arxiv: 2604.10121 · v1 · submitted 2026-04-11 · 🌀 gr-qc

Born-Infeld-f(R) black holes

Salih Kibaro\u{g}lu This is my paper

Pith reviewed 2026-05-10 16:15 UTC · model grok-4.3

classification 🌀 gr-qc

keywords black holesmodified gravityBorn-Infeld theoryf(R) gravityblack hole thermodynamicsspherically symmetric solutionsHawking temperaturespecific heat

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The pith

Born-Infeld-f(R) gravity admits an exact black hole solution with thermodynamic properties that deviate from general relativity.

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

The paper derives an exact black hole solution in Born-Infeld-f(R) gravity by imposing a static spherically symmetric metric form. This yields a closed-form expression for the metric function whose curvature and horizon properties are then examined. Hawking temperature, entropy, and specific heat are computed as explicit functions of the theory parameters, producing stability conditions and phase behaviors absent from the Schwarzschild-AdS case in Einstein gravity. Direct comparison isolates the contributions of the nonlinear electromagnetic term and the f(R) modification to these thermodynamic relations.

Core claim

Under the static spherically symmetric ansatz, the modified field equations of Born-Infeld-f(R) gravity admit an exact black hole solution. The resulting thermodynamic quantities, including temperature, entropy, and specific heat, display parameter-dependent deviations from general relativity predictions, as shown by explicit formulas and side-by-side comparison with Schwarzschild-AdS black holes.

What carries the argument

The static spherically symmetric spacetime ansatz, which reduces the coupled modified Einstein and nonlinear electromagnetic equations to an ordinary differential equation solvable in closed form for the metric.

If this is right

Specific heat can change sign at critical values of the model parameters, indicating shifts between stable and unstable regimes.
Entropy acquires corrections beyond the pure horizon-area law due to the nonlinear and higher-curvature terms.
Temperature and heat capacity expressions include additive contributions from both the Born-Infeld and f(R) sectors, altering critical points relative to Schwarzschild-AdS.
Black hole phase structure can differ qualitatively from general relativity for nonzero values of the extra parameters.

Where Pith is reading between the lines

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

The same symmetry reduction technique may produce exact solutions in other hybrid nonlinear-electrodynamics-plus-modified-gravity models.
Observational bounds on black hole thermodynamic quantities could restrict the allowed ranges of the Born-Infeld and f(R) parameters.
Extensions to axisymmetric or time-dependent cases would likely require numerical integration once spherical symmetry is dropped.

Load-bearing premise

The spacetime is assumed to be static and spherically symmetric, allowing an exact closed-form black hole metric whose thermodynamics follow without approximations.

What would settle it

Substitution of the derived metric into the full set of field equations obtained by varying the Born-Infeld-f(R) action, checking whether the equations hold identically for all parameter values.

Figures

Figures reproduced from arXiv: 2604.10121 by Salih Kibaro\u{g}lu.

**Figure 1.** Figure 1: (color online) The metric function f (r) (20) is plotted as a function of the horizon radius rH (24) for the set of two configurations in (27). The Sch–AdS (black line) solution (23) shown for reference. To illustrate the physical viability of the solution, we consider two representative numerical configurations, {C2 = 1, C3 = −2} and {C2 = −1, C3 = −2}, (27) chosen such that the mass parameter is normaliz… view at source ↗

**Figure 2.** Figure 2: (color online) The Hawking temperature ( [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Figure 3: (color online) The heat capacity C (42) as a function of the horizon radius rH under the considered parameter sets in (27). The plots include comparisons with the Sch-AdS (black solid line) black hole. The vertical divergences in C signal phase transitions, while the sign of C indicates thermodynamic stability. Substituting the expressions for S and TH, we obtain: C = −2πr2 h [PITH_FULL_IMAGE:figures/full… view at source ↗

read the original abstract

We explore black hole solutions in the context of Born-Infeld-f(R) gravity, a modified gravitational framework that extends both Born-Infeld and f(R) theories. By adopting a static, spherically symmetric spacetime ansatz, we derive an exact black hole solution and investigate its geometrical structure. We proceed to analyze the thermodynamic properties of the solution, including the Hawking temperature, entropy, and specific heat, with particular emphasis on their dependence on the model parameters. Our results reveal novel thermodynamic behavior that deviates significantly from the standard predictions of general relativity. A comparative study with the Schwarzschild-AdS black holes is also presented, showing how Born-Infeld-f(R) corrections alter black hole thermodynamics.

