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A Self-Interacting Dark-Matter Route to Supermassive Kerr Black Holes via Super-Eddington Bondi Accretion: Mass-Spin Evolution

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Chian-Shu Chen, Feng-Li Lin

High Energy Physics - Phenomenology · Submitted 9 Nov 2026 · 35 references

Pith's verdict: The critical SIDM Bondi growth mechanism survives inclusion of Kerr spin and inflow angular momentum; the paper is a careful, self-contained analytic extension with explicit caveats.

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arXiv ID2611.12282 (version 1)
Pith IDX23MV4DE, Pith's permanent record of this paper and its review
CitationChian-Shu Chen, Feng-Li Lin. "A Self-Interacting Dark-Matter Route to Supermassive Kerr Black Holes via Super-Eddington Bondi Accretion: Mass-Spin Evolution." arXiv:2611.12282 (2026). https://pith.science/paper/X23MV4DE
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The paper

The paper claims

Critical dark-matter accretion survives black-hole spin

The reading

This paper extends the self-interacting dark matter (SIDM) critical Bondi accretion mechanism from Schwarzschild to Kerr black holes. The central result is that the rapid super-Eddington growth channel persists for rotating black holes, provided the inflow angular momentum lies within the Kerr marginally bound capture values. Rotation shifts the sonic radius, changes the accretion efficiency by a geometric factor Ψ(χ,ℓ), and allows the black hole to spin up as it grows. The critical density cancellation that made the rate independent of the local halo density in the Schwarzschild case carries over unchanged. Stellar-mass primordial black hole seeds can therefore reach supermassive scales with a final spin largely controlled by the dark matter's angular momentum.

What carries the argument

The key identity is the critical cancellation: the apparent pole in the rest-mass flux (∼ 1/ζ, where ζ=c²_s,∞) is cancelled by the asymptotic SIDM density ρ_∞∝ζ, leaving a finite rate 64πΨ(χ,ℓ)ρ_B M². The outer critical sonic branch is selected by a quartic equation (32) whose physical root must satisfy x_c > x_+, 0 < c²_s,c < 1/3, A_c>0 and the future-horizon condition. The geometric factor Ψ(χ,ℓ) = ½ c_{s,c}^{3/2} $A_c^{{3/2}}$ / ($x_c^{{1/2}}$Δ_c) compresses all spin and angular-momentum dependence into a single number.

Extended reading notes

Core claim

The authors prove that repulsively self-interacting dark matter (ϕ⁴ fluid) can drive critical Bondi accretion onto Kerr black holes over a finite interval of inflow angular momentum ℓ bounded by the prograde and retrograde marginally bound Kerr values ℓ±(χ)=±2(1+√(1∓χ)). Within this domain the sonic-point regularity reduces to a quartic equation for the critical radius x_c, and the universal M² growth law survives with a two-dimensional geometric factor Ψ(χ,ℓ) multiplying the Schwarzschild rate. The exact ℓ=0 branch yields Ψ=1 for all spins, showing that frame dragging alone does not suppress the rate. Inflow carrying angular momentum simultaneously spins up the hole; in the Bondi-dominated limit the dimensionless spin approaches ℓ/2. The mechanism is robust against the inclusion of Kerr spin and fluid rotation.

Load-bearing premise

The flow is modelled as equatorial, quasi-spherical, stationary, inviscid, and adiabatic with an effective 4π flux normalization, ignoring viscosity, magnetic fields, self-gravity, nonaxisymmetric structure, and shocks.

Editorial extensions

If this is right

  • Rapid SIDM Bondi growth, previously established for Schwarzschild black holes, is viable for rotating black holes without fine-tuning, provided the dark matter inflow angular momentum stays within the marginally bound range.
  • Black holes can be spun up by the same SIDM inflow that feeds them; an initially nonrotating stellar-mass seed can reach moderate spin (χ≈ℓ/2) while growing by many orders of magnitude in mass.
  • The final mass distribution of early supermassive black holes in this model is primarily set by the finite dark matter halo supply, whereas the spin distribution strongly separates different inflow angular momenta, offering complementary observational probes.
  • The analytic ℓ=χ (L=J/M) subfamily, while useful for closed-form checks, cannot generate spinning SMBHs from nonrotating seeds because χ∝M^{-1}, so the generic (χ,ℓ) analysis is essential for realistic population studies.

Reading between the lines

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

  • If this mechanism operates in nature, the spin distribution of high-redshift supermassive black holes (e.g., from JWST samples) could encode the typical angular momentum of the dark matter inflow, providing a window into dark-sector dynamics.
  • The quasi-spherical equatorial assumption likely breaks down near the marginally bound boundaries; full 2D/3D GR hydrodynamic simulations are needed to test whether shocks or disk formation modify the critical crossing and the resulting mass–spin relation.
  • Combining the SIDM Bondi channel with a baryonic Eddington component (neglected for spin in this work) could produce a broader range of final spins; the fixed spin-up prediction χ→ℓ/2 is a clean target for numerical tests.
  • The revised ambient-density normalization (δ_env=300) dramatically lowers the scalar-mass bound for criticality, but maintains the growth-motivated fiducial mass m∼10⁻² eV; future surveys of Bondi radii could independently test the particle-physics scale.
Original abstract

Recent JWST observations motivate mechanisms for rapid black-hole growth in the early Universe. Extending our previous Schwarzschild study, we show that critical relativistic Bondi accretion of repulsively self-interacting dark matter remains an efficient super-Eddington channel for Kerr black holes with rotating inflow. Within a stationary equatorial quasi-spherical framework, smooth critical solutions exist over a finite range of inflow angular momentum set by the Kerr marginally bound capture values. Rotation changes the sonic structure and accretion efficiency, while the critical density cancellation and dark-sector/halo matching retain their Schwarzschild form. The resulting rapid growth persists until the finite halo supply becomes limiting. Because the inflow also carries angular momentum, stellar-mass seeds can grow and spin up simultaneously; illustrative population evolutions therefore provide a joint mass--spin route to early supermassive Kerr black holes.

Figures
Figure 1. FIG. 1. Generic critical Kerr flows. Left: the universal rate factor Ψ(
Figure 2. FIG. 2. Mass-scale diagnostics across the generic critical Kerr domain. Left: the normalized
Figure 3. FIG. 3. Analytic diagnostics on the special
Figure 4. FIG. 4. Bondi-radius evolution using the revised ambient-density normalization with
Figure 5. FIG. 5. Coupled mass–spin evolution of an initially Schwarzschild 10
Figure 6. FIG. 6. Self-consistent evolution on the special
Figure 7. FIG. 7. Illustrative black-hole populations at

Figures reproduced from arXiv:2611.12282 by the authors.

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