pith. sign in

arxiv: 2605.18205 · v1 · pith:P4ST5AIUnew · submitted 2026-05-18 · 🌀 gr-qc

Kerr-like black holes shadow surrounded by dark matter halos: Comparison between various dark matter profiles

Malihe Heydari-Fard , Mohaddese Heydari-Fard This is my paper

Pith reviewed 2026-05-20 09:32 UTC · model grok-4.3

classification 🌀 gr-qc
keywords black hole shadowdark matter haloKerr-like black holesNewman-Janis algorithmrotating black holesgalactic centerscuspy profilescored profiles
0
0 comments X

The pith

Rotating black holes in dark matter halos cast slightly larger shadows than pure Kerr black holes, but the change in size and shape stays negligible across profiles.

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

The paper constructs static black hole solutions immersed in King, Hernquist, and Moore dark matter halo profiles, then applies the Newman-Janis algorithm to generate the corresponding rotating metrics. It examines how the characteristic density, characteristic radius, and spin parameter affect the horizons, ergoregion, and shadow radius, comparing these to the standard Kerr case and to other dark matter profiles. The central finding is that the shadow radius grows in the presence of dark matter, yet the overall size and shape of the shadow show only tiny differences that do not depend on whether the halo is cuspy or cored. This leads the authors to conclude that black hole shadows are not an effective way to distinguish the nature of dark matter distributions near galactic centers.

Core claim

By immersing static black hole solutions in various dark matter halo profiles and rotating them via the Newman-Janis algorithm, the authors show that the shadow radius of the resulting Kerr-like black holes increases relative to the vacuum Kerr solution, but the effect on shadow size and shape remains negligible for the King, Hernquist, Moore, and other considered profiles, independent of cuspy or cored structure; therefore black hole shadows are unsuitable for distinguishing the nature of dark matter in galactic centers.

What carries the argument

Kerr-like rotating metrics obtained from static dark-matter-immersed solutions via the Newman-Janis algorithm, from which the shadow radius is computed as a function of dark-matter parameters and spin.

If this is right

  • The shadow radius increases compared to the pure Kerr black hole in the absence of dark matter.
  • The impact on the size and shape of the shadow remains negligible for King, Hernquist, and Moore profiles.
  • The negligible effect holds for all other dark matter halo profiles considered in the paper.
  • The result is independent of whether the halo is cuspy or cored.
  • Black hole shadows are not a suitable tool for distinguishing the nature of dark matter distributions in galactic centers.

Where Pith is reading between the lines

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

  • If the negligible change holds, then Event Horizon Telescope images of Sgr A* or M87* will offer limited power to constrain the specific form of dark matter near the center.
  • Other observables such as stellar orbits or accretion disk spectra may be needed to probe differences between dark matter profiles.
  • The conclusion applies directly to the family of metrics constructed in this way; different rotation-generation methods could yield different sensitivity.

Load-bearing premise

The static black hole solutions immersed in the chosen dark matter halo profiles can be extended to rotating solutions via the Newman-Janis algorithm without introducing additional instabilities or metric corrections that would alter the shadow calculation.

What would settle it

A precise measurement or numerical computation of the shadow radius and shape for the same black hole spin that shows large, profile-dependent differences between different dark matter halos would falsify the negligible-impact claim.

Figures

Figures reproduced from arXiv: 2605.18205 by Malihe Heydari-Fard, Mohaddese Heydari-Fard.

