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arxiv: 2604.06632 · v2 · pith:PVTUNXU3new · submitted 2026-04-08 · 🌀 gr-qc

Charged Black Holes in Quasi-Topological Gravity Coupled to Born-Infeld Nonlinear Electrodynamics

Jose Pinedo Soto , Valeri P. Frolov This is my paper

Pith reviewed 2026-05-21 10:00 UTC · model grok-4.3

classification 🌀 gr-qc
keywords black holesquasi-topological gravityBorn-Infeld electrodynamicsnonlinear electrodynamicsregular black holescurvature singularitiesspherically symmetric solutionshypergeometric functions
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The pith

In quasi-topological gravity coupled to Born-Infeld electrodynamics, some models produce charged black holes with interior curvature singularities while others keep them regular.

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

The paper derives exact solutions for charged black holes in quasi-topological gravity with nonlinear Born-Infeld electrodynamics. It provides closed-form expressions for the metric function using hypergeometric functions after reducing the action for spherical symmetry. For certain quasi-topological models that have regular neutral black holes, introducing charge leads to a curvature singularity at a finite radius inside the event horizon. In a specific Born-Infeld-type quasi-topological gravity, however, the charged black holes stay regular throughout their interior. This regularity comes at the cost of replacing the de Sitter core of the neutral solution with an anti-de Sitter core.

Core claim

We construct static, spherically symmetric black hole solutions in quasi-topological gravity coupled to Born-Infeld nonlinear electrodynamics. Starting from the spherically reduced action, we derive closed-form expressions for the electric field, the nonlinear Lagrangian, and the metric function involving hypergeometric functions. We consider specific versions of QTG in which vacuum black holes are regular, and show that for some of these models charged black holes develop a curvature singularity at a finite radius in their interior. In contrast, in models such as a Born-Infeld-type QTG, charged black holes remain regular, though the de Sitter core is replaced by an anti-de Sitter core.

What carries the argument

The spherically reduced action of quasi-topological gravity coupled to Born-Infeld electrodynamics, yielding metric functions expressed with hypergeometric functions that determine the regularity properties.

If this is right

  • Charged black holes in some QTG models develop curvature singularities at finite interior radii.
  • Born-Infeld-type QTG models maintain regularity for charged black holes.
  • The core of regular charged solutions is anti-de Sitter rather than de Sitter.
  • Several limiting regimes of these black hole solutions can be analyzed explicitly.

Where Pith is reading between the lines

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

  • This indicates that the specific form of the quasi-topological terms can be chosen to avoid singularities in charged cases.
  • Similar nonlinear electrodynamics couplings could be tested in other higher-curvature gravity theories for regular black hole constructions.
  • The change to an anti-de Sitter core may affect the causal structure or thermodynamic properties of the black holes.

Load-bearing premise

The analysis assumes specific versions of quasi-topological gravity where the vacuum black holes are regular.

What would settle it

Computing the curvature invariants such as the Kretschmann scalar from the derived metric function and checking whether they diverge at a finite radius for charged solutions in the non-Born-Infeld models.

Figures

Figures reproduced from arXiv: 2604.06632 by Jose Pinedo Soto, Valeri P. Frolov.

Figure 1
Figure 1. Figure 1: shows plots of the function JD(ρ) for spacetime dimensions D = 4, D = 5 and D = 6. 0.0 0.2 0.4 0.6 0.8 1.0 0 1 2 3 4 FIG. 1. Plot of the function JD(ρ) for D = 4 (solid), D = 5 (dashed) and D = 6 (dot-dashed) The integral representation for JD(ρ) in (3.11) implies that it is a positive function of ρ which monotonically decreases from J (0) D = JD(ρ = 0) at ρ = 0 until it reaches 0 at ρ → ∞. The asymptotic … view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Plot of the function [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Plot of the primary curvature invariant ˆp [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: shows the metric function f as a function of the dimensionless coordinate ˆr = r/ℓ for singular and regular charged black holes in the Hayward-type QTG. 2 4 6 8 10 -1 1 2 FIG. 4. Plot of the metric function f(ˆr), ˆr = r/ℓ, for the Hayward-type QTG model for β = 1 and D = 4. Two cases are displayed for different (ˆµ, σ) parameters, a divergent met￾ric with parameters (8, 0.8) (solid) and a regular black ho… view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Plot of the metric function [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The behaviour of the metric function [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Plot of the functions [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Ratio [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Ratio [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Plot of functions [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
read the original abstract

We construct static, spherically symmetric black hole solutions in quasi-topological gravity (QTG) coupled to Born-Infeld nonlinear electrodynamics. Starting from the spherically reduced action, we derive closed-form expressions for the electric field, the nonlinear Lagrangian, and the metric function, the latter involving hypergeometric functions. We consider specific versions of QTG in which vacuum black holes are regular, and show that, for some of these models, charged black holes develop a curvature singularity at a finite radius in their interior. In contrast, in models such as a Born-Infeld-type QTG, charged black holes remain regular. In this case, however, the de Sitter core of the neutral solution is replaced by an anti-de Sitter core. We also discuss several limiting regimes of these solutions.

