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arxiv: 2511.05273 · v2 · submitted 2025-11-07 · 🌀 gr-qc · hep-th

Born-Infeld Electrogravity and Dyonic Black Holes

Guadalupe Ahumada Acu\~na , Cecilia Bejarano , Rafael Ferraro This is my paper

Pith reviewed 2026-05-18 00:01 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords Born-Infeld electrogravitydyonic black holesPalatini formalismdeterminantal Lagrangianextremal black holesnonlinear electrodynamicshorizon structure
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The pith

Born-Infeld electrogravity admits a fundamental extremal black hole whose mass and horizon area are set solely by the Born-Infeld parameter, Newton's constant, and the speed of light in the small-charge limit.

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

The paper introduces Born-Infeld electrogravity through a single determinantal Lagrangian that unifies the gravitational curvature scalar with electromagnetic invariants. Using the Palatini formalism with independent variations of the metric, connection, and vector potential, the gravitational sector reduces exactly to Einstein's equations while the electromagnetic sector permits two equivalent descriptions. Analysis of spherically symmetric dyonic black hole solutions then shows that an extremal configuration exists when charges are small, with both mass and horizon area fixed exclusively by the theory parameters and fundamental constants rather than by the charge values themselves. This result establishes a definite minimal scale for extremal black holes within the model.

Core claim

Born-Infeld electrogravity is defined through a Lagrangian that couples gravity and electromagnetism within a single determinantal structure. The field equations are derived in Palatini's formalism, where the metric, connection, and vector potential are varied independently in the action. As a result, the gravitational sector reduces to Einstein's equations with a torsion-free, metric-compatible connection. The electrodynamic sector admits two equivalent interpretations: it can be seen either as a standard Born-Infeld electrodynamics in an effective background geometry, or as an anomalous Born-Infeld electrodynamics in the physical metric. Analysis of the horizon structure, extremality, and

What carries the argument

A single determinantal Lagrangian coupling the curvature scalar and the electromagnetic invariants, varied independently for metric, connection, and vector potential in Palatini formalism.

If this is right

  • The gravitational dynamics coincide exactly with Einstein gravity for a torsion-free metric-compatible connection.
  • The electromagnetic sector supports two equivalent pictures: standard Born-Infeld electrodynamics on an effective geometry or anomalous Born-Infeld electrodynamics on the physical metric.
  • Spherically symmetric dyonic solutions possess well-defined horizon structures whose extremality conditions can be stated explicitly.
  • Thermodynamic quantities for these black holes follow directly from the horizon analysis in the small-charge regime.

Where Pith is reading between the lines

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

  • The fixed mass and area scale may provide a natural ultraviolet cutoff for black-hole evaporation in related models.
  • The two electromagnetic interpretations could produce distinct predictions for strong-field or high-curvature regimes not explored in the spherical case.
  • Extension of the same Lagrangian to axisymmetric or rotating solutions would test whether the fundamental extremal state persists beyond spherical symmetry.

Load-bearing premise

A single determinantal Lagrangian coupling curvature and electromagnetic invariants yields consistent dynamics when the metric, connection, and vector potential are varied independently in the Palatini formalism.

What would settle it

Explicit solution of the field equations for dyonic configurations in the small-charge limit that fails to produce an extremal state whose mass and horizon area depend only on the Born-Infeld parameter, Newton's constant, and the speed of light.

Figures

Figures reproduced from arXiv: 2511.05273 by Cecilia Bejarano, Guadalupe Ahumada Acu\~na, Rafael Ferraro.

Figure 1
Figure 1. Figure 1: shows how the existence and number of horizons depend on the relation between the parameters α and C. For C (the parameter proportional to the black-hole mass) greater than Cextr the curve exhibits two roots, which indicates the presence of two horizons. For C < Cextr, there are no horizons. A similar graphic is obtained for the solution (74) associated with an imaginary value of β in the determinantal Lag… view at source ↗
read the original abstract

Born-Infeld electrogravity is defined through a Lagrangian that couples gravity and electromagnetism within a single determinantal structure. The field equations are derived in Palatini's formalism, where the metric, connection, and vector potential are varied independently in the action. As a result, the gravitational sector reduces to Einstein's equations with a torsion-free, metric-compatible connection. The electrodynamic sector, in turn, admits two equivalent interpretations or $pictures$: it can be seen either as a standard Born-Infeld electrodynamics in an effective background geometry, or as an $anomalous$ Born-Infeld electrodynamics in the physical metric. We illustrate the dynamics by analyzing the horizon structure, the extremality conditions, and the thermodynamics of spherically symmetric dyonic solutions. Remarkably, in the small-charge limit, Born--Infeld electrogravity admits a fundamental extremal black hole whose mass and horizon area are determined exclusively by the Born--Infeld and Newton constants and the speed of light.

