Pith. sign in

REVIEW 3 major objections 6 minor 1 cited by

Relativistic structure of a supermassive black hole embedded in the dark matter halo of NGC 4649 (M60)

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read The paper constructs an exact Schwarzschild-type black hole embedded in the dark matter halo of NGC 4649 (M60), with halo-modified horizon, shadow, curvature, and thermodynamics.

desk verdict The claimed exact metric does not solve the paper's own Eq. (8) — off by ~14 orders of magnitude at large r — so the shadow, Kretschmann, and thermodynamic results are built on a solution that is not one. read the letter →

arxiv 2505.04222 v2 pith:Q35LSHI7 submitted 2025-05-07 gr-qc astro-ph.HEhep-th

Francisco S. N. Lobo , Jorde A. A. Ramos , Manuel E. Rodrigues This is my paper · ORCID
classification gr-qcastro-ph.HEhep-th
keywords blackholedarkmatterhaloNGC4649M60SchwarzschildsolutionshadowKretschmannscalarextremal
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 constructs a static, spherically symmetric black hole solution whose exterior is not vacuum but is filled by a dark matter halo modeled on observations of the elliptical galaxy NGC 4649 (M60). The halo is described by a cored density profile with two parameters, the asymptotic circular velocity $V_c$ and the scale radius $a$, and the black hole adds a mass $m_{\rm BH}$; the authors claim that solving the coupled field equations (7)–(9) produces the metric (16), which reduces to Schwarzschild when $V_c,a\to0$. A sympathetic reading takes this as a concrete template for how a realistic galactic environment modifies the near-horizon geometry: the horizon radius, photon sphere, shadow, curvature invariants, and thermodynamic relations all acquire halo-dependent corrections. If the construction is right, it gives a way to use strong-field observations of supermassive black holes to probe their surrounding dark matter halos.

What carries the argument

The central object is the anisotropic stress-energy tensor $T^{(\rm DM)\mu}_{\ \ \nu}=\mathrm{diag}(-\rho_{\rm DM},0,P,P)$, with $\rho_{\rm DM}$ given by Eq. (1), $P$ by Eq. (9), and the mass function $M(r)=m_{\rm BH}+r^3V_c^2/(a^2+r^2)$. The mechanism is the first-order equation $F'/F=2M(r)/[r(r-2M(r))]$, whose solution the paper obtains as $F(r)=(r-\lambda)^\xi/r$. This $F$ controls the event horizon through $F=0$, the photon sphere through $F-rF'/2=0$, the surface gravity, and therefore every derived geometric and thermodynamic quantity.

What would settle it

Evaluate Eq. (8) at a radius well inside the halo scale, e.g. $r=10^{20}$ m with Data I. The proposed $F$ gives $d\ln F/dr\approx(\xi-1)/r\approx1.26\times10^{-20}/r$, while $2M/[r(r-2M)]\approx3.74\times10^{-6}/r$; the fourteen-order-of-magnitude mismatch means a direct numerical integration of Eq. (8) would produce a different $F$, settling whether Eq. (16) follows from the field equations.

Watch

Extended reading notes

Core claim

On its own terms, the central discovery is that the coupled Einstein equations (7)–(9) with the halo density $\rho_{\rm DM}(r)=\frac{V_c^2}{4\pi G}\frac{3a^2+r^2}{(a^2+r^2)^2}$ admit an exact static, spherically symmetric solution, written as $$$ds^{2}$=-\frac{(r-\$\lambda$)^\xi}{r}\,$dt^{2}$+\frac{$dr^{2}$}{1-\frac{2}{r}\left(m_{\rm BH}+\frac{$r^{3}$$V_c^{2}$}{$a^{2}$+$r^{2}$}\right)}+$r^{2}$d\$\Omega$^2,$$ with $\lambda$ the real root of Eq. (13) and $\xi$ given by Eq. (12). In the limit $V_c,a\to0$, $\lambda\to2m_{\rm BH}$ and $\xi\to1$, recovering Schwarzschild. The authors then use this metric to show that the halo shifts the horizon to $r_h=\lambda$, moves the photon sphere to $r_{\rm ph}=3\lambda/(3-\xi)$, changes the shadow by a fractional amount of order $10^{-7}$, and alters the Kretschmann scalar through subleading terms that decay as $1/r^5$ and $1/r^4$. Thermodynamically, the horizon temperature vanishes while the entropy stays nonzero, giving an extremal configuration with finite tangential pressure.

Load-bearing premise

The construction depends on the unshown integration step in which $F(r)=(r-\lambda)^\xi/r$ is asserted to solve Eq. (8) exactly; if that substitution is not an identity, the metric and all derived properties collapse.