Figure 1
Figure 1. Figure 1: The behavior of function ∆(r) for different values of DM parameters ρs and rs, with M = 1. The rotation parameter is set to a = 0.6 and a = 0.9 in the top and bottom rows, respectively. In each panel the solid red curve corresponds to the Kerr BH in the absence of DM. r+ r￾0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 2.0 a r± [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The behavior of the inner (r−) and outer (r+) horizons as a function of spin parameter a for ρs = 0.04, rs = 0.02 and M = 1. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The shape of ergosphere of the Kerr-like BH in a King DM halo with different rotation parameter a in the xz-plane. The DM halo parameters is set to ρs = 0.2 and rs = 0.08, with M = 1. 3 Null geodesics in galactic DM halo In this section, we are interested to study the photon motion around Kerr-like BHs in a King DM halo, which can be expressed with Hamilton-Jacobi equations ∂S ∂λ = − 1 2 g µν ∂S ∂xµ ∂S ∂xν… view at source ↗
Figure 4
Figure 4. Figure 4: Celestial coordinates [72]. Substituting dθ dr and dφ dr from Eqs. 21-23, one can rewrite the above coordinates in terms of two parameters η and ξ as follows α = − ξ sin θ , (35) β = √ η − ξ 2 cot2 θ + a 2 cos2 θ. (36) Taking (29) and (30) into account, and choosing θo = π 2 , we have plotted the shadow of the rotating BHs surrounded by a King-type DM halo for different values of ρs and rs parameters in [… view at source ↗
Figure 5
Figure 5. Figure 5: The shape of shadow of the Kerr-like BH in a King DM halo for different DM densities ρs with rs = 0.2 (left panel), and for different halo radius rs with ρs = 0.2 (right panel). We set a = 0.99, θo = π 2 and M = 1. In each panel the solid red curve corresponds to the Kerr BH in the absence of DM. rs=0.04 0.0 0.1 0.2 0.3 0.4 0.5 4.838 4.840 4.842 4.844 4.846 4.848 4.850 ρs Rsh ρs=0.04 0.0 0.1 0.2 0.3 0.4 0.… view at source ↗
Figure 6
Figure 6. Figure 6: The dependence of the shadow radius Rsh on the core density ρs for rs = 0.04 (left panel), and on the core radius rs with ρs = 0.04 (right panel). The BH spin is a = 0.9 and the inclination angle is set to θo = π 2 . 9 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The shape of shadow of the Kerr-like BH in a King DM halo for different rotation parameter with θo = π 2 (left panel), and for different inclinations angles with a = 0.99 (right panel). The DM halo parameters are set to ρs = 0.2 and rs = 0.08, with M = 1. Finally, a comparison between DM halo profiles with the Kerr BH without DM is presented in [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The shape of shadow for rotating BHs in the King, isothermal, Moore, Burkret, NFW, Hernquist and the Dehnen DM halo models with ρs = 0.04 and rs = 0.2 (left panel). The right panel represents zoom of the left panel, and the solid red curve corresponds to the Kerr BH in the absence of DM. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
read the original abstract

The study of shadows of static and rotating black holes immersed in various dark matter halo profiles has gained significant attention in recent years. In this paper, we consider the static black hole solution immersed in three dark matter halo profiles (King, Hernquist, and Moore) and, by using the Newman-Janis algorithm, obtain the corresponding rotating black hole solutions. The main goal of the paper is to study the influence of the characteristic density, characteristic radius, and the spin parameter on the inner and outer horizons, the ergoregion, and the shadow radius, and to compare the results with Kerr black holes and other dark matter profiles. Our findings indicate that the shadow radius of rotating black holes immersed in dark matter increases compared to that of the Kerr black hole in the absence of dark matter; however, the impact on the size and shape of the shadow is negligible for King, Hernquist, and Moore profiles, and for all other dark matter halo profiles considered, and is independent of whether the halo is cuspy or cored. Therefore, at least for these Kerr-like black holes, the black hole shadow is not a suitable tool for distinguishing the nature of the dark matter distribution in galactic centers.

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

2 major / 1 minor

Summary. The paper constructs static black hole solutions immersed in King, Hernquist, and Moore dark matter halo profiles, applies the Newman-Janis algorithm to generate the corresponding rotating Kerr-like metrics, and examines the dependence of horizons, ergoregions, and shadow radii on the halo parameters (characteristic density and radius) and spin. It reports that the shadow radius increases relative to the vacuum Kerr case, yet the change in size and shape remains negligible across the profiles considered and is independent of whether the halo is cuspy or cored, concluding that black hole shadows are not a suitable probe for distinguishing dark matter distributions at galactic centers.

Significance. If the rotating metrics and shadow calculations are valid, the result would indicate that shadow observables are largely insensitive to the detailed radial structure of common dark matter halo profiles, limiting their utility for constraining dark matter properties via high-resolution imaging. This adds to the literature on modified black hole spacetimes but would benefit from explicit quantification of the reported negligible deviations.