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 constructs static, spherically symmetric black hole solutions in quasi-topological gravity (QTG) coupled to Born-Infeld nonlinear electrodynamics. Starting from the spherically reduced action, closed-form expressions are obtained for the electric field, the nonlinear Lagrangian, and the metric function (involving hypergeometric functions). Specific QTG models that yield regular vacuum black holes are examined; the authors show that charged solutions in some of these models develop a curvature singularity at finite interior radius, while a Born-Infeld-type QTG model remains regular, albeit with an anti-de Sitter core replacing the de Sitter core of the neutral solution. Limiting regimes are also discussed.

Significance. If the explicit derivations hold, the work supplies analytic black-hole solutions in a higher-curvature gravity theory coupled to nonlinear electrodynamics. The ability to distinguish, via closed-form expressions, between models that acquire interior singularities upon charging and those that remain regular (with an AdS core) offers concrete insight into how nonlinear electrodynamics modifies interior structure in quasi-topological gravity. The hypergeometric representation of the metric function is a technical strength that permits direct examination of curvature invariants without numerical integration.

major comments (1)
  1. [§4 (regularity analysis)] The central regularity claims rest on the explicit hypergeometric metric functions derived from the reduced action. The manuscript should supply a direct verification (e.g., asymptotic expansion or plot of the Kretschmann scalar) that a curvature singularity indeed appears at finite radius for the models discussed after Eq. (the electric-field solution), rather than relying solely on the formal expression.
minor comments (2)
  1. [Abstract] The abstract states that vacuum black holes are regular for the chosen QTG models; a brief reminder of the vacuum metric function (or reference to the appropriate earlier equation) would help readers connect the charged and neutral cases.
  2. [Metric-function derivation] Notation for the hypergeometric parameters appearing in the metric function should be defined explicitly when first introduced, to avoid ambiguity when taking the various limiting regimes mentioned in the final section.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript on charged black hole solutions in quasi-topological gravity coupled to Born-Infeld electrodynamics. The suggestion for explicit verification of the curvature singularity is constructive, and we address it below.

read point-by-point responses

  1. Referee: [§4 (regularity analysis)] The central regularity claims rest on the explicit hypergeometric metric functions derived from the reduced action. The manuscript should supply a direct verification (e.g., asymptotic expansion or plot of the Kretschmann scalar) that a curvature singularity indeed appears at finite radius for the models discussed after Eq. (the electric-field solution), rather than relying solely on the formal expression.

    Authors: We agree that an explicit verification strengthens the presentation of the regularity analysis. Although the closed-form hypergeometric metric function allows direct analytic computation of curvature invariants, we will add in the revised manuscript an asymptotic expansion of the Kretschmann scalar approaching the finite interior radius for the models that develop singularities. This expansion will confirm the divergence without relying only on the formal expression, while leaving the core derivations and conclusions unchanged. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained from the action

full rationale

The paper begins with the spherically reduced action for quasi-topological gravity coupled to Born-Infeld nonlinear electrodynamics and derives closed-form expressions for the electric field, nonlinear Lagrangian, and metric function (involving hypergeometric functions) directly from the equations of motion. Regularity properties for charged solutions in selected models (including those regular in vacuum) are then analyzed from these explicit expressions, with distinctions such as interior singularities versus AdS cores following from the solutions themselves. No load-bearing step reduces by construction to a fitted input, self-definition, or unverified self-citation chain; the construction remains independent of the target results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on the established framework of quasi-topological gravity and Born-Infeld electrodynamics; specific regular vacuum models are selected without new postulates.

axioms (1)
  • domain assumption Specific versions of quasi-topological gravity admit regular vacuum black holes
    Invoked when selecting models for the charged case analysis.

pith-pipeline@v0.9.0 · 5672 in / 1217 out tokens · 38846 ms · 2026-05-21T10:00:48.699796+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We construct static, spherically symmetric black hole solutions in quasi-topological gravity (QTG) coupled to Born-Infeld nonlinear electrodynamics. Starting from the spherically reduced action, we derive closed-form expressions for the electric field, the nonlinear Lagrangian, and the metric function, the latter involving hypergeometric functions.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    In the presence of charge, Hayward-type black holes can develop a curvature singularity at a finite radius within their interior, whereas Born–Infeld-type solutions remain regular for all values of the parameters.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Cosmologically viable non-polynomial quasi-topological gravity: explicit models, $\Lambda$CDM limit and observational constraints

    gr-qc 2026-04 unverdicted novelty 7.0

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  2. All $2D$ generalised dilaton theories from $d\geq 4$ gravities

    hep-th 2026-03 conditional novelty 7.0

    Generic 2D Horndeski theories arise from dimensional reduction of d≥4 gravities, yielding a Birkhoff theorem for quasi-topological gravities where static spherically symmetric solutions satisfy g_tt g_rr = -1 and are ...

  3. $g_{tt}g_{rr} =-1$ black hole thermodynamics in extended quasi-topological gravity

    gr-qc 2026-04 unverdicted novelty 6.0

    A unified framework links the generating function for static black holes satisfying g_tt g_rr=-1 in extended quasi-topological gravity to thermodynamic mass and Wald entropy via an effective 2D dilaton theory.

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