Editorial extensions

If this is right

  • The event horizon is fixed by $F(r)=0$, giving $r_h=\lambda$; with the reported Data I and Data II parameters the horizon sits at $1.034\times10^{13}$ m and $1.33\times10^{13}$ m, bracketing the halo-free Schwarzschild value $1.27\times10^{13}$ m.
  • The photon-sphere radius is $r_{\rm ph}=3\lambda/(3-\xi)$; the associated shadow radius is larger than Schwarzschild by a fractional amount of order $10^{-7}$, corresponding to a few times $10^{-5}$ percent.
  • The Kretschmann scalar diverges as $48m_{\rm BH}^2/r^6$ near the center, gains halo-dependent $1/r^5$ corrections, and decays as $1/r^4$ at large radius, so the halo prolongs curvature effects out to roughly the halo scale radius.
  • Thermodynamically, the mass–entropy relation tends to $M\sim(1-2V_c^2)M^{(\rm Sch)}$ as $S\to\infty$, and because $r_h=\lambda$ with $\xi>1$, the horizon temperature and surface gravity vanish, producing an extremal configuration with nonzero entropy and finite tangential pressure.
  • All quantities reduce to standard Schwarzschild when both halo parameters vanish.

Reading between the lines

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

  • The same integration pipeline could be applied to any cored spherical density profile, since the mass function follows from a simple quadrature; each profile would generate its own family of halo-dressed Schwarzschild metrics, not just the one written in Eq. (16).
  • Because the shadow shift is so small, the practical observational signature of this halo will likely appear elsewhere—in lensing time delays, orbital precession, or the mass–entropy relation—rather than in the shadow itself.
  • The extremal zero-temperature endpoint, with finite tangential pressure at the horizon, is a classical analogue of the extremal Kerr–Newman state; the next natural question is whether the equilibrium is stable under linear perturbations.
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 / 6 minor

Summary. The paper proposes a static, spherically symmetric line element, Eq. (16), claimed to be an exact solution of the Einstein equations with an anisotropic dark-matter fluid whose density profile, Eq. (1), is calibrated to observations of NGC 4649 (M60). From this metric the authors derive the horizon radius, Kretschmann scalar, photon-sphere and shadow radii, thermodynamic quantities, and tangential pressure, using two parameter sets (Data I and Data II) taken from Shen & Gebhardt [36]. The central mathematical claim is that the functions (12)-(14) solve the coupled system (7)-(9). I find that this claim is incorrect: Eq. (16) does not satisfy Eq. (8), so the line element is not a solution of the stated field equations and the subsequent derived quantities are not properties of such a solution.

Significance. If the construction were correct, the paper would provide a simple analytic black-hole solution with an observationally calibrated halo and a systematic study of its shadow and thermodynamic signatures, which would be a useful contribution to the dark-matter-black-hole literature. The authors are transparent about the parameter inputs and provide many explicit formulas, tables, and figures. However, the exactness of Eq. (16) is the foundation of every subsequent result; because that foundation fails, the horizon radius, Kretschmann scalar, shadow radius, and temperature computed in Sections III.A-III.E are not properties of the Einstein system (7)-(9). The paper's astrophysical motivation does not compensate for the algebraic error at the core of the construction.

major comments (3)
  1. [II.C, Eqs. (8), (10), (16)] The proposed metric does not solve Eq. (8). Substituting M(r)=m_BH+r^3 V_c^2/(a^2+r^2) and F(r)=(r-lambda)^xi/r into Eq. (8) and clearing denominators yields a polynomial identity in r. The r^4 coefficient requires xi-1=2V_c^2/(1-2V_c^2); for Data I (V_c=13.68e-4) this required value is about 3.74e-6, whereas Eqs. (12)-(14) give xi-1=1.26e-20, a discrepancy of roughly 14 orders of magnitude. The r^2 coefficient of the same identity independently requires (xi-1)a^2=0, so the identity fails for any nonzero halo scale radius. Equivalently, at large r Eq. (8) forces d ln F/dr ~ [2V_c^2/(1-2V_c^2)]/r, while Eq. (16) gives d ln F/dr ~ (xi-1)/r. The step from Eq. (8) to Eq. (11) is not derived in the paper and is not supplied by the cited reference [27]. The residual is an algebraic inconsistency, not a numerical-precision issue.
  2. [III.C, Eqs. (34)-(36)] The shadow-radius formula is derived under an asymptotic-flatness assumption that the proposed metric does not satisfy. For xi>1, which holds for both Data I and Data II, F(r)=(r-lambda)^xi/r ~ r^(xi-1) as r tends to infinity, so F(r_O) diverges rather than approaching 1. The simplified expression (34) is therefore not the correct asymptotic limit for Eq. (16), and Eq. (36) implies r_sh proportional to r_O^((xi-1)/2), which grows without bound with the observer distance. The shadow radius is not a well-defined asymptotic observable for the metric as written, independently of whether Eq. (16) were a solution.
  3. [III.D, Eqs. (42)-(44)] The claimed extremal temperature T=0 rests on an invalid temperature expression. For the metric (2), which has g_rr=1/G(r), the standard surface-gravity formula involves F'(r)G'(r) (equivalently F' times dG/dr), not F'(r) times d[1/G(r)]/dr as written in Eq. (42). In the Schwarzschild limit, d[1/G]/dr diverges at the horizon, so Eq. (42) does not reproduce the Hawking temperature. The conclusion T=0 in Eq. (44) is therefore not a valid consequence of the system (7)-(9).
minor comments (6)
  1. [II.C, Eq. (11)] The line appears to read 'F(r)F(r)=...'; the duplicate F(r) should be removed.
  2. [Table IV caption] The caption contains 'Tabela I'; this should read 'Table I'.
  3. [I, last paragraph] The word 'Throuhgout' is a typo for 'Throughout'.
  4. [III.B, Eq. (21)] The symbol g(r) is used in Eq. (21) but is never defined; please clarify whether it denotes G(r) or 1/G(r) and verify that the displayed expression follows from the general formula (4).
  5. [III.C, Figs. 5-6] The horizontal lines labeled 'Sgr A* (1 sigma, Keck+VLTI)' and 'Sgr A* (2 sigma, Keck+VLTI)' should be explained, since the paper models the M60 black hole; state explicitly that the Sgr A* bounds are used only as a generic test of the shadow-mass ratio.
  6. [Throughout] The notation for the black hole mass alternates between M in the abstract and Table I and m_BH in the equations; the notation should be unified.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: all fitted parameters (M, Vc, a) are imported from the independent NGC 4649 observational fit [36], and the shadow, curvature, and thermodynamic quantities are evaluated downstream as one-way consequences. The problematic step from Eq. (8) to Eq. (11) is an apparent non-solution of the stated equations, but that is a correctness defect, not a circularity.

