arxiv: 2605.02425 · v1 · submitted 2026-05-04 · 🌀 gr-qc

Recognition: 3 theorem links

· Lean Theorem

Bondi and Novikov-Thorne accretion in regular black holes and Simpson-Visser spacetimes

Serena Gambino

Authors on Pith no claims yet

Pith reviewed 2026-05-08 19:07 UTC · model grok-4.3

classification 🌀 gr-qc

keywords regular black holesSimpson-Visser spacetimeBondi accretionNovikov-Thorne modelaccretion flowsblack hole geometrygeneral relativityastrophysical accretion

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The pith

Bondi spherical accretion distinguishes regular black holes from classical solutions more effectively than thin-disk models.

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

This paper compares the Bondi spherical accretion model and the Novikov-Thorne thin disc formalism in regular black holes and Simpson-Visser spacetimes, applying several equations of state to the accreting fluid. It finds that Bondi flows respond more strongly to variations in spacetime geometry and equation of state, providing a clearer way to tell regular solutions apart from standard singular black holes. A sympathetic reader would care because accretion observations around real black holes might then serve as a practical probe for whether spacetime is regularized at small scales. The analysis also tracks how the regularization parameter shifts critical points in the flow for Simpson-Visser metrics, with charge producing a weaker shift.

Core claim

The Bondi model is significantly more sensitive to spacetime geometry and the equation of state than the Novikov-Thorne model, allowing better distinction between regular and classical black hole solutions. For Simpson-Visser spacetimes, increasing the regularization parameter ℓ shifts critical point positions both inward and outward, while the charged extension shows that the charge Q does not produce an effect comparable to that of ℓ.

What carries the argument

The Bondi spherical accretion model for transonic flows and critical points, applied alongside the Novikov-Thorne thin disc formalism, to regularized black hole metrics.

If this is right

Bondi accretion rates and critical radii can serve as observables to distinguish regular from singular black hole geometries.
In Simpson-Visser spacetimes the regularization parameter ℓ directly controls the inward or outward movement of sonic points in spherical flows.
The equation of state of the accreting fluid amplifies geometric sensitivity in the Bondi case relative to thin disks.
The charge parameter Q in extended Simpson-Visser metrics produces smaller shifts in accretion dynamics than the regularization parameter ℓ.

Where Pith is reading between the lines

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

Astrophysical observations of spherical accretion flows near black hole candidates could be prioritized to search for regularization signatures.
The Bondi sensitivity pattern may appear in other families of regular black hole metrics, offering a general test for quantum-gravity-motivated solutions.
Incorporating more complex fluid equations of state in future modeling could confirm whether the Bondi advantage holds beyond the cases examined.

Load-bearing premise

The standard Bondi and Novikov-Thorne formalisms apply directly to these regular spacetimes without needing extra corrections for regularization effects.

What would settle it

An observation or simulation in which critical point locations and accretion rates for Bondi flows remain unchanged when the regularization parameter ℓ is varied would undermine the claimed sensitivity difference.

Figures

Figures reproduced from arXiv: 2605.02425 by Serena Gambino.

**Figure 1.** Figure 1: Composite 2 × 2 of luminosity profiles for RBH solutions (M = 1 AU). Upper panels: Bondi luminosity in logarithmic scale, log10[L(x)], as a function of x = r/M. Upper left (dark fluid, P = −0.75, C = 1.5, C3 = 50): solutions span several orders of magnitude. The Fan-Wang trend is noticeably higher than the other solutions, which are more closely clustered together. Upper right (exponential profile, ρ0 = 0.… view at source ↗

**Figure 2.** Figure 2: Bondi luminosity L(x) as a function of x in the SV spacetime (M = 1 AU, η = 0.1). Upper panels: neutral SV (Q = 0). Lower panels: charged SV (Q = 0.3). Left column (barotropic fluid, C1 = 10, C3 = 1.9): luminosity profiles for w = 0 and w = 1, from ℓ = 0 to ℓ = 2.5, with wormhole profiles extended symmetrically to negative x. Increasing the value of ℓ results in a slower decline of the profiles as they mov… view at source ↗

read the original abstract

We compare the Bondi spherical accretion model and the Novikov-Thorne thin disc formalism around regular black holes and Simpson-Visser spacetimes, using several equations of state for the accreting fluids. The Bondi model is significantly more sensitive to spacetime geometry and the equation of state, making it more effective at distinguishing between regular and classical solutions. For the Simpson-Visser solutions, however, increasing the regularisation parameter, $\ell$, shifts critical point positions both inward and outward. However, the charged Simpson-Visser extension, modeled by the charge $Q$, does not produce an effect comparable to that of $\ell$.

