arxiv: 2605.01602 · v1 · submitted 2026-05-02 · 🌀 gr-qc · hep-th

Recognition: unknown

Dyonic Ellis-Bronnikov wormholes from warped extra dimensions

Francisco S. N. Lobo , Miguel A. S. Pinto , Manuel E. Rodrigues

Authors on Pith no claims yet

Pith reviewed 2026-05-09 17:45 UTC · model grok-4.3

classification 🌀 gr-qc hep-th

keywords traversable wormholesEllis-Bronnikov wormholeKaluza-Klein reductionhigher-dimensional gravitydyonic fieldsphantom dilatonscalar-tensor theoryChern-Simons action

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The pith

Regular asymptotically flat traversable wormholes in four dimensions arise from a five-dimensional Einstein-Maxwell-Chern-Simons theory via warped compactification.

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

The paper derives an effective four-dimensional Einstein-frame theory by applying warped Kaluza-Klein reduction to a five-dimensional action containing the Einstein-Maxwell-Chern-Simons term and a non-minimally coupled scalar. This reduction produces a phantom dilaton, a canonical axion, a Maxwell field, and a Kaluza-Klein vector whose couplings are fixed by the higher-dimensional origin. The authors then solve the field equations for the Ellis-Bronnikov wormhole metric, obtaining analytic expressions for dyonic configurations of both vector fields together with the required scalar kinetic term and potentials. Solutions range from purely phantom-supported cases to fully coupled dilaton-axion-gauge setups while remaining regular and asymptotically flat. The construction shows that such wormholes emerge directly from the dimensional reduction without extra ad-hoc ingredients.

Core claim

By performing a warped Kaluza-Klein compactification on the five-dimensional Einstein-Maxwell-Chern-Simons action with non-minimally coupled scalar, we obtain an effective four-dimensional theory whose Einstein equations admit regular, asymptotically flat traversable Ellis-Bronnikov wormhole solutions. For exponential gauge couplings the metric fixes the scalar kinetic term and the sum of the potentials, while the remaining equations reduce to algebraic relations that determine the individual potentials and the radial profiles of the dyonic charges. The resulting family of solutions includes both the pure phantom case and configurations in which the Kaluza-Klein vector participates, all of 1

What carries the argument

The warped Kaluza-Klein reduction of the five-dimensional Einstein-Maxwell-Chern-Simons action with non-minimally coupled scalar, which fixes the couplings of the effective four-dimensional phantom dilaton, canonical axion, Maxwell field, and Kaluza-Klein vector that support the Ellis-Bronnikov metric.

If this is right

The Ellis-Bronnikov geometry remains regular and traversable when supported by the combined phantom dilaton and dyonic vector fields.
The Kaluza-Klein vector enriches the solution space with additional analytic configurations while preserving asymptotic flatness.
A continuous classification exists from the pure phantom-supported wormhole to fully coupled dilaton-axion-gauge cases.
The radial dependence of the electric charges is fixed algebraically once the metric and exponential gauge couplings are chosen.

Where Pith is reading between the lines

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

The same reduction technique could be applied to other traversable wormhole metrics to generate new analytic solutions.
Perturbations around these dyonic solutions would test whether the higher-dimensional origin affects linear stability.
Signatures of the extra Kaluza-Klein charge might appear in the lensing or accretion properties of the wormhole throat.

Load-bearing premise

The effective four-dimensional field content and couplings produced by the warped reduction can be made to satisfy the Einstein equations for the Ellis-Bronnikov metric without introducing singularities or energy-condition violations.

What would settle it

An explicit check that the stress-energy tensor of the reduced scalar-vector fields fails to satisfy the null energy condition at the wormhole throat while keeping the metric regular and asymptotically flat.

Figures

Figures reproduced from arXiv: 2605.01602 by Francisco S. N. Lobo, Manuel E. Rodrigues, Miguel A. S. Pinto.

**Figure 1.** Figure 1: FIG. 1. Dilaton field Ψ as a function of the adimensional view at source ↗

read the original abstract

We investigate traversable wormhole solutions within a four-dimensional effective theory derived from a five-dimensional Einstein-Maxwell-Chern-Simons action with a non-minimally coupled scalar field. A warped Kaluza-Klein compactification yields an Einstein-frame theory containing a phantom dilaton, a canonical axion, a Maxwell field, and a Kaluza-Klein vector, with the couplings fixed by the higher-dimensional origin. Focusing on the Ellis-Bronnikov geometry, we construct solutions that incorporate both dyonic Maxwell and Kaluza-Klein fields. For exponential gauge couplings, the Einstein equations determine the scalar kinetic term and the combined potentials, while the remaining field equations reduce to algebraic relations fixing the individual potentials and the radial behaviour of the electric charges. We obtain a systematic classification of configurations, ranging from the pure phantom-supported wormhole to fully coupled dilaton-axion-gauge configurations. The Kaluza-Klein sector enriches the solution space with additional structure while preserving analytic tractability. These results show that regular, asymptotically flat traversable four-dimensional wormholes arise naturally from higher-dimensional scalar-tensor theories.

