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REVIEW 3 major objections 4 minor 22 references

Geometry-Induced Termination of the Repetitive Penrose Process in Rotating Simpson-Visser Black Holes

T0 review · 3 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read The endpoint of the repetitive Penrose process in rotating Simpson–Visser black holes is governed by a competition: for large enough regularization, the evolving solution leaves the two-horizon black-hole branch before the minimum-spin limi

desk verdict New mechanism, incomplete numerical support: the branch-crossing endpoint in RSV is plausible but the tables don't implement the paper's own termination criterion. read the letter →

arxiv 2607.19904 v1 pith:IDWDR5SF submitted 2026-07-22 gr-qc

Mohammad Ali S. Afshar , Mohammad Reza Alipour , Saeed Noori Gashti , J. Sadeghi This is my paper · ORCID
classification gr-qc MSC 83C5783C15 PACS 04.70.-s04.70.Bw
keywords repetitivePenroseprocessSimpson-Visserspacetimeregularblackholesenergyextractionbounceminimumspinconditionirreduciblemassrotating
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that in the rotating Simpson–Visser geometry — a family that interpolates between Kerr black holes, black-bounce objects, and traversable wormholes via a regularization parameter ξ — the repeated Penrose process does not always terminate because the black hole spins down to the conventional kinematic limit. When ξ is large, the cumulative change in mass and angular momentum pushes the solution across the boundary of the two-horizon black-hole branch, so the iterative sequence ends because the assumed geometry no longer exists, not because energy extraction has been exhausted. The authors frame this as a 'geometry-induced termination' that competes with the familiar dynamical spin-threshold termination, and they trace how the number of admissible iterations, the extracted energy, and two efficiency measures all drop as ξ grows. A sympathetic reader would care because it shows the spacetime structure itself — not just particle kinematics — can set the ceiling on idealized rotational energy extraction.

What carries the argument

The rotating Simpson–Visser metric and its regularization parameter ξ: the geometry replaces r by sqrt(r^2 + ξ^2), and its two-horizon branch exists only for 0 ≤ ξ < M − sqrt(M^2 − a^2). Because ξ is held fixed while M and a are updated at each Penrose event (using the triple turning-point solution of the mass, angular-momentum, and radial-momentum conservation equations), the admissible parameter domain itself moves, letting the evolving solution cross the branch boundary before the kinematic spin limit is reached.

What would settle it

Re-run the iterative sequence while allowing ξ to vary with the absorbed negative-energy particles (e.g., tied to M or a by a conservation law); if the evolving solution then stays within the two-horizon branch beyond the iterations reported here, the structural termination is an artifact of the fixed-ξ assumption. Alternatively, a direct check: at ξ0=0.55 and r̂=1.5, verify that the post-iteration pair (M, a) crosses M − sqrt(M^2 − a^2) while â still exceeds âmin.

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Extended reading notes

Core claim

The central claim is that, assuming the regularization parameter ξ stays fixed while the black hole mass M and spin a evolve, the endpoint of the repeated Penrose process in the rotating Simpson–Visser spacetime is set by whichever comes first: the minimum-spin threshold at which negative-energy orbits cease to exist, or the boundary at which the spacetime leaves the two-horizon regular black-hole branch. The paper shows numerically (Tables 2–3, Fig. 1) that for ξ ≳ 0.44–0.55 the structural boundary is crossed first, so the process halts even though the black hole still has extractable rotational energy; near ξ ≈ 0.9 even a single Penrose event pushes the solution off the branch.

Load-bearing premise

The regularization parameter ξ is assumed to stay fixed while the black hole's mass and spin evolve under repeated particle absorption; if ξ shifts with back-reaction, the geometry-induced termination could be delayed, advanced, or absent.

Editorial extensions

If this is right

  • For small ξ the R-S-V evolution is qualitatively Kerr-like, but above a ξ-dependent threshold the termination is structural rather than kinematic.
  • The number of admissible Penrose iterations falls sharply with ξ; near the upper edge of the two-horizon regime a single decay suffices to exit the branch.
  • Cumulative extracted energy, final irreducible-mass growth, EROI, and EUE are all suppressed as ξ grows, largely because the sequence is cut short.
  • The decay radius matters: near-horizon decays give the most favorable extraction, and the optimal radius shifts inward as ξ increases.
  • A single Penrose event may be enough to push the spacetime out of the two-horizon branch, so the framework itself defines its own validity limit.

