Notices of the Royal Astronomical Society 416, 3083 (2011)

    2011

  18. [26]

    Cardoso, K

    V. Cardoso, K. Destounis, F. Duque, R. P. Macedo, and A. Maselli, Black holes in galaxies: Environmental im- pact on gravitational-wave generation and propagation, Phys. Rev. D 105, L061501 (2022)

    2022

  19. [27]

    Patra and B

    S. Patra and B. R. Majhi, Effect of dark matter halo on transonic accretion flow around a galactic black hole (2025), arXiv:2501.07456 [astro-ph.HE]

    2025 arXiv

  20. [28]

    Z. Shen, A. Wang, Y. Gong, and S. Yin, Analytical mod- els of supermassive black holes in galaxies surrounded by dark matter halos, Physics Letters B 855, 138797 (2024)

    2024

  21. [29]

    Z. Shen, A. Wang, and S. Yin, A class of analytical models for black holes surrounded by dark matter halos (2024), arXiv:2408.05417 [gr-qc]

    2024 arXiv

  22. [30]

    P. S. Letelier, Clouds of strings in general relativity, Phys. Rev. D 20, 1294 (1979)

    1979

  23. [31]

    Hamil and B

    B. Hamil and B. C. L¨ utf¨ uo˘ glu, Schwarzschild black hole surrounded by a cloud of strings in the background of perfect fluid dark matter (2024), arXiv:2410.09551 [gr- qc]

    2024 arXiv

  24. [32]

    Kaplinghat, S

    M. Kaplinghat, S. Tulin, and H.-B. Yu, Dark matter ha- los as particle colliders: Unified solution to small-scale structure puzzles from dwarfs to clusters, Phys. Rev. Lett. 116, 041302 (2016)

    2016

  25. [33]

    Alvarez and H.-B

    G. Alvarez and H.-B. Yu, Density spikes near black holes in self-interacting dark matter halos and indirect de- tection constraints, Phys. Rev. D 104, 043013 (2021), arXiv:2012.15050 [hep-ph]

    2021 arXiv

  26. [34]

    E. H. T. C. et al., First sagittarius a* event horizon tele- scope results. i. the shadow of the supermassive black hole in the center of the milky way, The Astrophysical Journal Letters 930, L12 (2022)

    2022

  27. [35]

    D. N. Spergel and P. J. Steinhardt, Observational ev- idence for selfinteracting cold dark matter, Phys. Rev. Lett. 84, 3760 (2000), arXiv:astro-ph/9909386

    2000 arXiv

  28. [36]

    Tulin and H.-B

    S. Tulin and H.-B. Yu, Dark Matter Self-interactions and Small Scale Structure, Phys. Rept. 730, 1 (2018), arXiv:1705.02358 [hep-ph]

    2018 arXiv

  29. [37]

    R. C. Tolman, Static solutions of Einstein’s field equa- tions for spheres of fluid, Phys. Rev. 55, 364 (1939)

    1939

  30. [38]

    J. R. Oppenheimer and G. M. Volkoff, On massive neu- tron cores, Phys. Rev. 55, 374 (1939)

    1939

  31. [39]

    J. F. Navarro, C. S. Frenk, and S. D. M. White, The Structure of cold dark matter halos, Astrophys. J. 462, 563 (1996), arXiv:astro-ph/9508025

    1996 arXiv

  32. [40]

    Gillessen, F

    S. Gillessen, F. Eisenhauer, S. Trippe, T. Alexander, R. Genzel, F. Martins, and T. Ott, Monitoring stellar orbits around the Massive Black Hole in the Galactic Center, Astrophys. J. 692, 1075 (2009), arXiv:0810.4674 [astro-ph]

    2009 arXiv

  33. [41]

    Sofue, A Grand Rotation Curve and Dark Matter Halo in the Milky Way Galaxy, Publ

    Y. Sofue, A Grand Rotation Curve and Dark Matter Halo in the Milky Way Galaxy, Publ. Astron. Soc. Jap. 64, 75 (2012), arXiv:1110.4431 [astro-ph.GA]

    2012 arXiv

  34. [42]

    T. G. Collaboration, K. A. E. Dayem, and et al., Improving constraints on the extended mass distribu- tion in the galactic center with stellar orbits (2024), arXiv:2409.12261 [astro-ph.GA]

    2024 arXiv

  35. [43]

    P. A. Seoane et al. (LISA), Astrophysics with the Laser Interferometer Space Antenna, Living Rev. Rel. 26, 2 (2023), arXiv:2203.06016 [gr-qc]

    2023 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.