major comments (2)
  1. [Rotating black hole solutions (obtained via Newman-Janis algorithm)] The rotating solutions are obtained by applying the Newman-Janis algorithm to the static metrics with extended dark matter density profiles (King, Hernquist, Moore). Because the Newman-Janis procedure does not in general yield exact solutions of the Einstein equations when non-vacuum matter is present, the resulting metric functions may contain spurious terms that alter the effective potential for null geodesics at the photon sphere. This directly affects the reported shadow radii and the claim that the impact is negligible and profile-independent; explicit verification that the rotated metric satisfies the field equations with a consistent rotating stress-energy tensor is required.
  2. [Shadow radius analysis and comparisons] The central conclusion that the shadow is insensitive to cuspy versus cored profiles rests on numerical comparisons of shadow radii for the chosen halos. Without tabulated values or plots showing the fractional change in shadow radius (e.g., as a function of characteristic density and radius for fixed spin), it is difficult to assess whether the “negligible” characterization is robust or merely an artifact of the parameter ranges explored.
minor comments (1)
  1. [Abstract] The abstract states that the impact is negligible “for all other dark matter halo profiles considered”; a brief list or reference to those additional profiles in the main text would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below, indicating the revisions we intend to make.

read point-by-point responses

  1. Referee: [Rotating black hole solutions (obtained via Newman-Janis algorithm)] The rotating solutions are obtained by applying the Newman-Janis algorithm to the static metrics with extended dark matter density profiles (King, Hernquist, Moore). Because the Newman-Janis procedure does not in general yield exact solutions of the Einstein equations when non-vacuum matter is present, the resulting metric functions may contain spurious terms that alter the effective potential for null geodesics at the photon sphere. This directly affects the reported shadow radii and the claim that the impact is negligible and profile-independent; explicit verification that the rotated metric satisfies the field equations with a consistent rotating stress-energy tensor is required.

    Authors: We thank the referee for highlighting this important technical point. The Newman-Janis algorithm is a standard and widely used method in the literature for generating rotating metrics from static seed solutions in the presence of matter distributions, including dark matter halos, as employed in numerous related studies. We acknowledge that the resulting metrics are generally approximate and may not satisfy the Einstein equations exactly with a transformed stress-energy tensor. Our shadow calculations are performed directly on the generated metric functions. In the revised manuscript we will add an explicit discussion of the approximate nature of the Newman-Janis procedure in this context, together with a clear statement of the limitations and the fact that our conclusions are obtained within this commonly adopted framework. revision: partial

  2. Referee: [Shadow radius analysis and comparisons] The central conclusion that the shadow is insensitive to cuspy versus cored profiles rests on numerical comparisons of shadow radii for the chosen halos. Without tabulated values or plots showing the fractional change in shadow radius (e.g., as a function of characteristic density and radius for fixed spin), it is difficult to assess whether the “negligible” characterization is robust or merely an artifact of the parameter ranges explored.

    Authors: We agree that explicit quantification of the deviations would improve the robustness of the presentation. In the revised version we will include additional plots and/or tables that show the fractional change in shadow radius relative to the Kerr case, as a function of the characteristic density and radius parameters, for representative spin values and across the different halo profiles. This will allow readers to directly evaluate the magnitude of the effect and confirm its profile independence. revision: yes

Circularity Check

0 steps flagged

No circularity: shadow radii computed directly from NJA-derived metric functions

full rationale

The derivation applies the Newman-Janis algorithm to obtain rotating metrics from given static DM-immersed solutions, then evaluates the photon-sphere conditions and shadow radius from the resulting metric coefficients. These steps are independent calculations from the input density profiles and do not reduce the reported shadow increase or negligibility claim to a fitted parameter, self-definition, or self-citation chain. The independence from cuspy/cored profiles follows from explicit comparison across profiles rather than any definitional equivalence.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the existence of static black hole solutions in the chosen halo profiles and on the validity of the Newman-Janis algorithm for generating rotating metrics; these are standard domain assumptions rather than new postulates.

free parameters (1)
  • characteristic density and radius of each halo profile
    These parameters are introduced to parameterize the dark matter density distribution and are varied to study their effect on horizons and shadows.
axioms (1)
  • domain assumption Static black hole solutions immersed in King, Hernquist, and Moore dark matter halos exist and admit rotating extensions via the Newman-Janis algorithm.
    This premise is required to obtain the Kerr-like metrics whose shadows are then computed.

pith-pipeline@v0.9.0 · 5751 in / 1412 out tokens · 54928 ms · 2026-05-20T09:32:52.129998+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

79 extracted references · 79 canonical work pages · 1 internal anchor

  1. [1]

    V. C. Rubin and W. K. Ford, Astrophys. J. 159 (1970) 379

    work page 1970

  2. [2]

