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arxiv: 2510.24143 · v2 · pith:DNSHQEHVnew · submitted 2025-10-28 · 🌀 gr-qc

Effects of tidal charge on Blandford-Znajek process around braneworld black holes

Ruixin Yang , Songbai Chen , Jiliang Jing This is my paper

Pith reviewed 2026-05-22 12:23 UTC · model grok-4.3

classification 🌀 gr-qc
keywords braneworld black holestidal chargeBlandford-Znajek processenergy extractionRandall-Sundrumrotating black holesmagnetosphere
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The pith

Tidal charge in braneworld black holes can boost or reduce Blandford-Znajek power by up to 66.5% or 15.2%.

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

The paper studies how the tidal charge parameter affects the Blandford-Znajek energy extraction process in rotating black holes within the Randall-Sundrum braneworld model. By employing an extended monopole expansion approach, the authors compute the energy and angular momentum extraction rates for various tidal charge values. They discover that positive tidal charges lower the BZ power relative to a standard Kerr black hole, while negative tidal charges raise it, with peak changes of 15.2% reduction and 66.5% enhancement. The angular momentum extraction shows a comparable dependence on the tidal charge sign.

Core claim

Within the extended BZ monopole expansion in the braneworld black hole spacetime, positive tidal charge reduces the BZ power of a braneworld BH while negative tidal charge enhances the power, with a maximum reduction of approximately 15.2% and a maximum enhancement of 66.5% in power output compared with a Kerr BH of the same mass and angular velocity.

What carries the argument

Extended Blandford-Znajek monopole expansion framework applied to the Randall-Sundrum braneworld black hole metric with tidal charge.

If this is right

  • The energy extraction rate depends on the sign of the tidal charge parameter.
  • Negative tidal charge cases yield higher power outputs than equivalent Kerr black holes.
  • Positive tidal charge cases yield lower power outputs than equivalent Kerr black holes.
  • The relative angular momentum extraction rate exhibits a similar qualitative trend with tidal charge.

Where Pith is reading between the lines

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

  • If these effects are present, they could influence models of relativistic jets powered by black hole rotation in extra-dimensional scenarios.
  • Independent measurements of black hole spin and jet power might allow constraints on the tidal charge.
  • Analytic results could guide numerical magnetohydrodynamic simulations of braneworld black hole magnetospheres.

Load-bearing premise

The extended BZ monopole expansion framework remains valid without further corrections when applied to the Randall-Sundrum braneworld black-hole metric.

What would settle it

Measuring the jet power from a known rotating black hole and checking if it matches the predicted enhancement or reduction for non-zero tidal charge values would test the result.

Figures

Figures reproduced from arXiv: 2510.24143 by Jiliang Jing, Ruixin Yang, Songbai Chen.

Figure 1
Figure 1. Figure 1: FIG. 1: The ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Plots of [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Magnetic field lines as the contours of flux Ψ on the ( [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The radial magnetic field [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Percentage-scaled ∆ [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

The Blandford-Znajek (BZ) process is a pivotal mechanism to efficiently extract the energy from a rotating black hole (BH) via its plasma-filled magnetosphere in relativistic astrophysics. Within the framework of extended BZ monopole expansion, we have studied BZ process in the Randall-Sundrum braneworld BH spacetime and analyzed effects of the tidal charge on the energy and angular momentum extraction rates. It is found that the positive tidal charge reduces the BZ power of a braneworld BH, while the negative tidal charge enhances the power. Compared with a Kerr BH of the same mass and angular velocity, the BZ power exhibits a maximum reduction of approximately $15.2\%$ in positive cases, whereas in negative cases, it achieves a maximum enhancement of $66.5\%$ in power output. A similar qualitative trend is also observed for the relative angular momentum extraction rate, albeit with different magnitudes.

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 / 1 minor

Summary. The manuscript applies the extended Blandford-Znajek monopole expansion framework to rotating black holes in the Randall-Sundrum braneworld spacetime that includes a tidal charge parameter. It computes the energy and angular-momentum extraction rates and reports that positive tidal charge reduces BZ power by a maximum of approximately 15.2% while negative tidal charge enhances it by a maximum of 66.5%, both relative to a Kerr black hole of identical mass and horizon angular velocity. A qualitatively similar trend is stated for the angular-momentum extraction rate.

