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arxiv: 2601.17864 · v2 · pith:VREFDRWLnew · submitted 2026-01-25 · 🌀 gr-qc · hep-ph· hep-th

Generation of gravitating solutions with Baryonic charge from Einstein-Scalar-Maxwell seeds

Fabrizio Canfora , Anibal Neira , Seung Hun Oh This is my paper

Pith reviewed 2026-05-16 11:07 UTC · model grok-4.3

classification 🌀 gr-qc hep-phhep-th
keywords Skyrme modelEinstein-scalar-Maxwellbaryonic chargeexact solutionssolution generationKerr-Newmangauged Skyrmegeneral relativity
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The pith

An exact correspondence maps Einstein-scalar-Maxwell solutions onto gauged Skyrme-Maxwell-Einstein spacetimes carrying baryonic charge.

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

The authors construct a simple ansatz in the gauged Skyrme-Maxwell-Einstein theory that reduces its equations exactly to those of Einstein-scalar-Maxwell theory. This equivalence lets them import known solution-generating methods from the simpler electrovacuum systems, which already include scalar fields, directly into the Skyrme setting. The resulting solutions automatically carry nonzero baryonic charge as long as the hadronic profile varies along the magnetic field lines. They demonstrate the method by dressing a rotating Kerr-Newman spacetime with a scalar field and mapping it to a Skyrme configuration where the baryonic charge quantizes the rotation parameter. This approach provides a systematic way to find exact gravitating solutions with topological charge in general relativity.

Core claim

We establish an exact correspondence between Einstein-scalar-Maxwell theory and gauged Skyrme-Maxwell-Einstein models by means of a specific ansatz in the latter. Under this ansatz, the Skyrme field equations are satisfied identically, and the system reduces to the Einstein-scalar-Maxwell equations. The correspondence preserves the gravitational and Maxwell sectors while the Skyrme profile contributes a baryonic charge that is nonzero whenever its derivative along the magnetic lines does not vanish. Applying this dictionary to a Kerr-Newman-like solution with scalar hair yields a Skyrme solution in which the quantization condition on the baryonic charge enforces quantization of the Kerr rot

What carries the argument

The simplest consistent ansatz for the gauged Skyrme field in the Maxwell-Einstein framework that enforces the exact reduction to Einstein-scalar-Maxwell equations.

Load-bearing premise

The construction assumes that a consistent ansatz exists in the gauged Skyrme model such that the full nonlinear equations reduce precisely to the Einstein-scalar-Maxwell system while maintaining a nonvanishing baryonic charge.

What would settle it

A counterexample would be a seed solution from Einstein-scalar-Maxwell theory whose image under the proposed mapping fails to satisfy the Skyrme field equation for some nonzero derivative of the hadronic profile.

Figures

Figures reproduced from arXiv: 2601.17864 by Anibal Neira, Fabrizio Canfora, Seung Hun Oh.

Figure 1
Figure 1. Figure 1: FIG. 1: spatial distribution of the topological charge [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Discrete spectrum of the specific angular [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
read the original abstract

We establish, for the first time, an exact correspondence between Einstein-scalar-Maxwell theory and gauged Skyrme-Maxwell-Einstein models in (3+1) dimensions. By constructing the simplest consistent ansatz within the gauged Skyrme-Maxwell framework, we reveal a remarkable equivalence in a sector that admits nonvanishing, highly magnetized baryonic charge. This correspondence has a particularly appealing consequence: it transfers the full power of solution-generating techniques developed for electrovacuum systems-many of which naturally accommodate scalar fields to the considerably more intricate setting of gauged Skyrme-Maxwell theory minimally coupled to General Relativity. As a result, it opens the door to a systematic and much broader exploration of exact solutions in Skyrme-Maxwell-Einstein theory and of their potential applications in cosmology and astrophysics. Notably, the resulting configurations carry nonzero baryonic charge whenever the derivative of the hadronic profile along the magnetic field lines does not vanish. As an illustrative example, we apply this new dictionary to a rotating Kerr-Newman-like spacetime dressed with a scalar field. In the corresponding Skyrme-Maxwell-Einstein solution, the quantization of the baryonic charge enforces a quantization of the Kerr rotation parameter. We derive an upper bound on the baryonic charge in terms of the integration constants of the solution and show that, in the regime of small baryonic charge, the rotation parameter depends linearly on the baryonic charge.

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 paper claims to establish, for the first time, an exact correspondence between Einstein-scalar-Maxwell theory and gauged Skyrme-Maxwell-Einstein models in (3+1) dimensions. This is achieved by positing a specific ansatz for the Skyrme field and gauge potential that reduces the Skyrme term to an effective scalar-Maxwell system while preserving the Einstein equations. The correspondence is used to generate solutions carrying nonzero baryonic charge from seed solutions in the simpler theory, with an illustrative example based on a rotating Kerr-Newman-like spacetime dressed with a scalar field. In this example, quantization of the baryonic charge enforces quantization of the Kerr rotation parameter, and an upper bound on the baryonic charge is derived in terms of the integration constants.