    Corbelli and P

    E. Corbelli and P. Salucci, Mon. Not. Roy. Astron. Soc. 311 (2000) 441

    work page 2000

  3. [3]

    Clowe, M

    D. Clowe, M. Bradac, A. H. Gonzalez, M. Markevitch, S. W. Randall, and et. al., Astrophys. J. Lett. 648 (2006) L109

    work page 2006

  4. [4]

    Davis, G

    M. Davis, G. Efstathiou, C. S. Frenk and S. D. M. White, Astrophys. J. 292 (1985) 371. 11

    work page 1985

  5. [5]

    Komatsu et al

    E. Komatsu et al. [WMAP], Astrophys. J. Suppl. 192 (2011) 18

    work page 2011

  6. [6]

    P. A. R. Ade et al. [Planck], Astron. Astrophys. 571 (2014) A16

    work page 2014

  7. [7]

    Massey, T

    R. Massey, T. Kitching and J. Richard, Rept. Prog. Phys. 73 (2010) 086901

    work page 2010

  8. [8]

    Vegetti, S

    S. Vegetti, S. Birrer, G. Despali, C. D. Fassnacht, D. Gilman and et.al., Space Sci. Rev. 220 (2024) 58

    work page 2024

  9. [9]

    Zavala and C

    J. Zavala and C. S. Frenk, Galaxies 7 (2019) 81

    work page 2019

  10. [10]

    J. Wang, S. Bose, C. S. Frenk, L. Gao, A. Jenkins, and et. al., Nature 585 (2020) 39

    work page 2020

  11. [11]

    Bhattacharya, S

    S. Bhattacharya, S. Habib, K. Heitmann and A. Vikhlinin, Theory vs. Observations, Astrophys. J. 766 (2013) 32

    work page 2013

  12. [12]

    B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. Lett 116 (2016) 061102

    work page 2016

  13. [13]

    A. M. Ghez, B. L. Klein, M. Morris and E. E. Becklin, Astrophys. J. 509 (1998) 678

    work page 1998

  14. [14]

    Schodel, T

    R. Schodel, T. Ott, R. Genzel, R. Hofmann, M. Lehnert, and et. al., Nature 419 (2002) 694

    work page 2002

  15. [15]

    Akiyama et al

    K. Akiyama et al. [Event Horizon Telescope], Astrophys. J. Lett. 875 (2019) L1

    work page 2019

  16. [16]

    Akiyama et al

    K. Akiyama et al. [Event Horizon Telescope], Astrophys. J. Lett. 930 (2022) L12

    work page 2022

  17. [17]

    J. L. Synge, Mon. Not. Roy. Astron. Soc. 131 (1966) 463

    work page 1966

  18. [18]

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

    work page 1979

  19. [19]

    J. M. Bardeen, in Black Holes (Les Astres Occlus), pp. 215-239, Gordon and Breach Science Publishers, New York, (1973)

    work page 1973

  20. [20]

    Kumaran and A

    Y. Kumaran and A. Övgün, Symmetry 14 (2022) 2054

    work page 2022

  21. [21]

    R. A. Konoplya, Phys. Lett. B 795 (2019) 1

    work page 2019

  22. [22]

    Jusufi, M

    K. Jusufi, M. Jamil and T. Zhu, Eur. Phys. J. C 80 (2020) 354

    work page 2020

  23. [23]

    Saurabh and K

    K. Saurabh and K. Jusufi, Eur. Phys. J. C 81 (2021) 490

    work page 2021

  24. [24]

    A. Das, A. Saha and S. Gangopadhyay, Class. Quant. Grav. 39 (2022) 075005

    work page 2022

  25. [25]

    S. J. Ma, T. C. Ma, J. B. Deng and X. R. Hu, Mod. Phys. Lett. A 38 (2023) 2350104

    work page 2023

  26. [26]

    X. Hou, Z. Xu, M. Zhou and J. Wang, JCAP 07 (2018) 015

    work page 2018

  27. [27]

    X. Hou, Z. Xu and J. Wang, JCAP 12 (2018) 040

    work page 2018

  28. [28]

    Vagnozzi, R

    S. Vagnozzi, R. Roy, Y. D. Tsai, L. Visinelli, M. Afrin, and et. al., Class. Quant. Grav. 40 (2023) 165007

    work page 2023

  29. [29]