Reading between the lines

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

  • If ξ is allowed to vary under back-reaction rather than staying fixed, the structural termination could be delayed, advanced, or replaced by a transition to the wormhole branch, so a natural extension is to couple ξ to M or a through a conservation law and re-run the sequence.
  • The same 'moving parameter domain' mechanism should appear in any regular black-hole family whose admissible branch depends on the pairing of evolving dynamical parameters and a fixed extra parameter — e.g., charged or de Sitter versions — making geometry-induced termination plausibly generic.
  • Observationally, the sharp cutoff of the iterative sequence implies that regular black holes with large ξ would show systematically lower radiative efficiency from Penrose-type extraction than Kerr, a feature that could be compared against thin-disk efficiency predictions which the paper notes are unchanged at ISCO.
  • The stopping point marks the limit of the two-horizon description, not of the physical spacetime; describing what happens next would require re-formulating the process on the single-horizon or wormhole branch, which the paper explicitly leaves open.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper studies the repetitive Penrose process (RPP) in the rotating Simpson–Visser (RSV) spacetime, assuming a fixed regularization parameter ξ while the black-hole mass M and angular momentum L evolve through successive capture of negative-energy fragments. Using the triple turning-point idealization, the authors iterate the RPP and identify two termination mechanisms: the conventional dynamical spin threshold and a new "geometry-induced" termination that occurs when the evolving solution leaves the two-horizon branch of the RSV parameter space. Numerical tables and figures quantify extracted energy, irreducible mass, EROI, and EUE for different ξ and decay radii, and the paper concludes that for sufficiently large ξ the geometry-induced mechanism dominates.

Significance. If the central claim is correct, the paper adds a conceptually new ingredient to the RPP literature: not only does the spacetime geometry modify the efficiency of energy extraction, but the very existence of additional geometric parameters can terminate the iterative sequence before the kinematic spin limit is reached. This is a clean, falsifiable extension of the RPP framework to a well-motivated regular black-hole family. The manuscript is transparent about its main assumption (fixed ξ), and the reported tables are internally consistent, e.g., ζ_n = E_extracted/(n E0). The main concern is that the paper's own stated termination criterion, Eq. (17), is not actually implemented in the reported numerics, which undercuts the central comparison between the two termination mechanisms.

major comments (3)
  1. [§2.3, Eq. (17); Tables 2–3] The stated termination criterion is â_n < max(â_min,0, â_min,1, â_min,2), with each â_min,i obtained from Eq. (16). However, the numerical tables report only â_min,0,n. For the decisive cases — e.g., Table 2, ξ0=0.55 at r̂=1.5, where the structural termination is claimed at n=23 (â=0.930063, â_min,0=0.923448) — the conclusion that the spin limit has not yet been reached depends on â_min,0 being the largest of the three thresholds. If either â_min,1 or â_min,2 exceeds ~0.93 at that iteration, the sequence would already have terminated dynamically. The paper must either tabulate â_min,1,n and â_min,2,n for the representative parameter sets, or prove analytically that â_min,0 is always the maximum. Without this, the central claim that the termination is geometry-induced rather than dynamical is not established.
  2. [§4, fixed-ξ assumption] The structural termination condition is computed by holding ξ fixed while M decreases, so ξ̂=ξ/M increases during the evolution. The paper explicitly states this assumption, but it is load-bearing: the entire mechanism relies on the two-horizon boundary being fixed in ξ while the dynamical parameters move. No physical mechanism or conservation law is given for why the regularization parameter — sourced, according to the paper's own summary, by phantom scalar and nonlinear-electrodynamics fields — is insensitive to the absorption of negative-energy particles. If ξ varied with the back-reaction, the structural termination could be delayed, advanced, or absent. I recommend the authors add a discussion of the plausibility of this assumption, or test robustness by letting ξ evolve according to a simple model.
  3. [§4 and Fig. 1] Fig. 1 and the surrounding text describe the termination regimes using the single threshold â_min,0, while Eq. (17) requires the maximum over three thresholds. This inconsistency is not merely notational: the phase diagram in Fig. 1 classifies the endpoint as dynamical or structural based on the â_min,0 criterion. If the maximum of the three thresholds is the actual dynamic bound, the boundary in Fig. 1 could shift. Please align the figure, the tables, and the text with the full criterion, or revise Eq. (17) if â_min,0 is intended as the operative bound.
minor comments (4)
  1. [Fig. 5 caption] The EROI is defined as ζ_n in Eq. (14), but the caption of Fig. 5 labels it "ξnf", which conflicts with the regularization parameter ξ. Please use ζ_{n_f} or a similar symbol.
  2. [Tables 2–3] The red/blue row coloring used to mark kinematic versus structural termination is not visible in the extracted manuscript. Please add explicit markers (e.g., bold, asterisks, or a separate column) so the termination row is unambiguous.
  3. [§4 text] The text sometimes refers to "the minimum-spin condition (â < â_min)" without specifying which particle index; this is inconsistent with Eq. (17). Please standardize the notation.
  4. [Appendix / Table 3 placement] The appendix contains a one-sentence discussion of Table 3, but Table 3 is presented in the main body. Either move the table to the appendix or expand the discussion in the main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the structural termination is a stated model-validity boundary, not a fitted or self-citation-dependent prediction.

