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REVIEW 4 major objections 5 minor 40 references

Outgoing electromagnetic flux from rotating wormholes

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper argues that rotating wormholes can emit a Poynting flux comparable to that of Kerr black holes while accreting magnetized matter.

desk verdict First BZ-type flux estimate for rotating wormholes, but the ad hoc field ansatz violates Maxwell and manufactures the sign and magnitude of the flux. read the letter →

arxiv 2411.13474 v1 pith:XDQYT4SL submitted 2024-11-20 gr-qc astro-ph.HE

Milos Ertola Urtubey , Daniela Pérez , Gustavo Esteban Romero This is my paper · ORCID
classification gr-qcastro-ph.HE
keywords rotatingwormholesDamour-SolodukhinmetricPoyntingfluxBlandford-Znajekmechanismergosphereaccretiondiskenergyextractiongeneralrelativity
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 rotating wormholes, not just black holes, can drive the kind of electromagnetic outflow thought to power astrophysical jets. Working with the Damour-Solodukhin metric, a Kerr-like wormhole spacetime with a deformation parameter $\lambda$, the authors show that a sufficiently fast spin and a small enough deformation allow part of a magnetized accretion disk to sit inside the ergosphere, where frame dragging twists the magnetic field and produces a net outward Poynting flux. They present this as the first demonstration that rotating wormholes can emit such a flux. For a $10\,M_\odot$ wormhole with $B_0=10^7\,\mathrm{G}$, spin $a/M=0.97$ and $\lambda=0.12$, the computed power is about $4\times10^{36}\,\mathrm{erg\,s^{-1}}$, the same order as a Kerr black hole of the same mass and spin.

What carries the argument

The machinery is the Blandford-Znajek mechanism, the extraction of rotational energy from a compact object's ergosphere by a force-free magnetosphere, transplanted to the Damour-Solodukhin rotating wormhole metric. That metric has an ergosphere with outer boundary $r_{S+}(\theta)$ and a throat at $r_+$, and an ergoregion exists as long as $\lambda \le \lambda_{\mathrm{crit}} = a c^2/(2GM)$. The model takes the external magnetic field to be the uniform poloidal solution $\vec{B}=B_0\hat{z}$ at large radius; inside the ergosphere it multiplies the poloidal components by the linear factor $y(r,\theta)=(r-r_+)/(r_{S+}-r_+)$, which vanishes at the throat, and adds a toroidal component $B^\phi$ chosen so that $|B|$ stays uniform, with sign fixed to make the energy flux outward. The radial energy flux is $E^r = -c^2\omega B^r_{\mathrm{new}}B^\phi \Delta \sin^2\theta$, and the total power $P_{BZ}$ is the integral of $\sqrt{-g}E^r$ over the polar angle at $r_{\mathrm{ISCO}}$. Requiring part of the disk to lie inside the ergosphere but outside the throat, $r_{\mathrm{ISCO}} \le r_{S+}(\theta=\pi/2)=2M$, selects the spin range $0.94281 \le a/M < 1$.

What would settle it

Compute the divergence and the force-free equations (30)-(31) for the magnetic field defined by eqs. (49)-(51) inside the ergosphere; if they fail, the quoted Poynting flux is not a solution of the stated equations. Alternatively, a force-free stream-equation solution or a GRMHD simulation for the Damour-Solodukhin metric with the ISCO inside the ergosphere would show whether a Poynting flux at the quoted level actually emerges.

Watch

Extended reading notes

Core claim

The central claim is that a rotating Damour-Solodukhin wormhole can power a Blandford-Znajek-like outflow: while accreting magnetized matter, it emits a Poynting flux of the same order as a Kerr black hole with the same mass and spin. The authors compute this for the first time for rotating wormholes. For spin $0.94281 \le a/M < 1$ and deformation $0 \le \lambda \le \tilde{\lambda}_{\mathrm{crit}}(a)$, the integrated flux is evaluated at the innermost stable circular orbit radius. Their tables give $P_{BZ} \simeq 4.134\times10^{36}\,\mathrm{erg\,s^{-1}}$ for $M=10\,M_\odot$, $B_0=10^7\,\mathrm{G}$, $a/M=0.97$, $\lambda=0.12$, compared with $4.080\times10^{36}\,\mathrm{erg\,s^{-1}}$ for the Kerr case with the same spin; in the sampled cases the maximum power sits near $a/M \approx 0.97$.

