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arxiv: 2606.13773 · v2 · pith:ZORJLN4Ynew · submitted 2026-06-11 · 🌀 gr-qc · hep-th· math-ph· math.MP

Constraints on regular black holes with nonminimally coupled electromagnetic fields

Ana Bokuli\'c , Tajron Juri\'c , Luka Kanai Peji\'c , Filip Po\v{z}ar , Ivica Smoli\'c This is my paper

Pith reviewed 2026-07-02 22:25 UTC · model grok-4.3

classification 🌀 gr-qc hep-thmath-phmath.MP
keywords regular black holesnonminimal couplingelectromagnetic fieldsEinstein gravitymagnetic chargecurvature singularitieseffective Lagrangians
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The pith

Magnetically charged regular black holes are excluded in nonminimally coupled electromagnetic theories except for finely tuned constants.

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

The paper investigates gravitational theories with nonminimal couplings between the electromagnetic field and curvature, terms that appear in low-energy effective Lagrangians. It establishes that magnetically charged regular black holes cannot exist under these interactions, with the exception of possible special values for the coupling constants. A parallel argument is made for electrically charged cases, and the result extends to a broader class of Lagrangians involving functions of the curvature and the electromagnetic dual. This constrains attempts to construct realistic regular black hole models that avoid central singularities. Such models matter because they could address issues like the black hole information paradox in a classical setting.

Core claim

We prove that magnetically charged regular black holes are excluded, except possibly for finely tuned choices of coupling constants, in theories with the interaction terms R F_ab F^ab, R_ab F^a_c F^bc and R_abcd F^ab F^cd. Similar conclusions apply to electrically charged regular black holes. The same holds for Lagrangian terms of the form f(R, F_ab ⋆F^ab).

What carries the argument

The nonminimal coupling terms R F_ab F^ab, R_ab F^a_c F^bc, and R_abcd F^ab F^cd between the Ricci and Riemann tensors and the electromagnetic field strength, which lead to contradictions with the regularity of curvature invariants for charged solutions.

If this is right

  • Magnetically charged regular black holes are ruled out in these theories without fine-tuning of constants.
  • Electrically charged regular black holes face similar restrictions.
  • Terms of the form f(R, F_ab ⋆ F^ab) also exclude such solutions.
  • Models for regular black holes must incorporate additional matter or higher-order terms beyond these couplings.

Where Pith is reading between the lines

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

  • Regularity in black holes may require couplings to other fields like scalars to evade these constraints.
  • This result highlights the difficulty of achieving singularity resolution in effective field theories with electromagnetic sources.
  • Future work could explore whether quantum corrections or modified gravity terms beyond nonminimal EM allow regular solutions.

Load-bearing premise

The spacetime and matter content are governed exactly by the Einstein equations with only the listed nonminimal electromagnetic interaction terms and no additional higher-order or matter contributions.

What would settle it

An explicit construction of a magnetically charged regular black hole solution for generic values of the coupling constants in these theories would falsify the exclusion result.

read the original abstract

Construction of physically realistic theories admitting regular black hole solutions remains an important open problem in gravitational physics. While theories with electromagnetic fields minimally coupled to gravity have been extensively studied over the past two decades, theories with nonminimal couplings remain comparatively unexplored. We investigate theories containing the interaction terms $R F_{ab}F^{ab}$, $R_{ab} F^a_{\ \, c} \, F^{bc}$ and $R_{abcd} F^{ab} F^{cd}$, which generically arise in low-energy effective Lagrangians. We prove that magnetically charged regular black holes are excluded, except possibly for finely tuned choices of coupling constants, and argue that a similar conclusion applies to electrically charged regular black holes. We further show that similar conclusions hold for Lagrangian terms of the form $f(R,F_{ab}{\star F}^{ab})$.

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

0 major / 2 minor

Summary. The manuscript examines Einstein-Maxwell theories supplemented by the nonminimal interaction terms R F_ab F^ab, R_ab F^a_c F^bc and R_abcd F^ab F^cd (and extensions to f(R, F_ab ⋆F^ab)). It proves that magnetically charged regular black holes are excluded except possibly for finely tuned choices of the coupling constants, and argues that an analogous conclusion holds for electrically charged cases. The proof proceeds by integrating the modified Einstein equations under the assumption of a regular center with finite curvature invariants.

Significance. If the derivation holds, the result supplies a concrete no-go theorem that constrains regular black-hole constructions inside the indicated class of low-energy effective theories. The integration approach under explicit regularity assumptions yields a direct obstruction from the field equations themselves, with the fine-tuning caveat stated explicitly rather than elided.

minor comments (2)
  1. The abstract states the main result but does not indicate the integration method; a brief clause on the proof strategy would improve readability.
  2. Notation for the dual tensor ⋆F and the precise definitions of the three coupling constants should be introduced uniformly in the first section where the action is written.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, the clear summary of our results, and the recommendation to accept. There are no major comments requiring a point-by-point response.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper derives a no-go result for magnetically charged regular black holes by integrating the modified Einstein equations obtained from the Einstein-Hilbert action plus the three specified nonminimal invariants (R F_ab F^ab, R_ab F^a_c F^bc, R_abcd F^ab F^cd), under the assumption of a regular center with finite curvature invariants. This is a direct algebraic consequence of the field equations within the stated theory class and does not reduce to any self-definitional equivalence, fitted inputs renamed as predictions, or load-bearing self-citations. The explicit caveat for finely tuned coupling constants further shows the result is not forced by construction. No ansatzes or uniqueness theorems imported via self-citation are indicated in the abstract or summary.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that the theory is exactly described by Einstein gravity plus the three listed nonminimal EM terms and on the standard definition of regularity; no free parameters are fitted because the result is an exclusion.

axioms (2)
  • domain assumption The gravitational theory is given by the Einstein-Hilbert action plus the specified nonminimal coupling terms R F_ab F^ab, R_ab F F, R_abcd F F
    Invoked to derive the field equations whose solutions are analyzed.
  • domain assumption Regularity requires all curvature invariants to remain finite at the center
    Standard definition used to exclude singular solutions.

pith-pipeline@v0.9.1-grok · 5699 in / 1202 out tokens · 30443 ms · 2026-07-02T22:25:34.783000+00:00 · methodology

discussion (0)

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Reference graph

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