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arxiv: 2505.20919 · v1 · pith:PH4PRC2Anew · submitted 2025-05-27 · 🌀 gr-qc

Scalarization and superradiant instability of black hole induced by dark matter halo in the scalar-tensor theory of gravity

Junya Tanaka This is my paper

Pith reviewed 2026-05-25 08:24 UTC · model grok-4.3

classification 🌀 gr-qc
keywords black holesdark matter haloscalarizationsuperradiant instabilityscalar-tensor gravityeffective massspontaneous scalarization
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0 comments X

The pith

Dark matter halos around black holes can trigger scalarization or superradiant instability in scalar-tensor gravity.

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

The paper studies black holes encircled by dark matter halos in scalar-tensor theories. The non-minimal coupling between matter and the scalar field produces an effective mass term that allows a bald black hole to acquire scalar hair through spontaneous scalarization. For rotating black holes the same effective mass can instead drive superradiant instability when its sign is positive. Calculations show these phenomena appear in certain ranges of halo size, halo mass, and coupling strength. Small halos make the instability strength depend on their physical size and mass, while astronomically large halos make the outcome depend mainly on the coupling constant.

Core claim

In the scalar-tensor theory the coupling of matter and the scalar field creates an effective mass; this effective mass causes the hairless black hole to develop scalar hair via spontaneous scalarization. For rotating black holes a positive effective mass produces superradiant instability instead. When the same mechanism is applied to black holes surrounded by dark matter halos, both scalarization and superradiant instability occur in some parameter regions. For small halos the halo size and mass affect the strength of scalarization and the number of unstable modes, but for large astronomical halos the dependence on the coupling constant α becomes dominant.

What carries the argument

The effective mass acquired by the scalar field through its coupling to the dark matter halo density, which replaces the usual tachyonic instability condition of spontaneous scalarization.

If this is right

  • Scalarization strength depends on halo size and mass only when the halo is small.
  • For large halos the outcome is controlled mainly by the value of the coupling constant α.
  • Superradiant instability strength and the number of unstable modes likewise vary with halo parameters for small halos.
  • The same effective-mass mechanism applies equally to both static and rotating black-hole cases.

Where Pith is reading between the lines

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

  • Galactic black holes embedded in realistic dark matter distributions may exhibit observable deviations from the no-hair theorem even when the halo is too large to resolve directly.
  • The transition between halo-size dependence and coupling-constant dominance offers a possible observational discriminant between small and large halo regimes.
  • Dynamical halo back-reaction or time-dependent scalar-field evolution could be studied as a direct extension of the fixed-background setup.

Load-bearing premise

The dark matter halo is treated as a fixed, non-dynamical background that only sources an effective mass for the scalar field, with no significant back-reaction on the metric or additional halo dynamics.

What would settle it

A rotating black hole with a measured dark matter halo whose parameters lie inside the region the model predicts to be unstable, yet showing neither scalar hair nor superradiant growth in gravitational-wave or electromagnetic observations.

Figures

Figures reproduced from arXiv: 2505.20919 by Junya Tanaka.

Figure 1
Figure 1. Figure 1: FIG. 1: The contour curves of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The value of S with changing [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The values of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: The value of [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: The [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: The value of S with changing [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: The value of [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: The value of [PITH_FULL_IMAGE:figures/full_fig_p009_14.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: Real part of eigenvalue [PITH_FULL_IMAGE:figures/full_fig_p010_16.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18: Real part of eigenvalue [PITH_FULL_IMAGE:figures/full_fig_p010_18.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21: Imginary part of eigenvalue [PITH_FULL_IMAGE:figures/full_fig_p012_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22: Real part of eigenvalue [PITH_FULL_IMAGE:figures/full_fig_p012_22.png] view at source ↗
Figure 24
Figure 24. Figure 24: FIG. 24: Real part of eigenvalue [PITH_FULL_IMAGE:figures/full_fig_p013_24.png] view at source ↗
Figure 26
Figure 26. Figure 26: FIG. 26: Real part of eigenvalue [PITH_FULL_IMAGE:figures/full_fig_p013_26.png] view at source ↗
Figure 28
Figure 28. Figure 28: FIG. 28: Real part of eigenvalue [PITH_FULL_IMAGE:figures/full_fig_p014_28.png] view at source ↗
Figure 30
Figure 30. Figure 30: FIG. 30: Real part of eigenvalue [PITH_FULL_IMAGE:figures/full_fig_p014_30.png] view at source ↗
Figure 32
Figure 32. Figure 32: FIG. 32: Real part of eigenvalue [PITH_FULL_IMAGE:figures/full_fig_p015_32.png] view at source ↗
Figure 34
Figure 34. Figure 34: FIG. 34: Real part of eigenvalue [PITH_FULL_IMAGE:figures/full_fig_p015_34.png] view at source ↗
Figure 36
Figure 36. Figure 36: FIG. 36: Real part of eigenvalue [PITH_FULL_IMAGE:figures/full_fig_p016_36.png] view at source ↗
Figure 38
Figure 38. Figure 38: FIG. 38: Real part of eigenvalue [PITH_FULL_IMAGE:figures/full_fig_p016_38.png] view at source ↗
read the original abstract

We investigate whether a black hole(BH) surrounded by a dark matter (DM) halo has scalar hair/superradiant instability in the scalar tensor theory of gravity. In the scalar tensor theory, the coupling of matter and the scalar field creates effective mass, this effective mass causes the hairless BH to have scalar hair (spontaneous Scalarization). In the case of rotating BHs, it is also known that if the sign of the effective mass is positive, superradiant instability can occur instead of scalarization. Our study applies this effect to BHs with dark matter haloes. As a result, we confirmed that scalarization and superradiant instability occur in some of the parameter regions. In the case of small haloes, the size and mass of the halo affect the strength of scalarization, but not for astronomically large haloes, where the dependence on the coupling constant $\alpha$ is stronger. In the case of superradiance, we also confirm that for small haloes, the size and mass of the halo affect the strength of the instability and the number of unstable modes.

