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arxiv: 2606.08603 · v1 · pith:4ZDHFWC7new · submitted 2026-06-07 · ✦ hep-th · hep-ph

Self-Gravitating Magnetic Monopoles and Dyons in String-Inspired Models: Structure and Stability

Nick E. Mavromatos , Sarben Sarkar , Dionysios P. Theodosopoulos This is my paper

Pith reviewed 2026-06-27 18:05 UTC · model grok-4.3

classification ✦ hep-th hep-ph
keywords magnetic monopolesdyonsglobal monopolesdilatonKalb-Ramond axionBorn-Infeld electrodynamicsstring-inspired gravitylinear stability
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The pith

Magnetic monopoles and dyons induced by global monopoles exist as stable, particle-like solutions in string-inspired gravitational models.

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

The paper constructs classical solutions for self-gravitating magnetic monopoles and dyons that arise when a global monopole from O(3) symmetry breaking couples through a dilaton field to the electromagnetic sector in Born-Infeld theory. In a second scenario a Kalb-Ramond axion participates and enables dyonic solutions. These configurations possess well-defined cores, positive ADM mass and obey all standard energy conditions, with a minimum nonzero magnetic charge in the zero-mass limit. Mechanical criteria and linear perturbative analysis confirm stability in the exterior region, where dyons display birefringent helicity from axion mixing. A reader cares because the work supplies explicit, regular realizations of monopoles within a gravitational string-theory setting.

Core claim

In string-inspired models with gravity, magnetic monopoles arise from the coupling of a non-trivial massless dilaton field to the electromagnetic sector, while dyonic solutions emerge in the presence of a non-trivial Kalb-Ramond axion field and a massless dilaton coupling the KR and EM sectors. Both configurations originate from a global monopole associated with spontaneous breaking of a global O(3) symmetry. The electromagnetic sector is described by Born-Infeld electrodynamics, which ensures regularity at the core and finite self-energy. The resulting solutions are particle-like with a well-defined core and positive ADM mass, satisfy all standard energy conditions, exhibit a minimum nonzer

What carries the argument

The global monopole arising from spontaneous O(3) symmetry breaking, which induces the electromagnetic monopoles and dyons once the dilaton and Kalb-Ramond axion couplings are activated.

Load-bearing premise

The global monopole from spontaneous O(3) symmetry breaking induces the electromagnetic monopoles and dyons once the dilaton and Kalb-Ramond axion couplings are turned on.

What would settle it

A demonstration that the linear perturbation equations admit modes with imaginary frequencies in the exterior region would falsify the claimed linear stability.

Figures

Figures reproduced from arXiv: 2606.08603 by Dionysios P. Theodosopoulos, Nick E. Mavromatos, Sarben Sarkar.

Figure 1
Figure 1. Figure 1: FIG. 1. Dimensionless de Sitter core radius [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Dimensionless monopole mass [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Left: Ratio of the [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Numerical solutions of the equations of motion. Top-left: Higgs function. Top-right: Dilaton field (numerical solution [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Mass function [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Energy conditions for the numerical magnetic monopole solution with a dilaton charge (Sec. III), shown as functions [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Dimensionless total SR radial (left) and polar (right) forces as functions of the dimensionless radius [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
read the original abstract

We present classical solutions for magnetic monopoles and dyons induced by global monopoles for string-inspired models, in the presence of gravity. Two distinct scenarios are analyzed. In the first, magnetic monopoles arise from the coupling of a non-trivial massless dilaton field to the electromagnetic (EM) sector. In the second, dyonic solutions emerge in the presence of a non-trivial Kalb-Ramond (KR) axion field and a massless dilaton field, which couples the KR and EM sectors. In both models, the monopole and dyon configurations originate from a global monopole associated with the spontaneous breaking of a global O(3) symmetry. The EM sector is described by Born-Infeld electrodynamics, ensuring regularity of the fields at the core of the monopole and a finite self-energy. The resulting solutions represent particle-like configurations with a well-defined core and positive ADM (Arnowitt-Deser-Misner) mass, and are shown to satisfy all standard energy conditions. We also demonstrate the existence of a minimum nonzero magnetic charge in the limiting case of a magnetic monopole with vanishing mass. We also discuss stability criteria for our magnetic-monopole and dyon solutions. We first demonstrate that the mechanical-stability criteria for these solutions are satisified. These require the finiteness of the total force components and also the outward-pointing nature of the radial component, which indicates the avoidance of collapse. Next we analyse the dynamical (linear perturbative) stability of the self-gravitating Born-Infeld monopole and dyon solutions within Einstein-Born--Infeld-dilaton-axion theory in the Gervalle-Volkov framework, and demonstrate that both monopole and dyonic configurations are linearly stable against electromagnetic perturbations in the exterior region, with dyons exhibiting a birefringent helicity structure due to axion-induced mixing.