Load-bearing premise

The load-bearing premise is that the magnetic field inside the ergosphere has the specific assumed form, a poloidal field scaled linearly to zero at the throat plus a toroidal component tuned to keep the field magnitude uniform, because this field is never checked to satisfy Maxwell's equations or the force-free condition.

Editorial extensions

If this is right

  • Rotating wormholes could power relativistic jets at the same level as black holes: for $M=10\,M_\odot$ and $B_0=10^7\,\mathrm{G}$, the extracted Poynting flux reaches about $4\times10^{36}\,\mathrm{erg\,s^{-1}}$.
  • The mechanism requires very fast rotation, $a/M \ge 0.94281$, and a deformation small enough that the accretion disk's ISCO remains outside the throat while part of the disk is inside the ergosphere.
  • For fixed spin, increasing $\lambda$ at first leaves the flux near the Kerr value and then suppresses it sharply as the throat approaches the ISCO, because the assumed poloidal field vanishes at the throat.
  • Because the process needs only an ergosphere and not an event horizon, the same Poynting-flux formalism should apply to other rotating wormhole spacetimes with ergoregions.
  • The flux depends nonlinearly on $a$ and $\lambda$, so no universal statement about wormholes being more or less efficient than Kerr black holes follows; each choice of mass, spin, and deformation must be compared case by case.

Reading between the lines

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

  • A step the paper leaves open is solving the force-free stream equation in the same metric, which would show whether the assumed field is close to a self-consistent solution and whether the flux peak near $a/M\approx0.97$ survives.
  • If wormholes and black holes produce comparable Poynting flux, then jet power alone cannot certify the presence of an event horizon; distinguishing the two would require additional signatures such as lensing or photon echoes.
  • Because the flux scales roughly as $B_0^2$ but nonlinearly with $a$ and $\lambda$, a measured jet power together with an assumed field strength could in principle constrain the deformation parameter, though only on a case-by-case basis.
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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

4 major / 5 minor

Summary. The paper studies a rotating Damour-Solodukhin wormhole and asks whether an accreting magnetized environment can produce a Blandford-Znajek-type Poynting flux. The authors first analyze the null energy conditions at the throat, then restrict the spin and deformation parameters so that the ISCO lies inside the ergosphere, and finally propose a magnetic field model: outside the ergosurface a Wald-type uniform field is assumed, while inside the ergoregion the poloidal components are rescaled by a linear function y(r,θ) that vanishes at the throat, and a toroidal component is added so that the field magnitude is uniform, with its sign chosen to give positive extraction rates. Integrating the radial energy flux at the ISCO yields PBZ values of order 10^36 erg/s for a 10 solar mass object, e.g. about 4×10^36 erg/s for a=0.97, λ=0.12, which the paper claims is the same order as for a Kerr black hole. The paper concludes that rotating wormholes can emit Poynting flux by a mechanism analogous to Blandford-Znajek.

Significance. If the derivation were sound, the result would be a novel and interesting extension of the Blandford-Znajek mechanism to wormhole spacetimes, with possible astrophysical implications for jet production and for distinguishing wormholes from black holes. The paper is clearly written, carefully identifies the parameter range 0.94281 ≤ a < 1, and gives an explicit energy-condition analysis. It also honestly acknowledges in Section 5 that the results depend on the adopted magnetic field geometry. However, the central quantitative claim is not supported by a solution of the field equations: the field model is an ansatz whose sign and magnitude encode the desired outgoing flux, and it is not checked against Maxwell's equations, the force-free condition, or the stream equation. The reported values should therefore be regarded as consequences of the assumed geometry, not physical predictions of the wormhole spacetime.