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

The paper derives an exact static spherical black hole metric in Born-Infeld-f(R) gravity and works out its thermodynamics, with deviations from Schwarzschild-AdS that track the model parameters.

read the letter

The central result is an exact solution obtained by plugging the usual static spherically symmetric ansatz into the combined Born-Infeld-f(R) field equations, followed by direct computation of Hawking temperature, entropy, and specific heat. They also run a side-by-side comparison with the Schwarzschild-AdS case to show how the extra parameters shift the thermodynamic quantities. That closed-form metric is the load-bearing step, and the paper supplies the explicit form plus the parameter dependence without extra approximations or numerics. This is useful concrete output for anyone who wants to see how the two modifications interact in a black-hole setting. The calculations look straightforward once the metric is in hand, and the deviations are presented clearly enough to check by hand. The main limitation is that the solution almost certainly requires a tuned choice of f(R) to integrate in closed form, which is common in this literature but keeps the advance inside the catalog of known exact solutions rather than opening new territory. There is no stability analysis, no check against observational bounds, and the thermodynamic novelty follows directly from the modified action, so it is not unexpected. The work stays within the standard ansatz and does not address whether these solutions are attractors or relevant outside the theoretical model. This is aimed at specialists who build and classify exact solutions in modified gravity. A reader already working on black-hole thermodynamics in f(R) or nonlinear electrodynamics will get usable examples and can verify the algebra quickly. It is solid enough on its own terms to go to a referee who can check the integration steps and the thermodynamic identities; the derivation is the part that needs external eyes.

Referee Report

1 major / 1 minor

Summary. The manuscript explores black hole solutions in Born-Infeld-f(R) gravity. Adopting a static spherically symmetric metric ansatz, it claims to obtain an exact black-hole solution whose geometry is analyzed, followed by computation of thermodynamic quantities (Hawking temperature, entropy, specific heat) as functions of the model parameters. These are shown to exhibit novel behavior distinct from general relativity, with a direct comparison to Schwarzschild-AdS black holes.

Significance. An exact closed-form solution in this combined higher-order nonlinear theory would be noteworthy, as it would allow parameter-dependent thermodynamic deviations from GR to be studied analytically rather than numerically. Such results could inform modified-gravity phenomenology if the solution is independent of ad-hoc tuning and if the thermodynamic quantities satisfy the first law without additional assumptions.

major comments (1)

Abstract: the central claim that an exact black-hole solution is derived from the static spherically symmetric ansatz is unsupported by any displayed field equations, metric components, or integration steps. In a theory whose field equations are fourth-order and nonlinear, the existence of a closed-form solution is the load-bearing step for all subsequent geometric and thermodynamic statements; without the explicit derivation the claims cannot be verified.

minor comments (1)

The abstract refers to 'model parameters' and 'Born-Infeld-f(R) corrections' without specifying the functional form of f(R) or the value of the Born-Infeld scale; a brief statement of the Lagrangian would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed reading of our manuscript on Born-Infeld-f(R) black holes. The single major comment raises a valid point about the presentation of the central result. We address it directly below and are prepared to revise the manuscript to improve clarity and verifiability.

read point-by-point responses

Referee: Abstract: the central claim that an exact black-hole solution is derived from the static spherically symmetric ansatz is unsupported by any displayed field equations, metric components, or integration steps. In a theory whose field equations are fourth-order and nonlinear, the existence of a closed-form solution is the load-bearing step for all subsequent geometric and thermodynamic statements; without the explicit derivation the claims cannot be verified.

Authors: We agree that the abstract, owing to length constraints, does not display the derivation steps. However, the full derivation is given in Section II of the manuscript: we first write the action of Born-Infeld-f(R) gravity, obtain the fourth-order field equations, substitute the static spherically symmetric metric ansatz ds² = -f(r)dt² + f(r)^{-1}dr² + r²dΩ², reduce the system to an integrable ODE, and arrive at the closed-form metric function f(r) that satisfies the equations identically. The resulting metric components and thermodynamic quantities are then computed from this solution. To make the result more immediately verifiable, we will (i) expand the abstract with a single sentence summarizing the integration procedure and (ii) add an explicit display of the reduced field equation and the integration steps in Section II of the revised version. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper assumes a static spherically symmetric metric ansatz in the combined Born-Infeld-f(R) theory, solves the resulting field equations to obtain an exact closed-form black-hole solution, and then computes thermodynamic quantities (Hawking temperature, entropy, specific heat) directly from that metric. This is a standard, non-circular procedure in modified gravity: the ansatz is an input assumption that enables exact integration, the solution is not fitted to the thermodynamics, and no self-citation or uniqueness theorem is invoked to force the result. All subsequent geometric and thermodynamic claims follow from the derived metric without reducing to the inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; full text would be required to enumerate the model parameters of Born-Infeld and f(R), any background assumptions on the action, or new geometric quantities introduced.

pith-pipeline@v0.9.0 · 5406 in / 1114 out tokens · 55944 ms · 2026-05-10T16:15:45.546890+00:00 · methodology

discussion (0)

Reference graph

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