Significance. If the ansatz is shown to be fully consistent with the complete gauged Skyrme equations for arbitrary seeds, the result would be significant: it would transfer the extensive solution-generating machinery developed for electrovacuum and scalar-Maxwell systems directly to the gauged Skyrme setting, enabling systematic construction of exact gravitating solutions with baryonic charge. The example further illustrates a concrete link between baryonic charge quantization and spacetime parameters, which could have implications for astrophysical and cosmological models.

major comments (2)
  1. [ansatz construction and verification] The central claim of an 'exact correspondence' (abstract and introduction) rests on the ansatz being on-shell for the full gauged Skyrme-Maxwell-Einstein system whenever the seed satisfies the Einstein-scalar-Maxwell equations. The manuscript must explicitly substitute the ansatz into every component of the gauged Skyrme equations and demonstrate that all nonlinear residual terms cancel identically, without imposing extra constraints on the seed. The abstract describes the ansatz as the 'simplest consistent' one but does not exhibit this component-by-component verification; this step is load-bearing for the claimed equivalence between the two theories.
  2. [illustrative example] In the illustrative example (Kerr-Newman-like seed), the statement that 'quantization of the baryonic charge enforces a quantization of the Kerr rotation parameter' requires a clear derivation showing how the topological baryon number integral reduces to a condition on the rotation parameter a. The upper bound on baryonic charge in terms of integration constants must also be derived explicitly from the ansatz, including the regime where the rotation parameter depends linearly on the baryonic charge.
minor comments (2)
  1. [ansatz construction] Clarify the precise form of the ansatz (field profiles and gauge potential) in a dedicated subsection so that readers can reproduce the reduction without ambiguity.
  2. [illustrative example] The abstract states that baryonic charge is nonzero 'whenever the derivative of the hadronic profile along the magnetic field lines does not vanish'; this condition should be stated explicitly in terms of the ansatz functions when the example is presented.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive comments. We address each major point below and will revise the manuscript to incorporate the requested clarifications and derivations.

read point-by-point responses

  1. Referee: [ansatz construction and verification] The central claim of an 'exact correspondence' (abstract and introduction) rests on the ansatz being on-shell for the full gauged Skyrme-Maxwell-Einstein system whenever the seed satisfies the Einstein-scalar-Maxwell equations. The manuscript must explicitly substitute the ansatz into every component of the gauged Skyrme equations and demonstrate that all nonlinear residual terms cancel identically, without imposing extra constraints on the seed. The abstract describes the ansatz as the 'simplest consistent' one but does not exhibit this component-by-component verification; this step is load-bearing for the claimed equivalence between the two theories.

    Authors: We agree that an explicit component-by-component verification is necessary to fully substantiate the on-shell equivalence. In the revised manuscript we will add a dedicated subsection (or appendix) that substitutes the ansatz into each component of the gauged Skyrme equations. We will demonstrate that all nonlinear residual terms cancel identically once the seed satisfies the Einstein-scalar-Maxwell system, without imposing further constraints on the seed. This will confirm that the ansatz is consistent with the complete gauged Skyrme-Maxwell-Einstein equations. revision: yes

  2. Referee: [illustrative example] In the illustrative example (Kerr-Newman-like seed), the statement that 'quantization of the baryonic charge enforces a quantization of the Kerr rotation parameter' requires a clear derivation showing how the topological baryon number integral reduces to a condition on the rotation parameter a. The upper bound on baryonic charge in terms of integration constants must also be derived explicitly from the ansatz, including the regime where the rotation parameter depends linearly on the baryonic charge.

    Authors: We will expand the illustrative example section to provide a transparent, step-by-step derivation of the baryon number integral. We will show explicitly how the topological integral reduces to a quantization condition on the rotation parameter a. We will also derive the upper bound on the baryonic charge directly from the ansatz and discuss the linear dependence of a on the baryonic charge in the small-charge regime. revision: yes

Circularity Check

0 steps flagged

No circularity: correspondence derived from explicit ansatz construction independent of inputs

full rationale

The paper's central claim is an exact correspondence obtained by constructing a specific ansatz in the gauged Skyrme-Maxwell-Einstein framework that reduces the equations to those of Einstein-scalar-Maxwell theory while preserving nonzero baryonic charge. This is a direct mapping via ansatz choice rather than any self-definitional loop, fitted parameter renamed as prediction, or load-bearing self-citation. No uniqueness theorem from prior author work is invoked to force the result, and the abstract presents the ansatz as constructed and consistent within the paper itself. The derivation chain therefore remains self-contained against external benchmarks with no reduction of outputs to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based on the abstract, the central claim rests on the validity of the constructed ansatz and the existence of the specified sector. No free parameters or invented entities are explicitly mentioned.

axioms (2)
  • domain assumption Existence of a consistent ansatz in the gauged Skyrme-Maxwell framework that reveals equivalence
    The abstract relies on constructing the simplest consistent ansatz to establish the correspondence.
  • domain assumption The sector admits nonvanishing, highly magnetized baryonic charge
    The equivalence is revealed in a sector that admits such charge, as stated in the abstract.

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Forward citations

Cited by 1 Pith paper

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