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 paper constructs classical solutions for self-gravitating magnetic monopoles (via dilaton-EM coupling) and dyons (via dilaton-KR axion-EM coupling) in Einstein-Born-Infeld theory, induced by a global O(3) monopole from spontaneous symmetry breaking. It claims these yield particle-like configurations with finite core, positive ADM mass, satisfaction of all standard energy conditions, a nonzero minimum magnetic charge in the massless limit, mechanical stability (finite outward radial force), and linear stability against EM perturbations in the exterior (with birefringent helicity for dyons due to axion mixing).

Significance. If the solutions are obtained from the fully coupled Euler-Lagrange equations of the string-inspired model (including backreaction on the global monopole sector) and the stability analysis is complete, the work would supply concrete examples of regular, stable monopoles/dyons with nonlinear electrodynamics and axion/dilaton couplings, potentially relevant for understanding non-perturbative objects in low-energy string theory.

major comments (2)
  1. [Abstract] Abstract and the description of the two scenarios: the statement that 'the monopole and dyon configurations originate from a global monopole associated with the spontaneous breaking of a global O(3) symmetry' and that 'the field equations are solved' leaves unclear whether the O(3) scalar triplet is treated as a fixed hedgehog background (no backreaction from dilaton, KR axion, or BI sector) or solved dynamically as part of the complete system. This distinction is load-bearing for the central claim that the configurations are self-consistent solutions of the string-inspired model with positive ADM mass and energy-condition compliance.
  2. [Abstract (stability discussion)] The mechanical-stability and linear-stability claims rest on the solutions satisfying the full set of field equations; if the O(3) sector is not dynamical, the force-balance and perturbation analysis cannot be taken as evidence for stability within the model under consideration.
minor comments (1)
  1. [Abstract] The abstract contains repetitive phrasing ('We also demonstrate... We also discuss...') that could be streamlined for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments. We address the concerns regarding potential ambiguity in the treatment of the O(3) scalar triplet and the implications for stability below. We believe the solutions are obtained from the fully coupled system, but agree that the abstract requires clarification for precision.

read point-by-point responses

  1. Referee: [Abstract] Abstract and the description of the two scenarios: the statement that 'the monopole and dyon configurations originate from a global monopole associated with the spontaneous breaking of a global O(3) symmetry' and that 'the field equations are solved' leaves unclear whether the O(3) scalar triplet is treated as a fixed hedgehog background (no backreaction from dilaton, KR axion, or BI sector) or solved dynamically as part of the complete system. This distinction is load-bearing for the central claim that the configurations are self-consistent solutions of the string-inspired model with positive ADM mass and energy-condition compliance.

    Authors: We agree that the abstract phrasing could be interpreted ambiguously. In the manuscript, the O(3) scalar triplet is treated dynamically: the full set of Euler-Lagrange equations for the Einstein-Born-Infeld-dilaton-axion system (including the global monopole sector) are solved numerically with backreaction from the dilaton, KR axion, and BI fields included. The resulting configurations are therefore self-consistent solutions of the complete model, yielding positive ADM mass and compliance with energy conditions. We will revise the abstract to state explicitly that the O(3) sector is solved as part of the coupled system. revision: yes

  2. Referee: [Abstract (stability discussion)] The mechanical-stability and linear-stability claims rest on the solutions satisfying the full set of field equations; if the O(3) sector is not dynamical, the force-balance and perturbation analysis cannot be taken as evidence for stability within the model under consideration.