full rationale

The derivation is self-contained. The iterative update rules (11)-(12) are explicit, the conventional spin threshold is defined as the marginal-stability condition (16) and used with the termination criterion (17), and the geometry-induced boundary is just the two-horizon condition Δ=0 from Eq. (20), combined with the paper's explicitly stated fixed-ξ assumption. The claimed structural termination is not obtained by fitting any parameter to the data it later predicts; it is a parameter-domain consistency check. The paper itself repeatedly and clearly labels it as a limitation of the chosen framework ('the endpoint identified here therefore marks the limit of validity of the original two-horizon black-hole description, not necessarily the end of the physical evolution'), which removes any appearance of presenting a definition as an independent discovery. The self-citations present ([17] for efficiency definitions and [22] for a comparative example in Einstein-Gauss-Bonnet gravity) are not load-bearing for the central claim: the efficiency ratios are definitions, and the EGB comparison is illustrative. Two non-circular caveats are worth noting as correctness risks: Eq. (17) requires max(âmin,0, âmin,1, âmin,2), but Tables 2-3 report only âmin,0,n; and the fixed-ξ assumption is physically unmotivated. These are modeling/implementation issues, not circular reasoning.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the fixed-ξ assumption and the representative kinematic parameters; the termination is set by the two-horizon domain boundary the authors impose. No new physical entities are introduced.

free parameters (7)
  • regularization parameter ξ = 0, 0.15, 0.35, 0.43, 0.55, 0.75, 0.8, 0.88, 0.92 (dimensionless, M0=1)
    Model parameter of the R-S-V family; the central variable controlling the geometry-induced termination.
  • initial dimensionless spin â0 = 1
    Extremal Kerr start; maximizes the number of RPP iterations and enables the branch-crossing. Sub-extremal initial spins are not explored.
  • incident particle specific energy Ê0 = 1
    Free kinematic input for the decay; part of the representative parameter set.
  • captured fragment angular momentum p̂φ1 = -19.434
    Large negative angular momentum chosen to support negative-energy states; free input.
  • fragment mass ratio ν=μ2/μ1 = 0.78345
    Free input determining the escaping fragment's mass.
  • incident particle rest mass μ0 = 10^{-2} M0
    Small perturbation; chosen so the back-reaction is gradual.
  • decay radius r̂ = 1.2, 1.5 in tables; scanned in figures
    Position of the Penrose decay; the results are sensitive to it.
assumptions (6)
  • domain assumption The black hole mass and angular momentum update by the captured fragment's conserved quantities (Eqs. 11-12).
    Assumes the negative-energy fragment is absorbed at the horizon and that energy/angular momentum conservation at infinity gives these updates. Standard for RPP; not re-derived here.
  • domain assumption The triple turning-point condition (Eq. 6) characterizes the maximum-energy extraction decay.
    Adopted from Ruffini et al. [11]; represents an idealization, not a generic decay.
  • domain assumption The RPP framework is only constructed within the two-horizon branch; crossing to the single-horizon/wormhole branch is treated as termination.
    The authors explicitly restrict to the two-horizon R-S-V regime (Table 1) and stop when the boundary is crossed.
  • domain assumption The metric retains the R-S-V form with the same ξ while M and a are updated.
    Keeps ξ fixed throughout; no dynamical equation for ξ is given.
  • standard math The effective potential formalism for timelike equatorial geodesics (Eqs. 4-5) applies.
    Standard geodesic mass-shell constraint for stationary axisymmetric metrics.
  • standard math The irreducible mass is Mirr = sqrt(A/(16π)) with horizon area A = 4π(R_+² + a²), R_+ = M + sqrt(M²−a²).
    Uses the horizon area formula generalized to R-S-V; consistent with the ξ=0 Kerr limit.