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

The paper builds analytic dyonic Ellis-Bronnikov wormholes in a 4D effective theory from a 5D Einstein-Maxwell-Chern-Simons reduction, with a clean classification of solutions but no escape from the usual exotic-matter requirement.

read the letter

These authors construct a set of analytic dyonic Ellis-Bronnikov wormhole solutions in an effective four-dimensional theory obtained from a warped reduction of five-dimensional Einstein-Maxwell-Chern-Simons gravity with a non-minimal scalar. The reduction produces a phantom dilaton, axion, Maxwell field, and Kaluza-Klein vector with specific couplings. What stands out is how they handle the field equations. By assuming the Ellis-Bronnikov geometry and exponential gauge couplings, the Einstein equations determine the scalar kinetic term and combined potentials, while other equations become algebraic constraints on the individual potentials and the radial dependence of the electric charges. They provide a systematic classification covering pure phantom cases up to fully coupled configurations involving the dilaton, axion, and both gauge fields. The Kaluza-Klein vector adds more options while keeping everything analytic and the spacetime regular and flat at infinity. The approach works because the phantom dilaton violates the null energy condition as needed, and the higher-dimensional origin sets the couplings without introducing extra singularities. That part looks clean. On the downside, this is still a standard wormhole construction where exotic matter is required, and the paper does not address stability or any dynamical aspects. The 'natural' emergence is relative to the assumed metric and the chosen reduction; it's not that wormholes pop out without assumptions. The evidence for the effective theory is the reduction itself, which seems standard but would benefit from explicit checks in the full text. This kind of work is useful for people building catalogs of exact solutions in scalar-tensor or higher-D theories. A reader focused on wormholes or Kaluza-Klein compactifications could use the classification. It is worth sending to peer review since the solutions are new in this setting and the math appears consistent.

Referee Report

2 major / 1 minor

Summary. The paper derives an effective 4D Einstein-frame action from a 5D Einstein-Maxwell-Chern-Simons theory with non-minimally coupled scalar via warped Kaluza-Klein reduction, producing a phantom dilaton, canonical axion, Maxwell field and Kaluza-Klein vector with couplings fixed by the reduction. Assuming the Ellis-Bronnikov metric, it constructs dyonic solutions for exponential gauge couplings by reducing the Einstein equations to algebraic constraints on potentials and charge profiles, yielding regular asymptotically flat traversable wormholes in configurations ranging from pure-phantom to fully coupled dilaton-axion-gauge cases.

Significance. If the reduction is fully verified and the solutions satisfy the complete set of 4D equations, the work provides a higher-dimensional origin for phantom-supported wormholes, with the Kaluza-Klein sector enriching the solution space while preserving analytic tractability. The systematic classification and explicit construction of regular solutions constitute a concrete advance in embedding wormhole geometries in scalar-tensor theories descending from higher dimensions.

major comments (2)

[Derivation of the effective 4D action] The reduction from the 5D Einstein-Maxwell-Chern-Simons action to the 4D effective theory is central to the claim that the solutions are consistent, yet the manuscript provides only an outline without explicit computation showing that all components of the reduced Einstein tensor match the stress-energy tensor contributions from the phantom dilaton, axion, Maxwell and KK vector fields. This verification is required to confirm that the Ellis-Bronnikov ansatz satisfies the full Einstein equations in the derived theory.
[Solution construction and classification] In the solution construction for exponential couplings, the Einstein equations are stated to fix the scalar kinetic term and combined potentials while the remaining equations reduce to algebraic relations; however, it is not shown that every independent component of the Einstein tensor (including off-diagonal or angular components) is satisfied by the chosen charge profiles and potentials, which is load-bearing for the regularity and asymptotic flatness claims.

minor comments (1)

[Abstract and introduction] The abstract and introduction would benefit from a brief statement of the precise 5D action (including the form of the non-minimal scalar coupling and Chern-Simons term) to allow readers to reproduce the reduction steps without external references.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The points raised help clarify the presentation of the Kaluza-Klein reduction and the verification of the field equations. We respond to each major comment below and will revise the manuscript to incorporate the requested explicit verifications.

read point-by-point responses

Referee: [Derivation of the effective 4D action] The reduction from the 5D Einstein-Maxwell-Chern-Simons action to the 4D effective theory is central to the claim that the solutions are consistent, yet the manuscript provides only an outline without explicit computation showing that all components of the reduced Einstein tensor match the stress-energy tensor contributions from the phantom dilaton, axion, Maxwell and KK vector fields. This verification is required to confirm that the Ellis-Bronnikov ansatz satisfies the full Einstein equations in the derived theory.