    R. C. Pantig and A. Övgün, Fortsch. Phys. 71 (2023) 2200164

    work page 2023

  30. [30]

    Faraji and J

    S. Faraji and J. L. Rosa, Astron. Astrophys. 699 (2025) A266

    work page 2025

  31. [31]

    Heydari-Fard, S

    M. Heydari-Fard, S. G. Honarvar and M. Heydari-Fard, Mon. Not. Roy. Astron. Soc. 521 (2023) 708

    work page 2023

  32. [32]

    Bamber, J

    J. Bamber, J. C. Aurrekoetxea, K. Clough and P. G. Ferreira, Phys. Rev. D 107 (2023) 024035

    work page 2023

  33. [33]

    T. K. Karydas, B. J. Kavanagh and G. Bertone, Phys. Rev. D 111 (2025) 063070

    work page 2025

  34. [34]

    Y. Cao, H. Feng, W. Hong and J. Tao, Commun. Theor. Phys. 73 (2021) 095403

    work page 2021

  35. [35]

    X. Zhou, Y. Xue, B. Mu and J. Tao, Phys. Dark. Univ. 39 (2023) 101168. 12

    work page 2023

  36. [36]

    R. B. Ndongmo, S. Mahamat, C. B. Tabi, T. B. Bouetou and T. C. Kofane, Phys. Dark. Univ. 42 (2023) 101299

    work page 2023

  37. [37]

    Z. Xu, X. Hou, J. Wang and Y. Liao, Adv. High Energy Phys. 2019 (2019) 2434390

    work page 2019

  38. [38]

    Jusufi, Phys

    K. Jusufi, Phys. Rev. D 101 (2020) 084055

    work page 2020

  39. [39]

    D. Liu, Y. Yang, A. Övgün, Z. W. Long and Z. Xu, Eur. Phys. J. C 83 (2023) 565

    work page 2023

  40. [40]

    D. Liu, Y. Yang and Z. W. Long, Eur. Phys. J. C 84 (2024) 731

    work page 2024

  41. [41]

    D. Liu, Y. Yang, S. Wu, Y. Xing, Z. Xu, and et. al., Phys. Rev. D 104 (2021) 104042

    work page 2021

  42. [42]

    Cardoso, K

    V. Cardoso, K. Destounis, F. Duque, R. P. Macedo and A. Maselli, Phys. Rev. D 105 (2022) L061501

    work page 2022

  43. [43]

    Z. Xu, X. Hou, X. Gong, and J. Wang, JCAP 09 (2018) 038

    work page 2018

  44. [44]

    X. X. Zeng, C. Y. Yang, M. I. Aslam, R. Saleem and S. Aslam, JCAP 08 (2025) 066

    work page 2025

  45. [45]

    Jusufi, M

    K. Jusufi, M. Jamil, P. Salucci, T. Zhu and S. Haroon, Phys. Rev. D 100 (2019) 044012

    work page 2019

  46. [46]

    Zhang, T

    C. Zhang, T. Zhu, and A. Wang, Phys. Rev. D 104 (2021) 124082

    work page 2021

  47. [47]

    J. F. Navarro, C. S. Frenk, and S. D. M. White, Astrophys. J. 490 (1997) 493

    work page 1997

  48. [48]

    Burkert, Astrophys

    A. Burkert, Astrophys. J. Lett. 447 (1995) L25

    work page 1995

  49. [49]

    Retana-Montenegro, E

    E. Retana-Montenegro, E. Van Hese, G. Gentile, M. Baes, and F. Frutos-Alfaro, Astron. Astrophys. 540 (2012) A70

    work page 2012

  50. [50]

    D. Liu, Y. Yang, Z. Xu and Z. W. Long, Eur. Phys. J. C 84 (2024) 136

    work page 2024

  51. [51]

    K. G. Begeman, A. H. Broeils, and R. H. Sanders, Mon. Not. Roy. Astron. Soc. 249 (1991) 523

    work page 1991

  52. [52]

    Y. Yang, D. Liu, A. Övgün, G. Lambiase and Z. W. Long, Eur. Phys. J. C 84 (2024) 63

    work page 2024

  53. [53]

    King, Astron

    I. King, Astron. J. 67 (1962) 471

    work page 1962

  54. [54]

    Al-Badawi and F

    A. Al-Badawi and F. Ahmed, Eur. Phys. J. C 86 (2026) 139

    work page 2026

  55. [55]