major comments (4)
  1. [Section 3.1, Eqs. (49)-(51)] The interior magnetic field is prescribed, not derived. Multiplying the Wald poloidal components (41)-(42) by y(r,θ) = (r - r+)/(rS+(θ) - r+) and adding a toroidal component does not generically yield a closed two-form: because y depends on θ through rS+(θ), the poloidal field is not compatible with a single flux function Ψ(r,θ), and the homogeneous Maxwell equation ∇·B=0 (equivalently dF=0) is not verified anywhere in the text. Since the Poynting flux (53) is computed from these components, the numerical results in Tables 2-4 are not guaranteed to correspond to any electromagnetic field configuration.
  2. [Section 3.1, Eq. (51)] The sign in Eq. (51) is explicitly chosen to obtain positive rates of energy extraction. Because E^r in Eq. (53) is proportional to Br_new Bφ, this choice fixes the direction of the Poynting flux. The claim of 'outgoing' electromagnetic flux is therefore an input of the model rather than a consequence of the wormhole spacetime.
  3. [Section 4.2, Tables 2-4] The λ=0 (Kerr) cases in Tables 2-4 use the same ad hoc interior field prescription with r+ identified with the Kerr horizon, not the standard Blandford-Znajek solution of the stream equation. The statement in the abstract that the wormhole flux is 'of the same order as for a Kerr black hole' is therefore not established by a comparison with the actual Kerr Blandford-Znajek result.
  4. [Section 3, Eqs. (29)-(31), (38)] The proposed field is never checked against the force-free condition (30), the ideal MHD condition (31), or the stream equation (38). The paper states these equations but does not verify that the ansatz (49)-(51) satisfies them. Without such a check, the reported extraction rates are outputs of a postulated geometry, not predictions of the wormhole magnetosphere.
minor comments (5)
  1. [Throughout] There are several typographical inconsistencies: 'Blanford-Znajek' appears in the Section 3 heading and in the Conclusions, while the standard spelling is 'Blandford-Znajek'; 'Solodhukin' appears in Sections 1 and 5, whereas the metric is 'Damour-Solodukhin'; 'transversable' should be 'traversable'.
  2. [Sections 4.1 and 4.2] The notation for the limiting deformation parameter is inconsistent: Section 4.1 defines ˜λcrit, but Section 4.2 refers to 'the parameter ˆλ(a)'.
  3. [Figure 2 caption] The caption of Figure 2 says 'a 2 M⊙ wormhole' while the text states the analysis uses a 10 M⊙ wormhole; please reconcile this discrepancy.
  4. [Equation (54)] Equation (54) contains 'θinicial'; this should be 'θinitial'.
  5. [Appendix, Eqs. (66)-(67)] Equations (66)-(67) repeat Eqs. (41)-(42); consider referencing the earlier equations instead of duplicating them.

Circularity Check

1 steps flagged · score 6.0 of 10

The outgoing Poynting flux is built into the model: Eq. (51) fixes the sign of Bφ to give positive energy extraction, so the central 'capability' claim is an input, not a result.

  1. self definitional [Section 3.1, Eq. (51) and Eq. (53)]
    "Bϕ(r, θ) = − 1 rg q B(rS+ , θ)2 − y(r, θ)2 Br(r, θ)2 + r2gBθ(r, θ)2 , (51) where the choice of the sign is made in order to obtain positive rates of energy extraction."

    Equation (53) gives E^r = −c^2 ω B^r_new B^φ Δ sin^2 θ. The sign of Bφ is explicitly chosen to make energy extraction positive, so the existence of an outgoing Poynting flux is guaranteed by construction. The magnitude of Bφ is then fixed by an imposed uniform-|B| condition rather than by Maxwell or force-free equations. Consequently, the abstract's claim that rotating wormholes 'are capable of emitting a Poynting flux' is an input of the assumed field geometry, and the quoted PBZ values are outputs of that ansatz rather than independent consequences of the wormhole spacetime. The derivation chain therefore reduces, at this step, to defining the field so that the desired sign of the flux is obtained.