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.

Desk Editor's Note private letter to a colleague

Bondi accretion picks up geometry and EOS differences more than Novikov-Thorne when both are run on regular black holes and Simpson-Visser metrics, but the unmodified equations are the assumption that needs checking.

read the letter

The paper's main finding is that Bondi spherical accretion is more sensitive to the spacetime geometry and the equation of state than the Novikov-Thorne thin disk model when both are applied to regular black holes and Simpson-Visser spacetimes. This makes Bondi better suited for distinguishing regular solutions from classical ones in their numerical tests. They also note that the regularization parameter ℓ shifts the critical point locations inward or outward depending on the setup, while the charge Q has little to no comparable effect. They do a straightforward numerical comparison across several equations of state. This extends existing accretion models to these particular metrics in a concrete way, and the results on sensitivity differences are presented clearly from the calculations. The soft spot is the assumption that the usual Bondi and Novikov-Thorne equations apply without modification. In Simpson-Visser cases with large ℓ there is no true horizon and curvature is regular at the center, which might require adjustments to the fluid conservation laws or critical point conditions. The abstract gives no sign that such corrections were derived or shown to be negligible, so the claimed sensitivity advantage rests on that unexamined step. If the full paper justifies why the standard formalism holds, that concern goes away; otherwise it weakens the central claim. This work is for people studying accretion in modified gravity or regular black hole models. A reader interested in observational signatures from these spacetimes would get some useful comparative numbers out of it. The thinking is clear and the approach is honest, with no circularity in the comparisons. I would send it to peer review. The specific findings on Bondi versus Novikov-Thorne are worth referee scrutiny, even if the foundational applicability needs to be addressed in revisions.

Referee Report

1 major / 2 minor

Summary. The paper compares Bondi spherical accretion and Novikov-Thorne thin-disk accretion onto regular black holes and Simpson-Visser spacetimes for several equations of state. It concludes that the Bondi model is significantly more sensitive to spacetime geometry and the equation of state, making it more effective than the Novikov-Thorne model at distinguishing regular from classical solutions. For Simpson-Visser metrics, increasing the regularization parameter ℓ shifts critical-point locations inward or outward, while the charge parameter Q produces negligible effects.

Significance. If the unmodified application of the standard accretion equations remains valid, the result would indicate that spherical Bondi flows provide a more discriminative observational probe of spacetime regularity than thin disks, potentially allowing accretion signatures to constrain the regularization parameter ℓ in Simpson-Visser geometries.

major comments (1)

[Bondi accretion analysis and critical-point conditions] The central claim that Bondi accretion is more sensitive to geometry and EOS (and thus better at distinguishing regular vs. classical solutions) rests on the direct application of the standard relativistic continuity and Euler equations plus critical-point conditions to the given metrics. No derivation or explicit check is provided that the finite curvature invariants at r=0 or the absence of a horizon for large ℓ in Simpson-Visser spacetimes do not introduce additional source terms or modify the sound-speed definition at the sonic point. This assumption is load-bearing for the sensitivity comparison and the stated conclusions about ℓ and Q.

minor comments (2)

[Abstract] The abstract states that 'several equations of state' are used but does not name them; listing the specific EOS (e.g., polytropic indices or relativistic forms) would improve clarity.
[Numerical results] Numerical details such as integration methods, grid resolution, convergence criteria, or error estimates on the reported critical-point shifts are not summarized, which limits assessment of the robustness of the claimed differences between models.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We are grateful to the referee for their detailed review and insightful comments on our manuscript. We have carefully considered the major concern raised regarding the application of the Bondi accretion model to regular black hole spacetimes and provide our response below. We believe the analysis remains valid but will incorporate additional clarifications in the revised version.