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Cite this review

Pith. "Pith review of Geometry-Induced Termination of the Repetitive Penrose Process in Rotating Simpson-Visser Black Holes." pith.science (2026). https://pith.science/paper/IDWDR5SF

@misc{pith2026260719904,
  author       = {Pith},
  title        = {Pith review of: Geometry-Induced Termination of the Repetitive Penrose Process in Rotating Simpson-Visser Black Holes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IDWDR5SF}},
  note         = {Machine review of arXiv:2607.19904}
}
read the original abstract

We examine the Repetitive Penrose Process in the rotating Simpson-Visser spacetime, whose parameter space includes regular black holes, black-bounce geometries, and traversable wormholes. Assuming that the regularization parameter remains unchanged throughout the evolution, the analysis shows that the endpoint of the repetitive process is not always determined solely by the conventional minimum spin condition. Instead, for sufficiently large values of the regularization parameter, the evolving solution may leave the parameter domain corresponding to the original two horizon black hole branch before the dynamical spin limit is reached. Within the present framework, this provides an additional geometry-induced condition that limits the continuation of the iterative sequence. The numerical results further show that the relative importance of the dynamical and geometry-induced termination mechanisms depends sensitively on the regularization parameter. For small deformations, the evolution remains qualitatively similar to that of the Kerr spacetime. As the regularization parameter increases, however, the cumulative extracted energy, the number of admissible Penrose iterations, and the efficiency of the process are progressively reduced. We also examine how the extracted energy, the final irreducible mass, and two complementary efficiency measures vary with both the regularization parameter and the particle decay radius. Overall, the present analysis indicates that, within the RSV geometry, the underlying spacetime structure influences not only the cumulative efficiency of the repetitive Penrose process but also the parameter range over which the iterative evolution remains self-consistent. These results highlight the role that spacetime geometry can play in shaping the long-term evolution of idealized Penrose-type energy extraction processes in regular rotating black-hole spacetimes.

Figures

Figures reproduced from arXiv: 2607.19904 by the authors.

Figure 1
Figure 1. The parameter space of the RPP in the (ˆrd, ˆξ) plane. The black solid curve with dots marks the boundary separating two termination regimes. The shaded pink region below the curve indicates the do￾main where the process is terminated by the minimum spin condition (a <ˆ aˆmin,0). The white region above the curve corresponds to the domain where the process is terminated by the structural condition (ˆξ ≥ ˆξmax), i.e.,… view at source ↗
Figure 2
Figure 2. The behavior of Extracted energy, normal [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 4
Figure 4. The final energy utilization efficiency Ξnf as a function of the dimensionless decay radius rˆ for various values of the deformation parameter ξ. final Energy Utilization Efficiency (EUE) as a function of the dimensionless decay radius. For all values of the regularization parameter, the efficiency decreases monotonically as the decay radius increases, indicating that repetitive Penrose events occurring closer to th… view at source ↗
Figures from the paper (2 more)
Figure 3
Figure 3. Figure 3: The behavior of the final irreducible mass, [PITH_FULL_IMAGE:figures/full_fig_p010_3.png]
Figure 5
Figure 5. Figure 5: The behavior of the final energy return on [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

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Reference graph

Works this paper leans on

22 extracted references · 2 linked inside Pith

  1. [1]

    Reversible and irreversible transformations in black-hole physics

    Christodoulou D. Reversible and irreversible transformations in black-hole physics. Physical Review Letters. 1970 Nov 30;25(22):1596

    1970

  2. [2]

    Extracting energy from a black hole through the transition region

    Li LX. Extracting energy from a black hole through the transition region. The Astrophysical Journal Letters. 2000 Sep 1;540(1):L17-20

    2000

  3. [3]

    Gravitational collapse: The role of general relativity

    Penrose R. Gravitational collapse: The role of general relativity. Nuovo Cimento Rivista Serie. 1969;1:252

    1969

  4. [4]

    Electromagnetic ex- traction of energy from Kerr black holes

    Blandford RD, Znajek RL. Electromagnetic ex- traction of energy from Kerr black holes. Monthly Notices of the Royal Astronomical Society. 1977 Jul 1;179(3):433-56

    1977

  5. [5]

    Fifty years of energy extraction from rotating black hole: revisiting magnetic Penrose process

    Tursunov A, Dadhich N. Fifty years of energy extraction from rotating black hole: revisiting magnetic Penrose process. Universe. 2019 May 22;5(5):125

    2019

  6. [6]

    Magnetic Pen- rose process in the magnetized Kerr spacetime

    Chakraborty C, Patil P, Akash G. Magnetic Pen- rose process in the magnetized Kerr spacetime. Physical Review D. 2024 Mar 15;109(6):064062

    2024

  7. [7]

    Kerr black holes as particle accelerators to arbitrarily high energy

    Bañados M, Silk J, West SM. Kerr black holes as particle accelerators to arbitrarily high energy. Physical review letters. 2009 Sep 11;103(11):111102

    2009

  8. [8]

