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arxiv: 2604.06632 · v1 · submitted 2026-04-08 · 🌀 gr-qc

Recognition: 2 theorem links

· Lean Theorem

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

Jose Pinedo Soto , Valeri P. Frolov
Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:17 UTC · model grok-4.3

classification 🌀 gr-qc
keywords quasi-topological gravityBorn-Infeld electrodynamicscharged black holesregular black hole solutionsspherically symmetric metricsnonlinear electrodynamicsanti-de Sitter corecurvature singularity
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The pith

Quasi-topological gravity coupled to Born-Infeld electrodynamics yields regular charged black holes with anti-de Sitter cores in specific models.

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

The paper constructs static spherically symmetric black hole solutions in quasi-topological gravity coupled to Born-Infeld nonlinear electrodynamics starting from the spherically reduced action. Closed-form expressions are derived for the electric field, the nonlinear Lagrangian, and the metric function involving hypergeometric functions. For some models where vacuum black holes are regular, adding charge produces a curvature singularity at finite interior radius. In contrast, the Born-Infeld-type version of quasi-topological gravity preserves regularity for the charged solutions, though the de Sitter core of the neutral case is replaced by an anti-de Sitter core. The work also examines various limiting regimes of the solutions.

Core claim

Starting from the spherically reduced action, closed-form expressions for the electric field, nonlinear Lagrangian, and metric function involving hypergeometric functions are derived. In specific versions of quasi-topological gravity where vacuum black holes are regular, charged black holes generally develop curvature singularities at finite radii in their interior. However, in the Born-Infeld-type quasi-topological gravity, charged black holes remain regular, with the de Sitter core of the neutral solution replaced by an anti-de Sitter core. Several limiting regimes of these solutions are also discussed.

What carries the argument

The spherically reduced action of quasi-topological gravity coupled to the Born-Infeld nonlinear electrodynamics Lagrangian, which integrates to give the metric function in terms of hypergeometric functions.

If this is right

  • Charged black holes stay regular at all radii in the Born-Infeld-type quasi-topological gravity model.
  • The spacetime geometry near the center changes from de Sitter to anti-de Sitter type.
  • Other regular-vacuum quasi-topological models develop interior curvature singularities once charge is included.
  • The electric field and nonlinear Lagrangian admit explicit closed-form expressions in all cases considered.
  • The solutions recover known limits when the Born-Infeld parameter or quasi-topological couplings take special values.

Where Pith is reading between the lines

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

  • These explicit regular solutions could be used to examine thermodynamic properties or quasinormal modes in modified gravity.
  • The core-type switch from de Sitter to anti-de Sitter may affect the motion of nearby test particles or fields.
  • Similar parameter-tuned couplings might be explored in other higher-curvature theories to generate nonsingular charged geometries.

Load-bearing premise

The parameters that make vacuum black holes regular in quasi-topological gravity extend without issue to the charged case and produce closed-form solutions with no extra gravity-electrodynamics interaction terms.

What would settle it

Explicit computation of curvature invariants such as the Kretschmann scalar using the hypergeometric metric function that shows a divergence at finite radius inside the Born-Infeld-type solution.

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 derived for the electric field, the nonlinear Lagrangian, and the metric function (involving hypergeometric functions). For specific QTG parameter choices that yield regular vacuum black holes, the paper shows that charged solutions develop curvature singularities at finite interior radii in some models, while Born-Infeld-type QTG yields regular charged black holes (with the neutral de Sitter core replaced by an anti-de Sitter core). Limiting regimes are also discussed.

