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arxiv: 2603.16147 · v2 · pith:YJC2BSCYnew · submitted 2026-03-17 · 🌀 gr-qc

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

Xiao-Xiong Zeng , Dong-Ping Su , Ke Wang This is my paper

Pith reviewed 2026-05-25 06:49 UTC · model grok-4.3

classification 🌀 gr-qc
keywords repetitive Penrose processKonoplya-Zhidenko black holedeformation parameterenergy extractionrotating black holesnon-Kerr metricenergy return on investment
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The pith

Larger initial deformation in Konoplya-Zhidenko black holes increases energy return on investment and utilization efficiency in repetitive Penrose processes at fixed decay radii.

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

The paper examines the repetitive Penrose process in the Konoplya-Zhidenko rotating non-Kerr black hole spacetime to determine how the dimensionless deformation parameter affects energy extraction. Numerical results show that, at the same decay radius, a larger initial deformation parameter produces greater energy return on investment and energy utilization efficiency, with the difference growing at higher decay radii. A smaller initial deformation yields a larger maximum energy return on investment, while an intermediate value of the parameter maximizes the peak efficiency. Larger initial deformation also reduces the maximum extractable energy overall.

Core claim

In the Konoplya-Zhidenko rotating non-Kerr black hole, the repetitive Penrose process yields higher energy return on investment and energy utilization efficiency for larger initial values of the dimensionless deformation parameter η̂ when the decay radius is held constant, with this advantage being more pronounced at higher decay radii. A smaller initial η̂ produces a larger maximum energy return on investment, whereas an intermediate initial η̂ maximizes the peak energy utilization efficiency. A larger initial η̂ results in a smaller maximum value of the extracted energy.

What carries the argument

The dimensionless deformation parameter η̂ in the Konoplya-Zhidenko metric, which modifies spacetime geometry and thereby controls particle trajectories and cumulative energy gains across repeated Penrose iterations.

If this is right

  • Larger initial η̂ increases both energy return on investment and utilization efficiency at any fixed decay radius.
  • The increase in these quantities with η̂ becomes more pronounced at larger decay radii.
  • Maximum energy return on investment is achieved when the initial deformation parameter is smaller.
  • Peak energy utilization efficiency occurs at an intermediate value of the initial deformation parameter.
  • Maximum extractable energy decreases as the initial deformation parameter increases.

Where Pith is reading between the lines

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

  • The radius dependence implies that energy extraction events occurring farther from the horizon are more sensitive to spacetime deformation than those near the ergosphere.
  • These parameter trends could be used to distinguish Konoplya-Zhidenko metrics from Kerr in numerical models of repeated particle scattering.
  • The results open the possibility of mapping deformation effects onto observable signatures in high-energy astrophysical outflows.
  • If the stopping conditions prove robust under small perturbations, the efficiency ordering with η̂ should persist in nearby deformed metrics.

Load-bearing premise

The iterative stopping conditions for repeating the Penrose process are correctly identified and implemented for particle trajectories in the Konoplya-Zhidenko spacetime.

What would settle it

A numerical run of particle trajectories in the Konoplya-Zhidenko metric in which increasing the initial deformation parameter fails to raise energy return on investment at higher decay radii would falsify the reported dependence.

Figures

Figures reproduced from arXiv: 2603.16147 by Dong-Ping Su, Ke Wang, Xiao-Xiong Zeng.

Figure 1
Figure 1. Figure 1: FIG. 1: Variation of [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Variation of the minimum spin lower limits with the decay radius [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Comparison of the minimum spin lower limits for the three particles [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: For different initial [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
read the original abstract

This paper investigates the repetitive Penrose process in Konoplya-Zhidenko rotating non-Kerr black hole, exploring the influence of the deformation parameter on the repetitive Penrose process. After a brief review of the Konoplya-Zhidenko rotating non-Kerr black hole, we study the fundamental equations of the Penrose process in this spacetime, examine the iterative stopping conditions required for the repetitive Penrose process, and obtain the corresponding numerical results. It is concluded that, in addition to previously observed phenomena, under the same decay radius, a larger initial dimensionless deformation parameter $\hat{\eta}$ leads to greater values of the energy return on investment and energy utilization efficiency, particularly at higher decay radii. Furthermore, a smaller initial $\hat{\eta}$ results in a larger maximum value of the energy return on investment. For energy utilization efficiency, the initial $\hat{\eta}$ should take an intermediate value to maximize its peak. Additionally, we find that a larger initial $\hat{\eta}$ corresponds to a smaller maximum value of the extracted energy.