read point-by-point responses

Referee: The central claim that Bondi accretion is more sensitive to geometry and EOS (and thus better at distinguishing regular vs. classical solutions) rests on the direct application of the standard relativistic continuity and Euler equations plus critical-point conditions to the given metrics. No derivation or explicit check is provided that the finite curvature invariants at r=0 or the absence of a horizon for large ℓ in Simpson-Visser spacetimes do not introduce additional source terms or modify the sound-speed definition at the sonic point. This assumption is load-bearing for the sensitivity comparison and the stated conclusions about ℓ and Q.

Authors: We appreciate the referee's point that the validity of the standard equations in these spacetimes requires justification. The Bondi accretion equations are derived from the covariant conservation of the energy-momentum tensor for a perfect fluid, ∇_μ T^{μν} = 0, and the continuity equation ∇_μ (n u^μ) = 0, where n is the particle number density. These are local equations that hold in any spacetime geometry, including regular black holes with finite curvature at the origin, as long as the metric is differentiable and the fluid is treated as a test field (no backreaction on the metric). The sound speed is defined locally from the equation of state as c_s² = (∂p/∂ρ)_s, which is independent of the global spacetime structure such as the presence or absence of horizons. The critical point conditions arise from requiring the numerator and denominator of the velocity gradient to vanish simultaneously, which follows directly from these conservation laws without assuming asymptotic flatness or the existence of an event horizon. For the Simpson-Visser metric, even in the horizonless case (large ℓ), the spacetime is smooth and the equations apply locally along the flow lines. In the revised manuscript, we will add a dedicated subsection in Section 2 deriving the critical point conditions explicitly from the conservation laws and confirming their applicability to the regular metrics considered. This will strengthen the foundation for our sensitivity comparisons. revision: yes

Circularity Check

0 steps flagged

No circularity: standard Bondi/Novikov-Thorne equations applied to given metrics

full rationale

The paper applies the established relativistic continuity/Euler equations and critical-point conditions of the Bondi spherical accretion model and the Novikov-Thorne thin-disk formalism directly to the supplied regular black-hole and Simpson-Visser line elements. Numerical solutions for critical radii, accretion rates, and disk properties are obtained for several equations of state; the reported sensitivity differences follow from these computations. No self-definitional identities, fitted parameters re-labeled as predictions, or load-bearing self-citations appear in the derivation chain. The central claim therefore rests on independent numerical comparison rather than reduction to the paper's own inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of two standard accretion models to a family of regular metrics whose parameters are varied numerically; no new entities are postulated and the equations of state are chosen from existing literature.

free parameters (2)

regularization parameter ℓ
Parameter of the Simpson-Visser metric that controls the degree of regularization; its value is varied to study shifts in critical points.
charge Q
Parameter of the charged Simpson-Visser extension; its effect is compared to that of ℓ.

axioms (1)

domain assumption Standard Bondi and Novikov-Thorne accretion equations remain valid when the background metric is replaced by a regular black hole or Simpson-Visser solution.
Invoked to justify direct substitution of the metric into the accretion equations.

pith-pipeline@v0.9.0 · 5396 in / 1321 out tokens · 107073 ms · 2026-05-08T19:07:53.219447+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

Constants / RSUnits — RS constants c, ℏ, G are φ-ladder outputs with zero parameters; these RBH metrics carry free phenomenological parameters reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Hayward solution: f(r)=1−2Mr²/(r³+2a²); Bardeen: f(r)=1−2Mr²/(r²+q_B²)^{3/2}; ... Fan-Wang: f=1−2Mr²/(r+l_FW)³, with l_FW≤8/27.
Cost.FunctionalEquation — RS sonic/critical structure would arise from J(x)=½(x+x⁻¹)−1 ratio-symmetric cost; paper's critical points are GR fluid conditions washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

V_c² = M / (2√(x_c²+ℓ²) − 3M), u_c² = M / (2√(x_c²+ℓ²)). ... the sonic-point equation must be solved numerically

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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