arxiv: 2604.23741 · v1 · submitted 2026-04-26 · 🌀 gr-qc

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On gravitating dyonic configurations in nonlinear electrodynamics

K.A. Bronnikov , S.V. Bolokhov , G.S. Nurbakova , B. Tynyshbay

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Pith reviewed 2026-05-08 05:43 UTC · model grok-4.3

classification 🌀 gr-qc

keywords nonlinear electrodynamicsdyonic configurationsgeneral relativityextended gravityelectromagnetic invariant fMaxwell limitspherically symmetric solutions

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The pith

Dyonic nonlinear electromagnetic fields with equal charges always allow a configuration where the invariant f vanishes everywhere, assuming the Maxwell limit.

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

The paper examines static spherically symmetric dyonic solutions of nonlinear electrodynamics with Lagrangian L(f) in general relativity and other metric gravity theories. It shows that when the electric and magnetic charges are equal in magnitude and L(f) recovers the Maxwell Lagrangian at weak fields, there always exists an electromagnetic field configuration making the invariant f identically zero throughout space. This condition removes the usual complications from the nonlinear electromagnetic stress-energy tensor, so the field equations reduce to simpler forms that admit exact solutions. The result applies directly when other gravitational sources such as fluids or scalars are present and extends to scalar-tensor and F(R) theories, where the nonlinear electromagnetic sector can be treated without solving the full nonlinear equations for f.

Core claim

Assuming a correct Maxwell limit of L(f), there always exists a configuration of the electromagnetic field with equal electric and magnetic charges such that the invariant f is zero in the whole space. This leads to the existence of the corresponding families of solutions both in GR in the presence of other sources of gravity and in a wide range of extended theories of gravity, in which the nonlinear electromagnetic field behaves in an especially simple manner.

What carries the argument

The dyonic electromagnetic configuration with equal electric and magnetic charges that forces the invariant f = F_mu nu F^mu nu to be identically zero.

If this is right

Exact solutions for gravitating dyonic fields exist in general relativity when other sources like fluids or scalar fields are present.
Families of solutions appear in scalar-tensor theories of gravity.
Solutions are available in F(R) gravity models.
The nonlinear electromagnetic field can be incorporated without solving the full nonlinear equations for f.

Where Pith is reading between the lines

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

The zero-f condition may simplify the construction of exact solutions for charged compact objects across a wider set of modified gravity models than those explicitly named.
Similar reductions could be explored in non-spherically symmetric or time-dependent settings, though separate analysis would be needed.

Load-bearing premise

The nonlinear Lagrangian L(f) must recover the Maxwell theory in the weak-field limit, and the electric and magnetic charges must be equal in magnitude.

What would settle it

An explicit nonlinear Lagrangian L(f) that satisfies the Maxwell limit yet admits no static spherically symmetric dyonic solution with equal charges for which f is identically zero.

read the original abstract

We consider static, spherically symmetric configurations of nonlinear electromagnetic fields with Lagrangians $L(f)$, where $f = F_{\mu\nu} F^{\mu\nu}$, in general relativity (GR) and other metric theories of gravity. The corresponding exact solutions are well known in the framework of GR in cases where only an electric charge ($q_e$) or a magnetic charge ($q_m$) are present, but only a few solutions in particular examples of $L(f)$ are known for dyonic systems with both nonzero $q_e$ and $q_m$. We study the properties of such systems in the special case of equal electric and magnetic charges and, assuming a correct Maxwell limit of $L(f)$, show that there always exists such a configuration of the electromagnetic field that the invariant $f$ is zero in the whole space. It leads to the existence of the corresponding families of solutions both in GR in the presence of other sources of gravity (like fluids or scalar fields) and in a wide range of extended theories of gravity (e.g., scalar-tensor and $F(R)$ gravity), in which the nonlinear electromagnetic field behaves in an especially simple manner.

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

For equal charges, any L(f) with a Maxwell limit admits a dyonic configuration with f identically zero, reducing the EM sector to linear Maxwell behavior.

read the letter

The main takeaway is that equal electric and magnetic charges allow a radial field configuration where the invariant f vanishes everywhere. Because L(f) has the correct Maxwell limit, the nonlinear equations then reduce exactly to the linear Maxwell equations, which this ansatz satisfies, and the stress-energy tensor likewise reduces to its Maxwell form. This holds independently of the metric functions under static spherical symmetry, so the same EM setup can be dropped into GR with extra matter or into scalar-tensor and F(R) theories without further adjustment to the electromagnetic part.

Referee Report

0 major / 2 minor

Summary. The manuscript claims that for any nonlinear electrodynamics Lagrangian L(f) with a correct Maxwell limit, static spherically symmetric dyonic configurations with equal electric and magnetic charges admit an electromagnetic field configuration in which the invariant f = F_{μν} F^{μν} vanishes identically everywhere. This reduces the nonlinear field equations and stress-energy tensor to their linear Maxwell forms (independent of the metric functions), enabling families of exact solutions when coupled to additional sources in GR or to modified gravity theories such as scalar-tensor and F(R) gravity.

Significance. If the central result holds, it supplies a general, parameter-free mechanism for constructing dyonic solutions across a wide range of nonlinear electrodynamics models and gravitational theories, extending beyond the limited known examples for specific L(f). The reduction to the linear Maxwell sector for equal charges, with automatic satisfaction of the Bianchi identity, is a useful structural observation that simplifies the search for exact solutions.

minor comments (2)

The derivation that the ansatz with equal radial electric and magnetic fields yields f ≡ 0 and reduces the nonlinear equation to the linear Maxwell equation should be written out explicitly with the relevant components of ∇_μ (L_f F^{μν}) = 0, even if brief, to make the independence from the metric functions fully transparent.
Clarify the precise normalization of f (e.g., whether f = F_{μν} F^{μν} or 1/4 F_{μν} F^{μν}) and the value of L_f(f=0) in the Maxwell limit, as this is central to the reduction.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and the accurate summary of its central result. The recommendation for minor revision is noted, but the report contains no specific major comments or requests for changes.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The central derivation proceeds directly from the Maxwell limit assumption on L(f): the equal-charge dyonic ansatz yields f ≡ 0 identically, causing L_f(f=0) to reduce to a nonzero constant so that the nonlinear equation collapses exactly to the linear Maxwell equation, which the ansatz satisfies by construction. The Bianchi identity and stress-energy tensor likewise reduce independently of the metric. No self-citations, fitted parameters, or ansatzes are invoked to force the result; the argument is self-contained in the field equations and holds for arbitrary additional sources or modified gravity actions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that L(f) has a correct Maxwell limit and on the choice of equal charges; no free parameters or invented entities are introduced in the abstract.

axioms (1)

domain assumption The Lagrangian L(f) possesses a correct Maxwell limit
Explicitly stated as the assumption under which the f=0 configuration exists.

pith-pipeline@v0.9.0 · 5518 in / 1303 out tokens · 22605 ms · 2026-05-08T05:43:18.498901+00:00 · methodology

discussion (0)

Reference graph

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