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arxiv: 2606.24917 · v1 · pith:WHH57FMRnew · submitted 2026-06-19 · 🌀 gr-qc · astro-ph.CO

Black bounce solutions in a realistic dark matter halo from M60*

Ednaldo L. B. Junior , Jos\'e Tarciso S. S. Junior , Francisco S. N. Lobo , Jorde A. A. Ramos , Manuel E. Rodrigues , Diego Rubiera-Garcia , Lu\'is F. Dias da Silva , Henrique A. Vieira This is my paper

Pith reviewed 2026-06-26 13:18 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.CO
keywords black bouncesdark matter haloSimpson-Visser solutionshadow radiusSagittarius A*regular black holesM60 galaxywormhole exclusion
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The pith

The Sagittarius A* shadow radius constrains black bounce solutions embedded in a realistic dark matter halo to regular black hole configurations.

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

The paper places the Simpson-Visser black bounce inside a dark matter halo whose density profile is taken from Hubble imaging, stellar velocities, and globular cluster data on the galaxy M60. It tracks the changes the halo produces in horizon radius, shadow size, curvature scalars, particle dynamics, and thermodynamic potentials. The central result is that the observed range of the Sagittarius A* shadow forces the regularization parameter into the regular black hole regime and rules out the wormhole branch of the same family. A reader cares because the work supplies a concrete astrophysical test that links regular black hole models to galactic observations rather than vacuum spacetimes alone.

Core claim

By embedding the Simpson-Visser black bounce in an empirical dark matter density profile calibrated from M60 observations, the authors obtain a metric depending on mass, asymptotic circular velocity, halo scale radius, and regularization parameter. Comparison of the resulting shadow radius with the Sagittarius A* observational range restricts the parameter space to regular black hole configurations and excludes wormhole solutions.

What carries the argument

Simpson-Visser black bounce solution directly embedded in the empirical dark matter halo density profile calibrated from M60 observations.

If this is right

  • The halo changes the event horizon radius and the photon sphere location.
  • Curvature invariants receive corrections proportional to the halo parameters.
  • Thermodynamic potentials, including entropy, are modified by the halo contribution.
  • Non-minimally coupled electromagnetic fields produce charged configurations that are either purely magnetic or purely electric.
  • Astrophysical environments therefore impose additional limits on the allowed parameter space of regular black hole models.

Where Pith is reading between the lines

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

  • The same embedding technique could be repeated for other galaxies once their dark matter profiles and shadow sizes are measured.
  • Thermodynamic stability and possible phase transitions may differ from the vacuum case when the halo is present.
  • Strong-field observations become more powerful tests of regular black holes once realistic galactic environments are included.

Load-bearing premise

The Simpson-Visser black bounce solution can be directly embedded in the empirical dark matter density profile calibrated from M60 observations to form a consistent spacetime metric.

What would settle it

A higher-precision measurement of the Sagittarius A* shadow radius that lies outside the interval permitted by the regular black hole branch of the embedded solution would falsify the claimed constraint.

Figures

Figures reproduced from arXiv: 2606.24917 by Diego Rubiera-Garcia, Ednaldo L. B. Junior, Francisco S. N. Lobo, Henrique A. Vieira, Jorde A. A. Ramos, Jos\'e Tarciso S. S. Junior, Lu\'is F. Dias da Silva, Manuel E. Rodrigues.

Figure 1
Figure 1. Figure 1: Graphical representation of the metric function [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Graphical representation of the evolution of the [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Graphical representation of the variation of the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Graphical representation of the variation of the [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Graphical representation of the shadow radius [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Graphical representation of the effective potential [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Graphical representation of the radial acceleration [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Graphical representation of the BH mass-entropy [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Graphical representation of the temperature [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 12
Figure 12. Figure 12: Graphical representation of the parameter Φ [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Graphical representation of the radial behaviour of [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Graphical representation of the radial behaviour [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 16
Figure 16. Figure 16: Graphical representation of the radial behaviour [PITH_FULL_IMAGE:figures/full_fig_p017_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Graphical representation of the radial behaviour [PITH_FULL_IMAGE:figures/full_fig_p018_17.png] view at source ↗
read the original abstract

We formulate a Simpson-Visser black bounce solution embedded in a dark matter halo. The latter is modeled using an empirical density profile calibrated from observations of the elliptical galaxy NGC 4649 (M60), based on imaging from the Hubble Space Telescope, stellar velocity dispersion data, and the dynamics of globular clusters. The resulting spacetime metric, in addition to retaining dependence on the mass parameter $m$, the asymptotic circular velocity $V_c$, and the halo scale radius $a$, also depends on the regularization parameter $q_H$. It reduces to the canonical black bounce solution without a halo in the limit $V_c\to0$ (or $a\to\infty$), and to the Schwarzschild solution with a dark matter halo when $q_H\to0$. We analyze the response of fundamental geometrical and physical quantities in the presence of a halo, such as the event horizon radius, the shadow size, and some curvature invariants. In particular, we show the observational range of the shadow radius, from the imaging of Sagittarius A*, constrains the parameter space of the solution to regular black hole configurations, excluding wormhole scenarios. We study the dynamics of massless particles here through the effective potential and examine thermodynamic properties, highlighting the impact on thermodynamic potentials in terms of entropy. Finally, we extend the analysis to scenarios with electromagnetic fields non-minimally coupled to a phantom scalar field, considering configurations with either purely magnetic or purely electric charge. Our results suggest that the dark matter halo influences both the internal geometry and the observational properties of black bounces, imposing constraints on the solution's parameter space from astrophysical data. This highlights the need to include astrophysical environments in modeling regular black holes and wormholes, offering new tests of gravity in the strong-field regime.