full rationale

The paper's parameter values are not fitted to its own target observables: it explicitly adopts M, Vc, and a from the independent mass-profile analysis of Shen & Gebhardt [36] (Table I), then integrates Eq. (7) to obtain M(r), proposes F(r), and computes K, r_sh, and T from that metric. None of these computed quantities is fed back to define the parameters, so no fitted input is renamed as a prediction. The only overlapping self-citation ([52], for the Kretschmann scalar expression) is formula-level and not load-bearing for the existence or uniqueness of the spacetime. The horizon radius r_h=lambda follows immediately from the chosen ansatz F(r)=(r-lambda)^xi/r, but this is a mathematical consequence of the ansatz, not an input used to construct the ansatz. If the central claim that Eq. (16) solves Eqs. (7)-(9) is incorrect (the reduction from Eq. (8) to Eq. (11) is not demonstrated and the large-r coefficient of d ln F/dr appears inconsistent with Eq. (8) by about 14 orders of magnitude), that would be a substantive correctness or completeness problem, but an equation that fails to solve the stated field equations is not an equation that is circularly equivalent to its inputs. The application of these parameters to shadow predictions for NGC 4649 is benchmark-dependent rather than circular: it is an illustrative use of an externally calibrated model, not a validation of the model by its own output.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The construction depends on the empirical density profile and its parameters from ref. [36], on the zero-radial-pressure anisotropic fluid ansatz from ref. [27], and on the asserted but incorrect integration of Eq. (8). No new particles, forces, or fields are introduced. The main uncharged input is the omitted mathematical step that turns Eq. (8) into Eq. (11).

free parameters (3)
  • Black hole mass m_BH = 5.17 x 10^12 m (Data I), 6.65 x 10^12 m (Data II)
    Supermassive black hole mass in geometrized units adopted from ref. [36]; the metric and all derived quantities depend on it.
  • Asymptotic circular velocity Vc = 13.68 x 10^-4 (Data I), 18.35 x 10^-4 (Data II)
    Parameter of the DM density profile, fitted in ref. [36] to NGC 4649 observations; controls halo density and large-radius behavior.
  • Halo scale radius a = 30.86 x 10^19 m (Data I), 46.29 x 10^19 m (Data II)
    Core radius of the empirical profile from ref. [36]; sets the scale where the halo mass becomes relevant.
assumptions (5)
  • domain assumption The dark matter halo is modeled by an anisotropic energy-momentum tensor diag(-rho_DM, 0, P, P) with zero radial pressure, Eq. (6).
    This is the modeling choice from ref. [27] used to derive Eq. (8). It describes matter on stable circular orbits, but it is not derived from dark matter microphysics.
  • domain assumption The DM density profile is rho_DM = Vc^2/(4 pi G) (3a^2+r^2)/(a^2+r^2)^2, Eq. (1).
    Adopted from ref. [36], fitted to HST imaging, stellar velocity dispersion, and globular cluster kinematics of NGC 4649. The paper does not derive this profile.
  • standard math In a static, spherically symmetric spacetime the event horizon is located where the temporal metric component vanishes, g_tt = 0, Eq. (3).
    Standard GR result invoked in Section II.A and used to identify r_h = lambda.
  • standard math The Bekenstein-Hawking entropy S = A/4 and the temperature formula of Eq. (42) apply to the solution.
    Standard black hole thermodynamics machinery used in Section III.D.
  • ad hoc to paper The spacetime is asymptotically flat, so F(r_O) -> 1 as r_O -> infinity is used in the shadow formula, Eq. (34).
    The paper asserts asymptotic flatness, but Eq. (16) with xi > 1 gives F ~ r^(xi-1), which diverges as r grows. This assumption is not satisfied by the proposed metric.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Relativistic structure of a supermassive black hole embedded in the dark matter halo of NGC 4649 (M60)." pith.science (2026). https://pith.science/paper/Q35LSHI7