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

1 major / 2 minor

Summary. The manuscript introduces Born-Infeld electrogravity through a single determinantal Lagrangian coupling the curvature scalar to the electromagnetic invariants. Field equations are obtained in Palatini formalism by independent variation with respect to the metric, connection, and vector potential. The gravitational sector is shown to reduce to Einstein equations with a torsion-free, metric-compatible connection. The electromagnetic sector admits two equivalent interpretations: standard Born-Infeld electrodynamics on an effective geometry or anomalous Born-Infeld electrodynamics on the physical metric. The authors then examine spherically symmetric dyonic black-hole solutions, deriving horizon structure, extremality conditions, and thermodynamic quantities. A central result is that, in the small-charge limit, the theory admits a fundamental extremal black hole whose mass and horizon area are fixed exclusively by the Born-Infeld scale, Newton’s constant, and the speed of light.

Significance. If the Palatini reduction to Einstein gravity is rigorously established and the small-charge extremal solutions are free of hidden assumptions, the work supplies a concrete example of a modified-gravity theory in which an extremal black hole is determined solely by fundamental constants. This could be relevant for studies of black-hole thermodynamics and for exploring whether extremality can be protected without fine-tuning. The explicit construction of dyonic solutions and the dual electromagnetic pictures provide concrete illustrations that strengthen the conceptual contribution.

major comments (1)
  1. [§2] §2 (field equations): the reduction of the Palatini variation of the determinantal Lagrangian to Einstein equations with a torsion-free, metric-compatible connection is asserted but not accompanied by the explicit connection equation or the cancellation of potential non-metricity terms arising from the mixing of R with the two electromagnetic invariants. Because the extremal mass and horizon-area expressions in the small-charge limit are computed on the standard Schwarzschild geometry, any surviving torsion or non-metricity would alter the effective metric and invalidate the parameter-free claim.
minor comments (2)
  1. [Abstract] The abstract states that the two electromagnetic pictures are “equivalent,” yet the precise mapping between the effective geometry and the physical metric is not summarized; a one-sentence clarification would aid readers.
  2. [Introduction] Notation for the two electromagnetic invariants (F and *F) and the Born-Infeld scale β should be introduced once in the introduction and used consistently thereafter.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive major comment. We address the point on the Palatini reduction below and will strengthen the presentation accordingly.

read point-by-point responses

  1. Referee: [§2] §2 (field equations): the reduction of the Palatini variation of the determinantal Lagrangian to Einstein equations with a torsion-free, metric-compatible connection is asserted but not accompanied by the explicit connection equation or the cancellation of potential non-metricity terms arising from the mixing of R with the two electromagnetic invariants. Because the extremal mass and horizon-area expressions in the small-charge limit are computed on the standard Schwarzschild geometry, any surviving torsion or non-metricity would alter the effective metric and invalidate the parameter-free claim.

    Authors: We agree that an explicit derivation of the connection equation is necessary for full rigor. The determinantal structure of the Lagrangian ensures that the independent variation with respect to the connection yields an algebraic equation whose only solution is the torsion-free, metric-compatible Levi-Civita connection of the physical metric; the electromagnetic invariants enter in a manner that produces no additional torsion or non-metricity sources. Nevertheless, the manuscript presents this reduction concisely rather than displaying every intermediate step. In the revised version we will insert the full connection field equation together with the explicit cancellation of non-metricity terms. This addition confirms that the background remains the standard Schwarzschild geometry in the small-charge limit, so the reported extremal mass and horizon area remain determined solely by the Born-Infeld scale, Newton’s constant and the speed of light. revision: yes

Circularity Check

0 steps flagged

No significant circularity; extremal mass/area follows from new Lagrangian in small-charge limit

full rationale

The paper defines a novel determinantal Lagrangian coupling R and EM invariants, performs independent Palatini variations w.r.t. metric, connection and A_μ, obtains the claimed reduction to Einstein equations plus torsion-free metric-compatible connection, then solves the resulting equations for spherically symmetric dyonic configurations. In the small-charge limit the extremal mass and horizon area emerge as fixed by β, G and c. This is a direct consequence of the field equations and the limit, not a fit, not a renaming of a known result, and not dependent on load-bearing self-citations or prior ansätze from the same authors. The derivation chain is self-contained once the Lagrangian is accepted; no step reduces by construction to its own input.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The paper introduces a new determinantal Lagrangian without supplying independent empirical or mathematical justification for its physical correctness beyond the resulting field equations; the Palatini variation is treated as a standard but non-trivial assumption.

free parameters (1)
  • Born-Infeld scale parameter
    The dimensionful constant that sets the nonlinear scale in the determinantal Lagrangian; its value is not derived from first principles in the abstract.
axioms (1)
  • domain assumption Independent variation of metric, connection, and vector potential in the Palatini formalism yields the correct dynamics for the coupled system.
    Invoked to obtain the reduction to Einstein equations with torsion-free, metric-compatible connection.
invented entities (1)
  • Born-Infeld electrogravity no independent evidence
    purpose: A single determinantal structure that unifies gravitational and electromagnetic degrees of freedom.
    New postulated theory whose physical viability is not supported by external evidence in the abstract.

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Reference graph

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