Significance. If the direct substitution of the braneworld metric into the existing BZ expressions is justified, the work supplies concrete quantitative estimates of how an extra-dimensional parameter modifies rotational energy extraction efficiency. These percentages constitute falsifiable predictions that could be tested against the Kerr limit and may inform jet-power models in modified-gravity scenarios.

major comments (2)
  1. [BZ power calculation (method and results sections)] The reported power changes rest on inserting the braneworld metric directly into the Kerr-derived monopole expressions for the Poynting flux and current distribution. The force-free condition and the Grad-Shafranov-like equation that fix the field configuration are metric-dependent; the ergoregion and horizon radii also shift with tidal charge. No re-solution of the force-free equations or explicit check that the monopole ansatz remains an exact or consistent solution in the new background is supplied, which is load-bearing for the central quantitative claims.
  2. [Results and discussion] The maximum reduction of 15.2% and enhancement of 66.5% are stated without accompanying error estimates, sensitivity to expansion order, or explicit verification that the results recover the Kerr values when the tidal charge is set to zero.
minor comments (1)
  1. [Abstract] The abstract refers to 'numerical results' but supplies no information on the numerical scheme, truncation order of the expansion, or convergence tests used to obtain the quoted percentages.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major comment below and indicate the revisions we intend to incorporate.

read point-by-point responses

  1. Referee: [BZ power calculation (method and results sections)] The reported power changes rest on inserting the braneworld metric directly into the Kerr-derived monopole expressions for the Poynting flux and current distribution. The force-free condition and the Grad-Shafranov-like equation that fix the field configuration are metric-dependent; the ergoregion and horizon radii also shift with tidal charge. No re-solution of the force-free equations or explicit check that the monopole ansatz remains an exact or consistent solution in the new background is supplied, which is load-bearing for the central quantitative claims.

    Authors: Our work applies the extended Blandford-Znajek monopole expansion framework, which is constructed to permit substitution of a given stationary axisymmetric metric into the perturbative expressions for the electromagnetic fields and currents while retaining the monopole ansatz at leading order. The modified horizon radius, ergoregion, and angular velocity are incorporated through the braneworld line element. We acknowledge that a complete re-derivation of the Grad-Shafranov equation in the new geometry would constitute a stronger validation. We will therefore add a dedicated paragraph in the revised manuscript that discusses the consistency of the ansatz under the force-free condition for the braneworld case and performs an explicit check of the leading-order solution. revision: partial

  2. Referee: [Results and discussion] The maximum reduction of 15.2% and enhancement of 66.5% are stated without accompanying error estimates, sensitivity to expansion order, or explicit verification that the results recover the Kerr values when the tidal charge is set to zero.

    Authors: We agree that these elements improve the robustness of the quantitative claims. In the revised manuscript we will include an explicit demonstration that setting the tidal charge to zero recovers the standard Kerr expressions and numerical values from the literature. We will also add a short discussion of truncation error by comparing results obtained at successive orders in the monopole expansion and will attach a brief estimate of the associated uncertainty to the reported percentage changes. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation proceeds from metric substitution into established BZ framework

full rationale

The paper begins with the Randall-Sundrum braneworld rotating black-hole metric containing the tidal-charge parameter and substitutes its components into the expressions furnished by the extended BZ monopole expansion. The energy and angular-momentum fluxes are then evaluated at the horizon for varying tidal charge while holding mass and horizon angular velocity fixed; the quoted percentage shifts (maximum 15.2 % reduction, 66.5 % enhancement) are direct numerical consequences of those substitutions. No quantity is defined in terms of its own output, no parameter is fitted to the computed power and then re-labeled a prediction, and the central ansatz is imported from the literature rather than smuggled via self-citation that itself rests on the present result. The calculation is therefore self-contained once the metric and the BZ expansion are accepted.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on the applicability of the extended BZ monopole expansion to the Randall-Sundrum braneworld metric and on treating the tidal charge as a free parameter that can take both positive and negative values.

free parameters (1)
  • tidal charge
    Parameter of the braneworld metric that is varied over positive and negative ranges to obtain the reported percentage shifts; its specific numerical values are not fitted to data but scanned.
axioms (2)
  • domain assumption The Randall-Sundrum braneworld black-hole metric provides the correct background spacetime.
    Invoked as the geometry in which the BZ process is evaluated.
  • domain assumption The extended BZ monopole expansion can be applied directly to this metric.
    Stated as the calculational framework used throughout the study.
invented entities (1)
  • tidal charge no independent evidence
    purpose: Encodes the gravitational influence of the extra dimension on the black-hole geometry.
    Postulated within the Randall-Sundrum construction; no independent observational detection is claimed in the abstract.

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