@misc{pith2026250504222,
  author       = {Pith},
  title        = {Pith review of: Relativistic structure of a supermassive black hole embedded in the dark matter halo of NGC 4649 (M60)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q35LSHI7}},
  note         = {Machine review of arXiv:2505.04222}
}
abstract

We construct a static, spherically symmetric black hole (BH) solution embedded within a dark matter (DM) halo, formulated as a non-vacuum extension of the Schwarzschild spacetime. The DM distribution is modeled via an empirical density profile calibrated to observations of the elliptical galaxy NGC 4649 (M60), incorporating Hubble Space Telescope (HST) imaging, stellar velocity dispersion data, and globular cluster dynamics. The resultant spacetime metric depends on three independent parameters: the black hole mass $M$, the asymptotic circular velocity $V_c$, and the halo scale radius $a$, and smoothly reduces to the Schwarzschild limit as $V_c \to 0$ and $a \to 0$. We analyze the influence of the halo on key geometric and physical quantities, including the event horizon radius, photon sphere, shadow size, and curvature invariants. The Kretschmann scalar exhibits an enhanced sensitivity to halo-induced modifications, particularly in the near-horizon regime. Thermodynamic properties of the solution are also examined. In the extremal limit, characterized by a vanishing surface gravity, the model supports a finite tangential pressure, implying a non-trivial extension of standard black hole thermodynamics. These results highlight the relevance of incorporating astrophysical environments into BH modeling and offer new avenues for testing strong-field gravity through precision observational data.

Figures

Figures reproduced from arXiv: 2505.04222 by the authors.

Figure 1
Figure 1. Graphical representation of a = a(Vc), from Eq. (20), due to the boundary condition ξ > 1. The con￾stant n = Mmax/Mmin, where Mmax = 8.86 × 1012m and Mmin = 3.69×1012m, come from the intervals originally pre￾sented in Table I. Solutions Data I Data II Schwarzschild 0 1×1013 2×1013 3×1013 4×1013 5×1013 -1.0 -0.5 0 0.5 1.0 r F ( r ) [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. shows that K(r), with a halo, retains the asymptotic behavior for Data I and II, analogous to the case without halo. From Eq. (21) it generally follows that limr→∞ K(r) → 0 , and limr→0 K(r) → ∞, (29) is a BH solution with a singularity in which spacetime becomes asymptotically flat at large distances from its center. Analogous to the case without a halo, [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. presents the ratio K0(r)/K(r), previously discussed in Table II, illustrating how the parameters Vc and a contribute to an increase in curvature as one approaches the black hole center. This ratio stabilizes within the halo’s “core” region, where it reaches the con￾stant value K0(r)/K(r) = M0/mBH. As shown in Ta￾ble II, we find K0(r) = 1.50857 KI (r) for Data I and K0(r) = 0.91181 KII (r) for Data II. These results … view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: Graphical representation of the ratio rsh/mBH, from Eq. (36), for Vc values within the 1σ and 2σ mea￾surement intervals. For the parameter sets: (aI , MI ) given by Data I, (aII , MII ) given by Data II and (0,M0) for the Schwarzschild-type solution without halo. Solut…
Figure 6
Figure 6. Figure 6: Graphical representation of the ratio rsh/mBH, from Eq. (36), for a values within the 1σ and 2σ measure￾ment intervals. For the parameter sets: (VcI , MI ), given by Data I, (VcII , MII ), given by Data II, and (0,M0) for the Schwarzschild-type solution without halo. a…
Figure 7
Figure 7. Figure 7: illustrates the behavior of the mass ratio M/M(sch) as a function of the entropy S for BH solutions embedded in a DM halo. Initially, this ratio remains close to unity, indicating that the presence of the halo does not significantly affect the mass. However, as S, Vc, …
Figure 8
Figure 8. Figure 8: Graphical representation of P(r). For the values: (MI , VcI , aI ) given by Data I, and (MII , VcII , aII ) given by Data II. IV. CONCLUSION In this study, we have proposed and analyzed a Schwarzschild-type BH solution embedded within a DM halo, as characterized by the…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Long-lived quasinormal modes and grey-body factors of supermassive black holes with a dark matter halo

    gr-qc 2025-11 conditional novelty 4.0 of 10

    Massive scalar fields around a Schwarzschild black hole with a dark matter halo ring longer as field mass grows, while realistic halo parameters leave quasinormal frequencies and grey-body factors almost unchanged.