Authors: We agree that an explicit component-by-component verification strengthens the consistency claim. Section 2 of the manuscript outlines the warped reduction and states the resulting 4D Einstein-frame action with the phantom dilaton, canonical axion, Maxwell field, and Kaluza-Klein vector, together with the couplings fixed by the higher-dimensional theory. To address the referee's concern directly, the revised manuscript will include a new appendix that computes the reduced Einstein tensor explicitly from the 5D action and demonstrates its equality with the stress-energy tensor of the four fields for the Ellis-Bronnikov ansatz. This will confirm that all components are satisfied. revision: yes
Referee: [Solution construction and classification] In the solution construction for exponential couplings, the Einstein equations are stated to fix the scalar kinetic term and combined potentials while the remaining equations reduce to algebraic relations; however, it is not shown that every independent component of the Einstein tensor (including off-diagonal or angular components) is satisfied by the chosen charge profiles and potentials, which is load-bearing for the regularity and asymptotic flatness claims.

Authors: We acknowledge that the manuscript focuses on the determining equations and the resulting algebraic constraints without separately displaying every component. The static, spherically symmetric ansatz ensures that off-diagonal components vanish identically, while the angular components are satisfied by the radial profiles obtained from the algebraic relations. In the revised version we will add an explicit verification subsection (or appendix) that lists all independent Einstein-tensor components and shows they are satisfied by the chosen potentials and charge functions. This will make the regularity and asymptotic-flatness arguments fully transparent. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper begins with an explicit 5D Einstein-Maxwell-Chern-Simons action containing a non-minimally coupled scalar, performs a warped Kaluza-Klein reduction to obtain a specific 4D Einstein-frame action with phantom dilaton, canonical axion, Maxwell field and Kaluza-Klein vector (couplings fixed by the reduction), then adopts the Ellis-Bronnikov line element as an ansatz and solves the resulting system of equations. The Einstein equations determine the scalar kinetic term and combined potentials for chosen exponential gauge couplings; the remaining equations reduce to algebraic constraints on individual potentials and charge profiles. Explicit analytic solutions are constructed. This is a standard constructive procedure: the 5D starting point and metric ansatz are independent inputs, the reduction is a direct calculation, and the solutions are outputs of the 4D equations rather than redefinitions of the inputs. No load-bearing self-citation, no fitted parameter renamed as prediction, and no self-definitional loop appear in the chain. The result is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the validity of the five-dimensional starting action and the warped reduction ansatz; no free parameters are fitted to data because the work is purely analytic, but the phantom character of the dilaton is an output of the reduction rather than an independent postulate.

axioms (2)

domain assumption The five-dimensional Einstein-Maxwell-Chern-Simons action with non-minimally coupled scalar field is the correct higher-dimensional theory.
Invoked in the first sentence of the abstract as the origin of the four-dimensional effective theory.
domain assumption The warped Kaluza-Klein compactification ansatz yields a consistent four-dimensional Einstein-frame theory without additional constraints.
Stated as the mechanism that produces the phantom dilaton, axion, Maxwell, and Kaluza-Klein vector.

invented entities (1)

phantom dilaton no independent evidence
purpose: Provides the negative kinetic energy needed to support the wormhole throat.
Emerges automatically from the reduction; its negative sign is required for the Ellis-Bronnikov geometry to satisfy the Einstein equations.

pith-pipeline@v0.9.0 · 5500 in / 1654 out tokens · 66586 ms · 2026-05-09T17:45:27.777776+00:00 · methodology

discussion (0)

Reference graph

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We adopt a warped Kaluza–Klein ansatz for the five-dimensional metric, ds2 (5) =e 2αΦ˜gµνdxµdxν +e 2βΦ dw+κA µdxµ 2 ,(A2) wherew∈[0, L) parametrises the compact direction

W arped Kaluza–Klein ansatz and dimensional reduction To extract the four-dimensional effective theory, we compactify the fifth dimension on a circle of circumfer- enceL. We adopt a warped Kaluza–Klein ansatz for the five-dimensional metric, ds2 (5) =e 2αΦ˜gµνdxµdxν +e 2βΦ dw+κA µdxµ 2 ,(A2) wherew∈[0, L) parametrises the compact direction. The constantsα...
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W eyl rescaling to the Einstein frame To remove the field-dependent gravitational cou- pling ˜f(Φ) and bring the action to the canonical Ein- stein–Hilbert form, we perform a Weyl rescaling of the metric, ˜gµν = Ω2gµν,Ω 2 = ˜f(Φ) −1 = 1 L e2αΦ(1−ξΦ 2) .(A7) Under this transformation, the Ricci scalar transforms as ˜R= Ω −2 h R−6g µν∇µ∇ν ln Ω−6g µν(∂µ ln Ω...
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F our-dimensional Einstein-frame action Putting everything together, the four-dimensional ef- fective action in the Einstein frame reads S(4) = Z d4x√−g h 1 2 R+ 1 2(∂Ψ)2 − 1 2(∂φ)2 − 1 4 B(Ψ)FµνF µν − 1 4 C(Ψ)FµνF µν −V(Ψ)− U(φ) i − λL 16 Z φ F∧F .(A12) The field-dependent couplings are inherited from the compactification: B(Ψ) =L e βΦ(Ψ),(A13) C(Ψ) = Lκ...