    Magnetic reconnection as a mechanism for energy extraction from rotat- ing black holes

    Comisso L, Asenjo F A. Magnetic reconnection as a mechanism for energy extraction from rotat- ing black holes. Physical Review D. 2021 Jan 15;103(2):023014

    2021

Show all 22 references
  1. [9]

    C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman, San Francisco, 1973), ISBN 978- 0-7167-0344-0, 978-0-691-17779- 3, [MTW73]

    1973

  2. [10]

    Single versus the Repetitive Penrose Process in a Kerr Black Hole

    Ruffini R, Prakapenia M, Quevedo H, Zhang S. Single versus the Repetitive Penrose Process in a Kerr Black Hole. Physical Review Letters. 2025 Feb 28;134(8):081403

    2025

  3. [11]

    Role of the irreducible mass in repetitive Penrose energy extraction processes in a Kerr black hole

    Ruffini R, Bianco CL, Prakapenia M, Quevedo H, Rueda JA, Zhang S. Role of the irreducible mass in repetitive Penrose energy extraction processes in a Kerr black hole. Physical Review Research. 2025 Feb;7(1):013203

    2025

  4. [12]

    Repetitive Penrose process in Kerr-de Sitter black holes

    Wang K, Zeng XX. Repetitive Penrose process in Kerr-de Sitter black holes. The European Physical Journal C. 2026 Apr;86(4):404

    2026

  5. [13]

    Repetitive Penrose Process in Accelerating Kerr Black Holes

    Zeng XX, Wang K. Repetitive Penrose Process in Accelerating Kerr Black Holes. arXiv preprint arXiv:2601.01414. 2026 Jan 4

    2026

  6. [14]

    Repetitive Penrose process in Konoplya-Zhidenko rotating non-Kerr black holes

    Zeng XX, Su DP, Wang K. Repetitive Penrose process in Konoplya-Zhidenko rotating non-Kerr black holes. Science China Physics, Mechanics , Astronomy. 2026 Jul;69(7):270414. 12 ξ0 n M/M 0 ˆan ˆξn Eextractable/M0 Eextracted/M0 Mirr/M0 ˜µ1,n ˆE1,n ˆpφ0,n ˆamin,0,n ζn Ξn 0 0 1 1 0 ...

    2026

  7. [15]

    Third law of repeti- tive electric Penrose processes

    Hu L, Cai RG, Wang SJ. Third law of repeti- tive electric Penrose processes. Physical Review D. 2026 Mar 15;113(6):L061501

    2026

  8. [16]

    Repetitive Penrose Process in Kerr-Taub-NUT black hole spacetime

    Alloqulov M, Ahmedov B, Yuan C. Repetitive Penrose Process in Kerr-Taub-NUT black hole spacetime. arXiv preprint arXiv:2603.25630. 2026 Mar 26

    2026

  9. [17]

    Repet- itive Penrose process for charged particles in Kerr-Newman black holes

    Alipour MR, Gashti SN, Afshar MA. Repet- itive Penrose process for charged particles in Kerr-Newman black holes. arXiv preprint arXiv:2606.30969. 2026 Jun 29

    2026 arXiv

  10. [18]

    Black-bounce to traversable wormhole

    Simpson A, Visser M. Black-bounce to traversable wormhole. Journal of Cosmology and Astroparti- cle Physics. 2019 Feb 1;2019(02):042-

    2019

  11. [19]

    Circular orbits and observational features of the rotating Simpson- Visser black hole surrounded by a thin accretion disk

    Li Z, Liu SQ, Huang JH. Circular orbits and observational features of the rotating Simpson- Visser black hole surrounded by a thin accretion disk. Chinese Physics C. 2026 Jul 1;50(7):075105

    2026

  12. [20]

    Constrain- ing alternatives to the Kerr black hole

    Shaikh R, Pal K, Pal K, Sarkar T. Constrain- ing alternatives to the Kerr black hole. Monthly Notices of the Royal Astronomical Society. 2021 Sep;506(1):1229-36

    2021

  13. [21]

    Field sources for Simpson-Visser spacetimes

    Bronnikov KA, Walia RK. Field sources for Simpson-Visser spacetimes. Physical Review D. 2022 Feb 15;105(4):044039

    2022

  14. [22]

    Repetitive Penrose Process in Rotating 4D Einstein- Gauss-Bonnet Black Holes

    Alipour MR, Afshar MA, Gashti SN. Repetitive Penrose Process in Rotating 4D Einstein- Gauss-Bonnet Black Holes. arXiv preprint arXiv:2607.08989. 2026 Jul 9. 14

    2026 arXiv

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