Reference graph

Works this paper leans on

59 extracted references · 25 canonical work pages · cited by 1 Pith paper

  1. [27]

    Black holes in galaxies: Environ- mental impact on gravitational-wave generation and propagation,

    V. Cardoso, K. Destounis, F. Duque, R. P. Macedo and A. Maselli, “Black holes in galaxies: Environ- mental impact on gravitational-wave generation and propagation,” Phys. Rev. D 105 (2022) no.6, L061501 [arXiv:2109.00005 [gr-qc]]

    arXiv 2022

  2. [36]

    The Supermassive Black Hole and Dark Matter Halo of NGC 4649 (M60),

    J. Shen and K. Gebhardt, “The Supermassive Black Hole and Dark Matter Halo of NGC 4649 (M60),” Astrophys. J. 711 (2010), 484-494 [arXiv:0910.4168 [astro-ph.CO]]

    arXiv 2010

  3. [1]

    On the gravitational field of a mass point according to Einstein’s theory,

    K. Schwarzschild, “On the gravitational field of a mass point according to Einstein’s theory,” Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys. ) 1916 (1916), 189-196 [arXiv:physics/9905030 [physics]]

    arXiv 1916

  4. [2]

    General Relativity,

    R. M. Wald, “General Relativity,” The University of Chicago Press, London 1984

    work page 1984

  5. [3]

    Particle Creation by Black Holes,

    S. W. Hawking, “Particle Creation by Black Holes,” Commun. Math. Phys. 43 (1975), 199-220 [erratum: Commun. Math. Phys. 46 (1976), 206]

    work page 1975

  6. [4]

    The Four laws of black hole mechanics,

    J. M. Bardeen, B. Carter and S. W. Hawking, “The Four laws of black hole mechanics,” Commun. Math. Phys. 31 (1973), 161-170

    work page 1973

  7. [5]

    Cosmological Event Horizons, Thermodynamics, and Particle Cre- ation,

    G. W. Gibbons and S. W. Hawking, “Cosmological Event Horizons, Thermodynamics, and Particle Cre- ation,” Phys. Rev. D 15 (1977), 2738-2751

    work page 1977

  8. [6]

    Thermodynamics of Black Holes,

    P. C. W. Davies, “Thermodynamics of Black Holes,” Proc. Roy. Soc. Lond. A 353 (1977), 499-521

    work page 1977

Show all 59 references
  1. [7]

    Matter - Antimatter Accounting, Thermodynamics, and Black Hole Radiation,

    D. Toussaint, S. B. Treiman, F. Wilczek and A. Zee, “Matter - Antimatter Accounting, Thermodynamics, and Black Hole Radiation,” Phys. Rev. D 19 (1979), 1036- 1045

    1979

  2. [8]

    Black hole thermodynamics and the Eu- clidean Einstein action,

    J. W. York, Jr., “Black hole thermodynamics and the Eu- clidean Einstein action,” Phys. Rev. D 33 (1986), 2092- 2099

    1986

  3. [9]

    Moduli, scalar charges, and the first law of black hole thermodynam- ics,

    G. W. Gibbons, R. Kallosh and B. Kol, “Moduli, scalar charges, and the first law of black hole thermodynam- ics,” Phys. Rev. Lett. 77 (1996), 4992-4995 [arXiv:hep- th/9607108 [hep-th]]

    1996

  4. [10]

    Particle dark matter: Evidence, candidates and constraints,

    G. Bertone, D. Hooper and J. Silk, “Particle dark matter: Evidence, candidates and constraints,” Phys. Rept. 405 (2005), 279-390 [arXiv:hep-ph/0404175 [hep-ph]]

    2005 arXiv

  5. [11]

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

    K. Freese, “Review of Observational Evidence for Dark Matter in the Universe and in upcoming searches for Dark Stars,” EAS Publ. Ser. 36 (2009), 113-126 [arXiv:0812.4005 [astro-ph]]

    2009 arXiv

  6. [12]

    How Dark Matter Came to Matter,

    J. de Swart, G. Bertone and J. van Dongen, “How Dark Matter Came to Matter,” Nature Astron. 1 (2017), 0059 [arXiv:1703.00013 [astro-ph.CO]]

    2017 arXiv

  7. [13]

    The Connection be- tween Galaxies and their Dark Matter Halos,

    R. H. Wechsler and J. L. Tinker, “The Connection be- tween Galaxies and their Dark Matter Halos,” Ann. Rev. Astron. Astrophys. 56 (2018), 435-487 [arXiv:1804.03097 [astro-ph.GA]]

    2018 arXiv

  8. [14]

    Planck 2018 results. VI. Cosmological parameters,

    N. Aghanim et al. [Planck], “Planck 2018 results. VI. Cosmological parameters,” Astron. Astrophys. 641 (2020), A6 [erratum: Astron. Astrophys. 652 (2021), C4] [arXiv:1807.06209 [astro-ph.CO]]

    2020 arXiv

  9. [15]