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 paper studies spontaneous scalarization of static black holes and superradiant instability of rotating black holes surrounded by dark matter halos in scalar-tensor gravity. The halo density induces a position-dependent effective mass for the scalar via the non-minimal coupling, triggering tachyonic instability (scalarization) or superradiance depending on the sign. Numerical exploration of parameter space shows these instabilities occur for certain ranges of the coupling α and halo parameters; for small haloes the instability strength depends on halo size and mass, while for astronomically large haloes the dependence on α dominates and halo parameters become irrelevant. Similar halo dependence is reported for the number of unstable superradiant modes.

Significance. If the results hold under the stated approximations, the work provides a concrete astrophysical realization of environment-triggered scalar hair, showing how realistic DM halos can source scalarization or superradiance where vacuum solutions would not. The distinction between small and large haloes supplies a practical criterion for when halo structure matters versus when the coupling alone controls the outcome, which could inform searches for scalarized black holes in galactic centers.

major comments (2)
  1. [effective mass and background setup (likely §2–3)] The central modeling choice treats the DM halo as a fixed external density profile ρ_DM(r) that sources m_eff²(α,ρ_DM) without back-reaction of the scalar on either the halo or the metric (see the effective-mass derivation and the background metric ansatz). This approximation is load-bearing for the reported claim that halo size and mass affect scalarization strength only for small haloes: a self-consistent solution could readjust ρ_DM and thereby shift the thresholds and mode counts that are presented as depending on those parameters.
  2. [results and discussion of halo-size dependence] No consistency check or estimate is given for the regime in which the fixed-halo approximation remains valid (e.g., comparison of scalar stress-energy to halo density or to the BH mass). Without such a bound, the distinction between “small” and “astronomically large” haloes cannot be assessed for robustness.
minor comments (2)
  1. Notation for the coupling constant is introduced as α in the abstract but should be cross-checked for consistency with the action definition in the main text.
  2. [abstract] The abstract contains the typographical concatenation “black hole(BH)” and “superradiance, we also confirm”; these should be corrected for readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and constructive feedback on our manuscript. We agree that the fixed-halo approximation requires further justification regarding its validity regime, and we will revise the manuscript accordingly to include consistency estimates. We address each major comment below.

read point-by-point responses

  1. Referee: The central modeling choice treats the DM halo as a fixed external density profile ρ_DM(r) that sources m_eff²(α,ρ_DM) without back-reaction of the scalar on either the halo or the metric (see the effective-mass derivation and the background metric ansatz). This approximation is load-bearing for the reported claim that halo size and mass affect scalarization strength only for small haloes: a self-consistent solution could readjust ρ_DM and thereby shift the thresholds and mode counts that are presented as depending on those parameters.

    Authors: We acknowledge the importance of this point. Our approach follows the standard treatment in the literature for environmental effects on black hole instabilities, where the dark matter halo is modeled as a fixed background density profile inducing an effective scalar mass. This allows us to isolate the effect of the halo on the scalar field dynamics. We agree, however, that a discussion of back-reaction is warranted. In the revised version, we will add an estimate comparing the scalar field's energy density to that of the DM halo to delineate the regime where the approximation holds. revision: yes

  2. Referee: No consistency check or estimate is given for the regime in which the fixed-halo approximation remains valid (e.g., comparison of scalar stress-energy to halo density or to the BH mass). Without such a bound, the distinction between “small” and “astronomically large” haloes cannot be assessed for robustness.

    Authors: We appreciate this suggestion. While our numerical results are based on the fixed-halo model, we will include in the revised manuscript an order-of-magnitude analysis of the scalar stress-energy relative to the halo density and black hole mass. This will help assess the robustness of the distinction between small and large haloes, particularly noting that for large haloes the coupling α dominates, potentially making back-reaction effects less significant. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The provided abstract and context describe a standard application of the known scalar-tensor effective-mass mechanism to a new DM-halo background model. No equations, fitting procedures, self-citations, or ansatze are shown that reduce any claimed prediction or result to the inputs by construction. The reported occurrence of scalarization/superradiance in parameter regions follows from solving the field equations on the given fixed background; the modeling assumption of a non-backreacting halo is an external approximation rather than a definitional loop. This is the most common honest non-finding for application papers.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Abstract-only review; the claim rests on the standard scalar-tensor effective-mass construction and an unspecified halo model whose parameters are varied but not detailed.

free parameters (2)
  • coupling constant α
    Controls the strength of scalar-matter coupling and dominates for large halos.
  • halo size and mass
    Affect instability strength and mode count for small halos.
axioms (1)
  • domain assumption Matter coupling in scalar-tensor theory produces an effective mass for the scalar field that can trigger scalarization or superradiance.
    This is the mechanism invoked in the abstract to explain the halo-induced effects.

pith-pipeline@v0.9.0 · 5731 in / 1204 out tokens · 38172 ms · 2026-05-25T08:24:32.399651+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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