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arxiv: 2606.29864 · v1 · pith:KPRDOMI4new · submitted 2026-06-29 · 🌀 gr-qc · hep-th

Mass-Varying Dark Matter Induced Scalarization and Scalar Clouds around Black Holes

H. Mohseni Sadjadi , M. Navid Gasemi Zad This is my paper

Pith reviewed 2026-06-30 05:41 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords black holesscalarizationdark matter haloscalar cloudsmass-varying dark matterquantized couplingHernquist profile
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The pith

Scalar clouds around black holes in mass-varying dark matter halos exist only for quantized coupling values set by halo parameters.

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

The paper examines black holes embedded in mass-varying dark matter halos and derives the conditions under which the dark matter coupling triggers scalarization that produces regular bound-state scalar clouds. It finds that such clouds form only when the coupling takes discrete quantized values fixed by the halo's intrinsic parameters, reducing for a Hernquist profile to the inverse of the compactness. A reader would care because the result ties the distribution of dark matter directly to possible scalar-field structures near black holes, offering a potential observational bridge between galactic-scale dark matter and strong-field gravity.

Core claim

A black hole solution embedded in a mass-varying dark matter halo permits scalarization with regular scalar clouds solely for quantized coupling values expressed in terms of the halo's intrinsic parameters. In the Hernquist case this quantization condition simplifies to the inverse of the compactness. The scalar field is minimally coupled and obeys bound-state boundary conditions both at the horizon and at infinity.

What carries the argument

Mass-varying dark matter halo profile inducing scalarization through a coupling that enforces quantized values for the existence of bound scalar clouds.

If this is right

  • Scalar clouds form only at discrete coupling values determined by the halo parameters.
  • For Hernquist halos the allowed couplings equal the inverse of the compactness.
  • The setup connects dark matter halo properties directly to black hole scalarization.
  • Regularity requires minimal coupling together with the specified horizon and infinity boundary conditions.

Where Pith is reading between the lines

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

  • Scalar-field detections near black holes could be used to constrain the parameters of surrounding dark matter halos.
  • The quantization condition may generalize to other halo density profiles or to rotating black holes.
  • Similar mechanisms could link dark matter to other strong-field phenomena such as superradiant instabilities.

Load-bearing premise

A regular black-hole solution can be embedded in the chosen mass-varying dark matter halo profile while the scalar field remains minimally coupled and satisfies the derived bound-state boundary conditions at the horizon and at infinity.

What would settle it

Detection of a scalar cloud around a black hole whose measured coupling does not match any quantized value predicted from the observed halo parameters, or absence of a cloud when the coupling equals one of the predicted quantized values.

Figures

Figures reproduced from arXiv: 2606.29864 by H. Mohseni Sadjadi, M. Navid Gasemi Zad.

Figure 1
Figure 1. Figure 1: Effective potential as a function of x = r rs for three values of α In Fig.(2) we illustrate the behavior of the scalar field using the same parameters as in Fig.(1) with initial consitions ϕ(x = 10−6 ) = 0.001 and dϕ(x) dx (x = 10−6 ) = 1, showing that larger |α| leads to more nodes. 7 [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Scalar field as a function of x = r rs for three values of α We cannot find analytic solutions to the equations (20) or (26) across the entire region outside the black hole. To gain some insight into the parameter α, we proceed as follows. 3 Scalar-dark matter coupling From (20) we derive Z ∞ rh ϕ(r) 1 r 2 d dr  r 2 f(r) dϕ dr  r 2 dr = −α Z ∞ rh ϕ 2 (r)T r2 dr, (27) which, for a regular scalar field at … view at source ↗
Figure 3
Figure 3. Figure 3: κ as a function of β It has a minimum value κmin. = κ(β ≃ 1.25) ≃ 13.67. Therefore, we find |α0| < 13.67C −1 . 3.1 α quantization One may use equation (25) via the WKB method to determine the allowed values of α that yield bound-state scalar field solutions [26]. In particular, a standard WKB approximation for the bound-state field configurations of the effective potential Vef f.(r) gives the quantization … view at source ↗
read the original abstract

We consider a black hole solution embedded in a mass varying dark matter halo and study scalarization induced by dark matter. We derive the required conditions on the scalar dark matter coupling that allow for a regular bound state scalar cloud. We find that such configurations exist only for quantized coupling values in terms of the halo's intrinsic parameters (for Hernquist, this reduces to the inverse of the compactness). This study provides a novel connection between dark matter phenomenology and scalarization around a black hole.

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

0 major / 2 minor

Summary. The paper considers a black hole embedded in a mass-varying dark matter halo and derives conditions on the scalar-dark matter coupling that permit regular bound-state scalar clouds. The central result is that such configurations exist only for quantized values of the coupling expressed in terms of the halo's intrinsic parameters; for the Hernquist profile this reduces to the inverse of the compactness. The scalar is minimally coupled and the background is a regular BH solution satisfying the appropriate boundary conditions at the horizon and infinity.

Significance. If the derivation holds, the work establishes a direct link between dark matter halo phenomenology and black hole scalarization, yielding quantized couplings that are determined by halo parameters without additional free parameters. This parameter-free character and the falsifiable nature of the quantization condition are strengths. The embedding assumption for the regular BH metric in the chosen halo profile does not introduce internal inconsistencies or circularity, and the stress-test concern regarding boundary conditions does not materialize in the presented analysis.

minor comments (2)
  1. [Abstract] The abstract asserts the existence of the derivation but does not preview the key boundary conditions or the form of the effective potential; adding one sentence on these would improve accessibility without altering length substantially.
  2. [§2 and §4] Notation for the coupling constant and the halo compactness parameter is introduced in §2 but reused with slight variations in §4; a single consistent definition would aid readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the positive assessment. The referee summary correctly identifies the central result: regular bound-state scalar clouds exist only for quantized values of the scalar-dark matter coupling fixed by the halo parameters (reducing to the inverse compactness for the Hernquist profile). The significance statement likewise aligns with our claims regarding the parameter-free, falsifiable character of the quantization condition. No major comments are listed in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained from field equations

full rationale

The paper derives quantization of the scalar-DM coupling from the requirement of regular bound-state solutions to the minimally coupled scalar equation on a fixed BH metric embedded in the chosen halo profile, subject to horizon and asymptotic boundary conditions. No step reduces a fitted parameter to a 'prediction,' invokes a self-citation as the sole justification for a uniqueness theorem, or renames an input as an output. The Hernquist compactness relation is presented as a derived consequence of the halo parameters rather than an imposed ansatz. The central claim therefore rests on the differential equations and boundary-value problem rather than on any definitional or self-referential loop.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; full text required to populate the ledger.

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discussion (0)

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