full rationale

The paper's calculation of PBZ is an evaluation of Eq. (54) on a prescribed magnetic-field ansatz (Eqs. 49–51). The decisive move is Eq. (51): after imposing a uniform |B| condition, the sign of Bφ is 'made in order to obtain positive rates of energy extraction.' Since Eq. (53) makes E^r proportional to B^r_new B^φ, the sign choice directly fixes the sign of the Poynting flux. Thus the abstract's claim that wormholes 'are capable of emitting a Poynting flux' is not derived from the Kerr-like wormhole geometry plus Maxwell/force-free equations; it is placed into the model by hand. The quoted magnitude (e.g., 4×10^36 erg/s) depends on the equally arbitrary uniform-|B| normalization and on the y-scaling of the Wald field, which is never checked to satisfy dF=0 or the stream equation. The paper is transparent about this dependence ('our results depend significantly on the geometry of the proposed magnetic field'), and there is no self-citation chain; nevertheless, the central 'first time' claim reduces by construction to the choice made for Bφ. A partial-circularity score of 6 is therefore appropriate: the non-circular remainder is the geometrical parameter study of where the ergosphere and ISCO conditions permit the ansatz to be applied.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the ad hoc magnetic field model inside the ergosphere, which is not validated against the field equations. The other inputs are standard in the Blandford-Znajek literature. The free parameters B0 and the rescaling function y are chosen by hand and directly control the output.

free parameters (2)
  • B0 = 10^7 G
    The assumed asymptotic magnetic field strength, chosen to represent a stellar-mass black hole accreting environment. The Poynting flux scales as B0^2, so all numerical output is proportional to this input.
  • y(r,theta) poloidal rescaling
    The linear interpolation (r - r+)/(rS+ - r+) is introduced ad hoc to make the poloidal field vanish at the throat and match the external field at the ergosphere. The amplitude and direction of the computed flux depend directly on this choice.
assumptions (5)
  • domain assumption The Damour-Solodukhin rotating wormhole metric (eq. 1) represents a physically admissible spacetime with an imperfect-fluid matter content.
    The entire calculation uses this metric; wormholes are hypothetical, and the matter content is only required to satisfy the field equations, with the null energy condition generally violated.
  • domain assumption The magnetosphere is force-free and ideal, with F_mu_nu J^nu = 0 and F*F = 0.
    Standard Blandford-Znajek assumptions; they break down where plasma inertia or resistivity is important.
  • ad hoc to paper Inside the ergosphere the magnetic field magnitude is uniform and equal to the external value at the ergosphere, with the poloidal component vanishing at the throat.
    This is the paper's model (eqs. 49-51) and is not derived from the stream equation or Maxwell's equations.
  • domain assumption The accretion disk is geometrically thin with its inner edge at the ISCO, and the ISCO radius is the same as for Kerr (independent of lambda).
    Standard thin-disk models [35-37]; the ISCO independence is cited to Karimov et al. [21].
  • domain assumption A uniform asymptotic magnetic field (Wald-type) is a valid external magnetosphere.
    Imported from Wald's solution [33]; the field is assumed to be generated by accretion disk currents.

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Pith. "Pith review of Outgoing electromagnetic flux from rotating wormholes." pith.science (2026). https://pith.science/paper/XDQYT4SL

@misc{pith2026241113474,
  author       = {Pith},
  title        = {Pith review of: Outgoing electromagnetic flux from rotating wormholes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XDQYT4SL}},
  note         = {Machine review of arXiv:2411.13474}
}
read the original abstract

We show for the first time that rotating wormholes are capable of emitting a Poynting flux in the process of accreting magnetized matter. To this end, we analyze the Damour-Solodukhin metric describing a Kerr-type wormhole and calculate the electromagnetic flux assuming a specific geometry for the magnetic field contained by the wormhole ergosphere. We find that for highly rotating wormholes a mechanism similar to that of Blandford and Znajek is possible, and the emitted electromagnetic flux is of the same order as for a Kerr black hole.

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.