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 / 2 minor

Summary. The manuscript formulates a Simpson-Visser black-bounce spacetime embedded in an empirical dark-matter halo whose density profile is calibrated to Hubble, stellar-dispersion and globular-cluster data for NGC 4649 (M60). The resulting metric depends on the mass m, halo parameters V_c and a, and regularization parameter q_H; it reduces to the vacuum Simpson-Visser solution when V_c o0 (or a o∞) and to the Schwarzschild-plus-halo metric when q_H o0. The authors compute the event horizon, shadow radius, curvature invariants, null-geodesic effective potential, thermodynamic quantities (including entropy), and extend the construction to non-minimally coupled electromagnetic fields with a phantom scalar (purely magnetic or electric cases). They conclude that the EHT-measured shadow radius of Sgr A* restricts the parameter space to regular black-hole configurations and excludes wormhole solutions.

Significance. If the metric is shown to satisfy the Einstein equations with the empirical halo density plus phantom-scalar stress-energy as source, the work supplies a concrete route for incorporating realistic galactic environments into regular-black-hole phenomenology and for using shadow observations to bound the regularization parameter. The explicit reduction to known limits and the use of an observationally calibrated halo profile are positive features.

major comments (2)
  1. [§2] §2 (metric construction, presumably around Eq. (3)–(7)): The central claim that the shadow radius constrains the solution to regular black holes requires the line element to be an exact solution of G_{\mu\nu}=8\pi T_{\mu\nu} with T_{\mu\nu} containing the M60-calibrated empirical density plus the phantom-scalar (or electromagnetic) contribution. The text appears to insert V_c and a directly into the Simpson-Visser mass function without deriving the resulting Einstein tensor or verifying consistency with the halo density profile; this step is load-bearing for all subsequent geometric and observational calculations.
  2. [§4] §4 (shadow analysis): The exclusion of wormhole configurations rests on the photon-sphere radius and critical impact parameter computed from the metric. Because the metric’s validity as a solution has not been established, the numerical bounds on q_H derived from the Sgr A* shadow radius (1.9–2.1 range cited) cannot yet be regarded as physical constraints.
minor comments (2)
  1. [§2] Notation for the halo density profile and the precise functional form of the mass function m(r) should be stated explicitly once, with all subsequent appearances cross-referenced to the same equation.
  2. [§4] Figure captions for the shadow-radius plots should include the exact numerical range adopted for the Sgr A* shadow and the value of the impact parameter b_c used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and for identifying the need to strengthen the justification of the metric as an exact solution. We address each major comment below and will revise the manuscript to include the requested derivations.

read point-by-point responses

  1. Referee: [§2] §2 (metric construction, presumably around Eq. (3)–(7)): The central claim that the shadow radius constrains the solution to regular black holes requires the line element to be an exact solution of G_{\mu\nu}=8\pi T_{\mu\nu} with T_{\mu\nu} containing the M60-calibrated empirical density plus the phantom-scalar (or electromagnetic) contribution. The text appears to insert V_c and a directly into the Simpson-Visser mass function without deriving the resulting Einstein tensor or verifying consistency with the halo density profile; this step is load-bearing for all subsequent geometric and observational calculations.

    Authors: We agree that an explicit verification is required. In the revised manuscript we will compute the non-zero components of the Einstein tensor for the proposed metric and show that they are sourced by the M60-calibrated halo density together with the stress-energy of the phantom scalar (or the non-minimally coupled electromagnetic field in the extended cases). This calculation will be placed immediately after the metric ansatz and will confirm consistency with the Einstein equations in the relevant limits. revision: yes

  2. Referee: [§4] §4 (shadow analysis): The exclusion of wormhole configurations rests on the photon-sphere radius and critical impact parameter computed from the metric. Because the metric’s validity as a solution has not been established, the numerical bounds on q_H derived from the Sgr A* shadow radius (1.9–2.1 range cited) cannot yet be regarded as physical constraints.

    Authors: We accept that the observational bounds on q_H are conditional on the metric satisfying the field equations. After adding the Einstein-tensor verification in §2, we will restate the shadow-radius constraints as applying to the now-validated family of solutions and will explicitly note that the exclusion of wormhole branches follows from the verified metric. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation applies external halo calibration to independent shadow data

full rationale

The paper takes an empirical DM density profile (with V_c and a) calibrated from M60 observations as an input, embeds the Simpson-Visser metric by modifying the mass function accordingly, and then computes the shadow radius as a function of m, V_c, a, q_H. The central claim applies the observed Sgr A* shadow radius range (an independent dataset) to bound q_H, excluding wormhole regimes. No equation reduces to its own input by construction, no self-citation chain bears the load of the embedding or the constraint, and the halo calibration is not re-derived from the Sgr A* result. The construction is an ansatz whose validity is an assumption, not a circularity.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 1 invented entities

The model depends on three free parameters from the halo (V_c, a) plus the regularization parameter q_H; the halo profile itself is empirically fitted to M60 observations and the embedding is postulated without independent derivation shown in the abstract.

free parameters (3)
  • q_H
    Regularization parameter that sets the scale of the bounce and distinguishes black-hole from wormhole regimes
  • V_c
    Asymptotic circular velocity of the dark matter halo, taken from M60 data
  • a
    Halo scale radius, taken from M60 observations
axioms (2)
  • domain assumption A Simpson-Visser black bounce solution can be embedded into a dark matter halo whose density follows the empirical M60 profile to produce a consistent spacetime metric
    Invoked when the resulting metric is formulated
  • domain assumption The empirical density profile calibrated from M60 observations accurately represents the dark matter distribution around the central object
    Used to calibrate the halo parameters
invented entities (1)
  • q_H no independent evidence
    purpose: Regularization parameter that smooths the center and allows black-bounce or wormhole geometries
    Introduced to control the transition between black-hole and wormhole regimes

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