    Dark matter and the early Universe: a review,

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

    2021 arXiv

  10. [16]

    Review on dark matter searches,

    S. Cebri´ an, “Review on dark matter searches,” J. Phys. Conf. Ser. 2502 (2023) no.1, 012004 [arXiv:2205.06833 [physics.ins-det]]

    2023 arXiv

  11. [17]

    Direct Detection of Dark Matter: A Critical Review,

    M. Misiaszek and N. Rossi, “Direct Detection of Dark Matter: A Critical Review,” Symmetry 16 (2024) no.2, 201 [arXiv:2310.20472 [hep-ph]]

    2024 arXiv

  12. [18]

    Dark Matter Candidates - Axions, Neu- tralinos, Gravitinos, and Axinos,

    F. D. Steffen, “Dark Matter Candidates - Axions, Neu- tralinos, Gravitinos, and Axinos,” Eur. Phys. J. C 59 (2009), 557-588 [arXiv:0811.3347 [hep-ph]]

    2009 arXiv

  13. [19]

    Dark Matter Candidates of a Very Low Mass,

    K. M. Zurek, “Dark Matter Candidates of a Very Low Mass,” Ann. Rev. Nucl. Part. Sci. 74 (2024), 287-319 [arXiv:2401.03025 [hep-ph]]

    2024 arXiv

  14. [20]

    Dark Matter Candidates from Particle 12 Physics and Methods of Detection,

    J. L. Feng, “Dark Matter Candidates from Particle 12 Physics and Methods of Detection,” Ann. Rev. Astron. Astrophys. 48 (2010), 495-545 [arXiv:1003.0904 [astro- ph.CO]]

    2010 arXiv

  15. [21]

    Difficulties with recovering the masses of supermassive black holes from stellar kinematical data,

    M. Valluri, D. Merritt and E. Emsellem, “Difficulties with recovering the masses of supermassive black holes from stellar kinematical data,” Astrophys. J. 602 (2004), 66-92 [arXiv:astro-ph/0210379 [astro-ph]]

    2004 arXiv

  16. [22]

    First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way,

    K. Akiyama et al. [Event Horizon Telescope], “First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way,” Astrophys. J. Lett. 930 (2022) no.2, L12 [arXiv:2311.08680 [astro-ph.HE]]

    2022 arXiv

  17. [23]

    First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole,

    K. Akiyama et al. [Event Horizon Telescope], “First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole,” Astrophys. J. Lett. 875 (2019), L1 [arXiv:1906.11238 [astro-ph.GA]]

    2019 arXiv

  18. [24]

    A uni- versal relation between the properties of supermassive black holes, galaxies, and dark matter haloes,

    A. Marasco, G. Cresci, L. Posti, F. Fraternali, F. Man- nucci, A. Marconi, F. Belfiore and S. M. Fall, “A uni- versal relation between the properties of supermassive black holes, galaxies, and dark matter haloes,” Mon. Not. Roy. Astron. Soc. 507 (2021) no.3, 4274-4293 [arXiv:2...

    2021 arXiv

  19. [25]

    Inner radius and energy conditions of dark matter halos surrounding Schwarzschild black holes,

    Z. Shen, A. Wang and S. Yin, “Inner radius and energy conditions of dark matter halos surrounding Schwarzschild black holes,” Phys. Lett. B 862 (2025), 139300 [arXiv:2408.05417 [gr-qc]]

    2025 arXiv

  20. [26]

    Galac- tic black hole immersed in a dark halo with its surround- ing thin accretion disk,

    M. Heydari-Fard, M. Heydari-Fard and N. Riazi, “Galac- tic black hole immersed in a dark halo with its surround- ing thin accretion disk,” Gen. Rel. Grav. 57 (2025) no.2, 49 [arXiv:2408.16020 [gr-qc]]

    2025 arXiv

  21. [28]

    Tidal effects of a dark mat- ter halo around a galactic black hole*,

    J. Liu, S. Chen and J. Jing, “Tidal effects of a dark mat- ter halo around a galactic black hole*,” Chin. Phys. C 46 (2022) no.10, 105104 [arXiv:2203.14039 [gr-qc]]

    2022 arXiv

  22. [29]

    Black Hole Space-time In Dark Matter Halo,

    Z. Xu, X. Hou, X. Gong and J. Wang, “Black Hole Space-time In Dark Matter Halo,” JCAP 09 (2018), 038 [arXiv:1803.00767 [gr-qc]]

    2018 arXiv

  23. [30]

    Dark matter annihilation at the galactic center,

    P. Gondolo and J. Silk, “Dark matter annihilation at the galactic center,” Phys. Rev. Lett. 83 (1999), 1719-1722 [arXiv:astro-ph/9906391 [astro-ph]]

    1999 arXiv

  24. [31]

    Dark matter distributions around massive black holes: A general rel- ativistic analysis,