    Hernquist, Astrophys

    L. Hernquist, Astrophys. J. 356 (1990) 359

    work page 1990

  56. [56]

    Jumaniyozov, Eur

    S. Jumaniyozov, Eur. Phys. J. C 85 (2025) 1267

    work page 2025

  57. [57]

    S. K. Jha, JCAP 06 (2025) 033

    work page 2025

  58. [58]

    Dehnen, Mon

    W. Dehnen, Mon. Not. Roy. Astron. Soc. 265 (1993) 250

    work page 1993

  59. [59]

    Uktamov, S

    U. Uktamov, S. Shaymatov, B. Ahmedov and C. Yuan, Eur. Phys. J. C 85 (2025) 1432

    work page 2025

  60. [60]

    M. M. Gohain, D. J. Gogoi, K. Bhuyan and P. Phukon, JHEP 51 (2026) 100539

    work page 2026

  61. [61]

    Al-Badawi, S

    A. Al-Badawi, S. Shaymatov and Y. Sekhmani, JCAP 02 (2025) 014

    work page 2025

  62. [62]

    M. M. Gohain, P. Phukon and K. Bhuyan, Phys. Dark. Univ. 46 (2024) 101683

    work page 2024

  63. [63]

    Cavaliere and R

    A. Cavaliere and R. Fusco-Femiano, Astron. Astrophys. 49 (1976) 137

    work page 1976

  64. [64]

    S. R. Wu, B. Q. Wang, Z. W. Long and H. Chen, Phys. Dark. Univ. 44 (2024) 101455

    work page 2024

  65. [65]

    Y. G. Liu, C. K. Qiao and J. Tao, JCAP 10 (2024) 075. 13

    work page 2024

  66. [66]

    Moore, T

    B. Moore, T. R. Quinn, F. Governato, J. Stadel and G. Lake, Mon. Not. Roy. Astron. Soc. 310 (1999) 1147

    work page 1999

  67. [67]

    R. C. Pantig and A. Övgün, JCAP 08 (2022) 056

    work page 2022

  68. [68]

    C. K. Qiao and P. Su, Eur. Phys. J. C 84 (2024) 1032

    work page 2024

  69. [69]

    Freundlich, F

    J. Freundlich, F. Jiang, A. Dekel, and et.al. Mon. Not. Roy. Astron. Soc. 499 (2020) 2912

    work page 2020

  70. [70]

    Jusufi, Phys

    K. Jusufi, Phys. Rev. D 101 (2020) 124063

    work page 2020

  71. [71]

    Xing-Hui Feng and H. Lu, Eur. Phys. J. C 80 (2020) 551

    work page 2020

  72. [72]

    S. E. Vazquez and E. P. Esteban, Nuovo Cim. B 119 (2004), 489-519 doi:10.1393/ncb/i2004-10121-y [arXiv:gr-qc/0308023 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1393/ncb/i2004-10121-y 2004

  73. [73]

    Mini monster black hole could hold clues to giant’s growth, (2024), chandra Press Room

    work page 2024

  74. [74]

    M. J. Bustamante-Rosell, E. Noyola, K. Gebhardt, M. H. Fabricius, X. Mazzalay, and et. al., Astrophys. J. 921 (2021) 107

    work page 2021

  75. [75]

    Pascale, C

    R. Pascale, C. Nipoti, F. Calura and A. Della Croce, Astron. Astrophys. 700 (2025) A77

    work page 2025

  76. [76]

    Aditya and A

    K. Aditya and A. Mangalam, Astrophys. J. 997 (2026) 194

    work page 2026

  77. [77]

    M. S. Ali, A. Negi and S. Pant, arXiv:2509.03507 [gr-qc]

    work page arXiv

  78. [78]

    Atamurotov, F

    F. Atamurotov, F. Sarikulov, S. G. Ghosh and G. Mustafa, Phys. Dark. Univ. 46 (2024) 101625

    work page 2024

  79. [79]

    Shodikulov, M

    B. Shodikulov, M. Mirov, F. Atamurotov, S. G. Ghosh and A. Abdujabbarov, Phys. Dark. Univ. 50 (2025) 102096. 14 Table 1: Summary of the papers presenting BHs surrounded by DM halos. Constants ρs and rs are the characteristic density and scale parameter. Density distribution Density profile ρ(r) Redshift function References Navarro-Frenk-White (NFW) [ 47] ...

    work page 2025