Significance. If the solutions satisfy the full field equations, the explicit closed-form expressions and the model-dependent distinction between singular and regular charged black holes provide concrete examples of how nonlinear electrodynamics interacts with higher-curvature gravity to control interior regularity. The replacement of dS by AdS cores and the analysis of limiting cases add to the catalog of regular black hole interiors in modified gravity, which may be useful for thermodynamic or stability studies.

major comments (1)
  1. [Derivation from the spherically reduced action (as outlined after the abstract)] The central claim that the derived metric functions solve the theory and allow direct reading of singularity/regularity properties rests on the assumption that the spherically reduced action contains no residual QTG-BI cross terms that would prevent the closed-form integration. The manuscript should explicitly verify that the obtained metric satisfies the complete 4D field equations obtained from the unreduced action, particularly for the chosen QTG invariants coupled to the Born-Infeld Lagrangian.
minor comments (2)
  1. [Abstract and introduction] The abstract states that 'for some of these models' charged black holes develop singularities, but does not enumerate the specific QTG versions considered; a short table or list in the introduction would clarify which parameter choices lead to each outcome.
  2. [Limiting regimes section] The discussion of limiting regimes would benefit from explicit comparison of the hypergeometric metric function to known solutions in Einstein-Born-Infeld gravity or other quasi-topological models to highlight the new features.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive recommendation. We address the single major comment below, agreeing that an explicit verification step strengthens the presentation.

read point-by-point responses

  1. Referee: [Derivation from the spherically reduced action (as outlined after the abstract)] The central claim that the derived metric functions solve the theory and allow direct reading of singularity/regularity properties rests on the assumption that the spherically reduced action contains no residual QTG-BI cross terms that would prevent the closed-form integration. The manuscript should explicitly verify that the obtained metric satisfies the complete 4D field equations obtained from the unreduced action, particularly for the chosen QTG invariants coupled to the Born-Infeld Lagrangian.

    Authors: We agree that an explicit check against the unreduced 4D equations provides additional reassurance, especially given the higher-curvature nature of QTG. Quasi-topological terms are constructed precisely so that their contribution to the spherically symmetric sector remains second-order and does not generate residual cross terms with the electromagnetic sector that would invalidate the reduction. The Born-Infeld Lagrangian, being a scalar function of the invariant F_{μν}F^{μν}, enters the reduced action in a manner consistent with this property. Nevertheless, to address the referee’s concern directly, the revised manuscript will include a dedicated subsection in which the derived metric function and electric field are substituted back into the full set of 4D field equations obtained by varying the unreduced action. We will demonstrate that these equations are satisfied identically (up to the integration constants already fixed) for the specific QTG parameter choices considered. This verification will be performed both analytically for the limiting cases and numerically for the general hypergeometric solutions, thereby confirming that no obstructing cross terms arise. revision: yes

Circularity Check

0 steps flagged

Derivation is self-contained from reduced action with no circular reductions

full rationale

The paper derives closed-form expressions for the electric field, nonlinear Lagrangian, and metric function (involving hypergeometric functions) directly from the spherically reduced action of QTG coupled to Born-Infeld NED. Regularity properties for charged solutions are read off from explicit integration under specific parameter choices that make vacuum solutions regular; these are input assumptions, not outputs redefined as predictions. No parameters are fitted to subsets of data and then used to predict closely related quantities, no self-definitional loops appear in the equations, and no load-bearing self-citations or smuggled ansatze are required for the central claims. The derivation chain remains independent of its target results.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard quasi-topological gravity action with parameters tuned for regular vacuum solutions and the Born-Infeld Lagrangian form; no new entities are introduced.

free parameters (2)
  • QTG coupling constants
    Specific values selected so that neutral black holes remain regular.
  • Born-Infeld nonlinearity parameter
    Sets the scale of nonlinear electromagnetic effects.
axioms (2)
  • domain assumption Static spherically symmetric metric ansatz
    Reduces the field equations to ordinary differential equations solvable in closed form.
  • domain assumption Direct additive coupling of QTG and BI NED actions
    No extra interaction terms between curvature and electromagnetic sectors.

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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

    Non-polynomial quasi-topological gravity models reproduce the standard thermal history, generate dynamical dark energy of geometric origin, and fit supernova, cosmic chronometer, and BAO data competitively with ΛCDM.

  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.

Reference graph

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