    L. Sadeghian, F. Ferrer and C. M. Will, “Dark matter distributions around massive black holes: A general rel- ativistic analysis,” Phys. Rev. D 88 (2013) no.6, 063522 [arXiv:1305.2619 [astro-ph.GA]]

    2013 arXiv

  25. [32]

    A Uni- versal density profile from hierarchical clustering,

    J. F. Navarro, C. S. Frenk and S. D. M. White, “A Uni- versal density profile from hierarchical clustering,” As- trophys. J. 490 (1997), 493-508 [arXiv:astro-ph/9611107 [astro-ph]]

    1997 arXiv

  26. [33]

    An Analytical Model for Spherical Galax- ies and Bulges,

    L. Hernquist, “An Analytical Model for Spherical Galax- ies and Bulges,” Astrophys. J. 356 (1990), 359

    1990

  27. [34]

    The Core-Cusp Problem,

    W. J. G. de Blok, “The Core-Cusp Problem,” Adv. Astron. 2010 (2010), 789293 [arXiv:0910.3538 [astro- ph.CO]]

    2010 arXiv

  28. [35]

    A Novel Density Profile for Isothermal Cores of Dark Matter Halos,

    V. Tran, X. Shen, M. Vogelsberger, D. Gilman, S. O’Neil and J. Gao, “A Novel Density Profile for Isothermal Cores of Dark Matter Halos,” [arXiv:2411.11945 [astro- ph.CO]]

  29. [37]

    Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Tele- scope image of Sagittarius A,

    S. Vagnozzi, R. Roy, Y. D. Tsai, L. Visinelli, M. Afrin, A. Allahyari, P. Bambhaniya, D. Dey, S. G. Ghosh and P. S. Joshi, et al. “Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Tele- scope image of Sagittarius A,” Class. Quant. Grav. 40...

    2023 arXiv

  30. [38]

    Calculating black hole shadows: Review of analytical studies,

    V. Perlick and O. Y. Tsupko, “Calculating black hole shadows: Review of analytical studies,” Phys. Rept. 947 (2022), 1-39 [arXiv:2105.07101 [gr-qc]]

    2022 arXiv

  31. [39]

    Eu- ler–Heisenberg black hole surrounded by perfect fluid dark matter,

    S. J. Ma, R. B. Wang, J. B. Deng and X. R. Hu, “Eu- ler–Heisenberg black hole surrounded by perfect fluid dark matter,” Eur. Phys. J. C 84 (2024) no.6, 595 [arXiv:2401.03187 [gr-qc]]

    2024 arXiv

  32. [40]

    Ejection of supermas- sive black holes and implications for merger rates in fuzzy dark matter haloes,

    A. El-Zant, Z. Roupas and J. Silk, “Ejection of supermas- sive black holes and implications for merger rates in fuzzy dark matter haloes,” Mon. Not. Roy. Astron. Soc. 499 (2020) no.2, 2575-2586 [arXiv:2009.10167 [astro-ph.GA]]

    2020 arXiv

  33. [41]

    Core-Halo Mass Relation in Scalar Field Dark Matter Models and its Consequences for the Formation of Supermassive Black Holes,

    L. E. Padilla, T. Rindler-Daller, P. R. Shapiro, T. Matos and J. A. V´ azquez, “Core-Halo Mass Relation in Scalar Field Dark Matter Models and its Consequences for the Formation of Supermassive Black Holes,” Phys. Rev. D 103 (2021) no.6, 063012 [arXiv:2010.12716 [astro- ph.GA]]

    2021 arXiv

  34. [42]

    Evo- lution of the mass relation between supermassive black holes and dark matter halos across the cosmic time,

    A. Bansal, K. Ichiki, H. Tashiro and Y. Matsuoka, “Evo- lution of the mass relation between supermassive black holes and dark matter halos across the cosmic time,” Mon. Not. Roy. Astron. Soc. 523 (2023) no.3, 3840-3847 [arXiv:2206.01443 [astro-ph.GA]]

    2023 arXiv

  35. [43]

    Gemini/GMOS imaging of globular clusters in the Virgo galaxy NGC 4649 (M60),

    D. A. Forbes, F. R. Faifer, J. C. Forte, T. Bridges, M. A. Beasley, K. Gebhardt, D. A. Hanes, R. Sharples and S. E. Zepf, “Gemini/GMOS imaging of globular clusters in the Virgo galaxy NGC 4649 (M60),” Mon. Not. Roy. Astron. Soc. 355 (2004), 608 [arXiv:astro- ph/0408396 [astro-ph]]

    2004

  36. [44]

    A chandra view of dark matter in early-type galaxies,

    P. J. Humphrey, D. A. Buote, F. Gastaldello, L. Zappa- costa, J. S. Bullock, F. Brighenti and W. G. Mathews, “A chandra view of dark matter in early-type galaxies,” As- trophys. J. 646 (2006), 899-918 [arXiv:astro-ph/0601301 [astro-ph]]

    2006 arXiv

  37. [45]

    Probing the Dark Matter and Gas Fraction in Relaxed Galaxy Groups with X-ray observations from Chandra and XMM,

    F. Gastaldello, D. A. Buote, P. J. Humphrey, L. Zap- pacosta, J. S. Bullock, F. Brighenti and W. G. Math- ews, “Probing the Dark Matter and Gas Fraction in Relaxed Galaxy Groups with X-ray observations from Chandra and XMM,” Astrophys. J. 669 (2007), 158-183 [arXiv:astro-ph/06...