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 manuscript numerically investigates the repetitive Penrose process in the Konoplya-Zhidenko rotating non-Kerr black hole spacetime. After reviewing the metric, it derives the geodesic equations for the process, specifies iterative stopping conditions, and reports trends in energy return on investment, energy utilization efficiency, and extracted energy as functions of the initial dimensionless deformation parameter η̂ at fixed decay radii.

Significance. If the numerical results prove robust, the work would extend prior studies of the Penrose process to a one-parameter family of deformed Kerr metrics, offering concrete predictions for how deviations from Kerr affect repetitive energy extraction efficiency; this could be relevant for testing modified gravity in strong-field regimes.

major comments (2)
  1. [Abstract; section on iterative stopping conditions] Abstract and the section on iterative stopping conditions: the headline claims rest on numerical outcomes of an iterative process, yet the stopping criteria, integration scheme (e.g., Runge-Kutta order, adaptive step-size control), accumulated error tolerances, and explicit validation against the Kerr limit (η̂=0) are referenced only generically; without these, the reported monotonic trends with η̂ cannot be confirmed to be free of premature termination or coordinate artifacts.
  2. [Numerical results section] Numerical results section: no error bars, convergence tests with respect to integration tolerance, or tables comparing extracted energies to analytic Kerr expectations are supplied, rendering the quantitative statements (e.g., larger η̂ yields higher ROI at high decay radii) unverifiable from the given data.
minor comments (2)
  1. [Metric review section] Notation: the symbol η̂ is introduced without an explicit definition equation linking it to the metric deformation parameter; a short equation would improve clarity.
  2. [Figures] Figure captions: several plots lack axis labels specifying the exact value of the decay radius or the range of η̂ sampled.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the major concerns point by point below and will revise the manuscript to incorporate the requested numerical details.

read point-by-point responses

  1. Referee: [Abstract; section on iterative stopping conditions] Abstract and the section on iterative stopping conditions: the headline claims rest on numerical outcomes of an iterative process, yet the stopping criteria, integration scheme (e.g., Runge-Kutta order, adaptive step-size control), accumulated error tolerances, and explicit validation against the Kerr limit (η̂=0) are referenced only generically; without these, the reported monotonic trends with η̂ cannot be confirmed to be free of premature termination or coordinate artifacts.

    Authors: We agree that the numerical implementation must be documented in greater detail to allow verification of the reported trends. In the revised manuscript we will expand the relevant section to specify the integration scheme (fourth-order Runge-Kutta with adaptive step-size control), the accumulated error tolerances, the exact iterative stopping criteria, and a validation subsection that explicitly recovers the known Kerr results when η̂ = 0. revision: yes

  2. Referee: [Numerical results section] Numerical results section: no error bars, convergence tests with respect to integration tolerance, or tables comparing extracted energies to analytic Kerr expectations are supplied, rendering the quantitative statements (e.g., larger η̂ yields higher ROI at high decay radii) unverifiable from the given data.

    Authors: We acknowledge that the current version lacks quantitative error analysis and direct comparisons to the Kerr limit. We will add error bars based on the integration tolerances, include convergence tests obtained by varying the tolerance parameters, and provide a table (or supplementary figure) comparing extracted energies in the η̂ = 0 case against known analytic Kerr expectations. revision: yes

Circularity Check

0 steps flagged

Numerical integration of geodesics yields independent results; no circular reduction

full rationale

The paper reviews the Konoplya-Zhidenko metric, writes the geodesic equations for the Penrose process, specifies iterative stopping conditions, and reports numerical trends in energy return, efficiency, and extracted energy as functions of the deformation parameter. These outputs are obtained by direct integration and do not reduce by the paper's own equations to any fitted input, self-defined quantity, or self-citation chain. No step equates a claimed prediction to a parameter fit on the same data or renames a known result via internal redefinition. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumed validity of the Konoplya-Zhidenko metric form and on the chosen numerical implementation of the iterative stopping conditions; the deformation parameter is treated as an input that is varied rather than derived.

free parameters (1)
  • initial dimensionless deformation parameter hat eta
    The parameter is varied across numerical runs to map its influence on the energy quantities; no independent derivation or measurement is supplied.
axioms (1)
  • domain assumption The background spacetime is exactly the Konoplya-Zhidenko rotating non-Kerr black hole metric.
    The paper begins with a brief review of this metric and performs all subsequent calculations inside it.

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Reference graph

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