    Authors: Because the O(3) scalar triplet is dynamical and the solutions satisfy the complete coupled field equations (as clarified above), the mechanical stability criteria (finite total force with outward radial component) and the linear perturbative stability analysis in the Gervalle-Volkov framework are performed within the full model. The birefringent helicity for dyons arises from axion mixing in the exterior region. We will update the abstract's stability discussion to reference the dynamical treatment of all sectors. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results are outputs of field-equation solutions

full rationale

The derivation proceeds by solving the coupled Einstein-Born-Infeld-dilaton-axion equations in two scenarios, with the global O(3) monopole providing the inducing background. ADM mass, energy conditions, minimum charge, and linear stability (via Gervalle-Volkov) are computed outputs, not inputs by construction. No self-definitional reduction, no fitted parameter renamed as prediction, and no load-bearing self-citation chain that collapses the central claim. The induction step is an explicit modeling choice stated in the abstract, not a hidden tautology. This is the normal non-circular case for a numerical/analytic solution paper.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard assumptions of general relativity and string-inspired effective field theory together with the specific choice of Born-Infeld electrodynamics and the O(3) global symmetry breaking; no new free parameters are introduced beyond the usual coupling constants of the model.

free parameters (1)
  • magnetic charge parameter
    The magnetic charge appears as a free parameter in the solutions, with a derived minimum nonzero value when the ADM mass vanishes.
axioms (2)
  • domain assumption Spontaneous breaking of global O(3) symmetry produces a global monopole that sources the electromagnetic fields once dilaton and axion couplings are present.
    Invoked in the abstract to generate the monopole and dyon configurations.
  • domain assumption Born-Infeld electrodynamics renders the core fields regular and the self-energy finite.
    Stated as the reason for choosing Born-Infeld over Maxwell theory.

pith-pipeline@v0.9.1-grok · 5885 in / 1660 out tokens · 29659 ms · 2026-06-27T18:05:58.020795+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

76 extracted references · 1 canonical work pages

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    III, we check whether they satisfy standard energy conditions

    Energy conditions and mechanical stability for Magnetic Monopoles To examine the physical consistency of the magnetic monopole solutions obtained in Sec. III, we check whether they satisfy standard energy conditions. In Fig. 6, the quantitiesρ E,ρ E +p R,ρ E +p θ, andρ E +p R + 2pθ are plotted as functions of the dimensionless radius ˜R, using the numeric...

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    We give explicit expressions for the energy–momentum components, verify the standard energy conditions, and check local force balance and shell stresses

    Energy conditions and mechanical stability for Dyons This subsection extends the purely magnetic analysis of Section V A to the dyonic solutions discussed in Section IV. We give explicit expressions for the energy–momentum components, verify the standard energy conditions, and check local force balance and shell stresses. For the exterior dyonic backgroun...

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    Magnetic monopole: decoupled helicities and positive potential For the purely magnetic monopole the only non-zero background field-strength component is ¯Fθφ =Q m sinθ, so the pseudoscalar invariant vanishes identically on the background: ¯Y= ¯Fµν ˜¯F µν = 0. 22 Since the off-diagonal termW(r) in (5.31) originates from theY-dependent part ofχ µν ρσ, it va...

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    Dyon: helicity mixing and the2×2Sturm–Liouville problem For the dyonic background (4.8), both electric and magnetic fields are present and the pseudoscalar invariant ¯Y= ¯Fµν ˜¯F µν is non-vanishing: ¯Y∝ Qm Qeff e (r) R4(r) ̸= 0.(5.40) The constitutive tensorχ µν ρσ therefore acquires an off-diagonal structure in the helicity basis: the term∂2L/∂Fµν∂Fρσ e...

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    Energy conditions With the explicit form (B1) in hand, it is straightforward to verify that the monopole field satisfies the standard energy conditions of general relativity throughout the exterior regionR≥R core. One checks in turn that ρ(m) E >0, ρ (m) E +p (m) R >0, ρ (m) E +p (m) R + 2p(m) θ >0, 28 so the null, weak, and strong energy conditions are a...

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