    2007 arXiv

  38. [46]

    Weighing the Quiescent Central Black Hole in an Elliptical Galaxy with X-ray Emitting Gas,

    P. J. Humphrey, D. A. Buote, F. Brighenti, K. Gebhardt and W. G. Mathews, “Weighing the Quiescent Central Black Hole in an Elliptical Galaxy with X-ray Emitting Gas,” Astrophys. J. 683 (2008), 161 [arXiv:0801.3461 [astro-ph]]

    2008 arXiv

  39. [47]

    The Globular Cluster Kinematics and Galaxy Dark Matter Content of NGC 4649 (M60),

    T. Bridges, K. Gebhardt, R. Sharples, F. Faifer, J. C. Forte, M. Beasley, S. Zepf, D. Forbes, D. Hanes and M. Pierce, “The Globular Cluster Kinematics and Galaxy Dark Matter Content of NGC 4649 (M60),” Mon. Not. Roy. Astron. Soc. 373 (2006), 157-166 [arXiv:astro- ph/0608661 [a...

    2006

  40. [48]

    The black hole mass, stel- lar mass-to-light ratio, and dark halo in M87,

    K. Gebhardt and J. Thomas, “The black hole mass, stel- lar mass-to-light ratio, and dark halo in M87,” Astro- phys. J. 700 (2009), 1690

    2009

  41. [49]

    Introducing Einstein’s relativity,

    R. D’Inverno, “Introducing Einstein’s relativity,” Claren- don Press, Oxford (1990)

    1990

  42. [50]

    Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity,

    M. S. Morris and K. S. Thorne, “Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity,” Am. J. Phys.56 (1988) no.5, 395–412. 13

    1988

  43. [51]

    Generalization of the Schwarzschild Surface to Arbitrary Static and Sta- tionary Metrics,

    C. V. Vishveshwara, “Generalization of the Schwarzschild Surface to Arbitrary Static and Sta- tionary Metrics,” J. Math. Phys. 9 (1968), no. 8, 1319–1322

    1968

  44. [52]

    Novel black-bounce space- times: wormholes, regularity, energy conditions, and causal structure,

    F. S. N. Lobo, M. E. Rodrigues, M. V. de Sousa Silva, A. Simpson and M. Visser, “Novel black-bounce space- times: wormholes, regularity, energy conditions, and causal structure,” Phys. Rev. D 103 (2021) no.8, 084052 [arXiv:2009.12057 [gr-qc]]

    2021 arXiv

  45. [53]

    Black hole shadow of Sgr A* in dark matter halo,

    X. Hou, Z. Xu, M. Zhou and J. Wang, “Black hole shadow of Sgr A* in dark matter halo,” J. Cosmol. Astropart. Phys. 07 (2018), 015

    2018

  46. [54]

    Hawking radiation from the dilatonic black holes via anomalies,

    Q. Q. Jiang, S. Q. Wu and X. Cai, “Hawking radiation from the dilatonic black holes via anomalies,” Phys. Rev. D 75 (2007), 064029 [erratum: Phys. Rev. D 76 (2007), 029904] [arXiv:hep-th/0701235 [hep-th]]

    2007 arXiv

  47. [55]

    Limitations on the statistical description of black holes,

    J. Preskill, P. Schwarz, A. D. Shapere, S. Trivedi and F. Wilczek, “Limitations on the statistical description of black holes,” Mod. Phys. Lett. A 6 (1991), 2353-2362

    1991

  48. [56]

    Temperatures of extremal black holes,

    A. Ghosh and P. Mitra, “Temperatures of extremal black holes,” [arXiv:gr-qc/9507032 [gr-qc]]

    arXiv

  49. [57]

    Metric of a Rotating, Charged Mass,

    E. T. Newman, R. Couch, K. Chinnapared, A. Exton, A. Prakash and R. Torrence, “Metric of a Rotating, Charged Mass,” J. Math. Phys. 6 (1965), 918-919

    1965

  50. [58]

    The Kerr-Newman metric: A Review,

    T. Adamo and E. T. Newman, “The Kerr-Newman metric: A Review,” Scholarpedia 9 (2014), 31791 [arXiv:1410.6626 [gr-qc]]

    2014 arXiv

  51. [59]

    Zero temperature black holes and the failure of semiclassical analysis,

    F. G. Alvarenga, A. B. Batista, J. C. Fabris and G. T. Marques, “Zero temperature black holes and the failure of semiclassical analysis,” [arXiv:gr-qc/0309022 [gr-qc]]

    arXiv

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.