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arxiv: 2605.23090 · v1 · pith:WMEXLK4Anew · submitted 2026-05-21 · 🌀 gr-qc

Horizon structure and extremal configurations of Kerr-Newman-anti-de Sitter black holes in f(R) gravity

Alikram N. Aliev This is my paper

Pith reviewed 2026-05-25 05:11 UTC · model grok-4.3

classification 🌀 gr-qc
keywords black holesextremal configurationsKerr-Newman-AdSf(R) gravityhorizon structureanti-de Sitter spacerotating charged black holes
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The pith

Solving extremality conditions for Kerr-Newman-AdS black holes in f(R) gravity produces closed analytic relations that bound the allowed parameter space with q_max equal to M/2.

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

The paper uses the exact match between constant-curvature solutions in f(R) gravity and Kerr-Newman-AdS metrics from general relativity to examine rotating charged black holes in anti-de Sitter space. It solves the conditions for extremality to obtain explicit formulas that express the squared rotation parameter and the inverse AdS radius in terms of each other. These formulas trace a finite extremal branch in parameter space and show that electric charge is limited to at most half the mass before the metric becomes singular. When charge is absent the rotation parameter falls to a minimum value of 3 sqrt(3) M over 8; nonzero charge widens the branch and lowers that minimum to M over 4. The same method applied to de Sitter space yields a different branch that includes an ultra-extremal regime, while an algebraic mass constraint eliminates all real horizons.

Core claim

By solving the extremality conditions with respect to the squared rotation parameter a squared and the inverse curvature scale l to the minus two, closed analytic relations are obtained that provide a transparent parametrization of the extremal branch in the (a squared, l to the minus two) parameter space. The physically admissible extremal domain is determined and an upper bound on the electric charge q_max equals M over 2 is derived, corresponding to the point at which the metric becomes singular and the extremal branch terminates. For vanishing electric charge the rotation parameter decreases monotonically along the extremal branch and remains bounded from below, implying a minimal value

What carries the argument

Closed analytic relations obtained by solving the extremality conditions simultaneously for a squared and l to the minus two, which parametrize the entire extremal branch in the two-dimensional parameter space.

If this is right

  • The extremal branch terminates at the singular point q equals M over 2.
  • For zero charge a minimum rotation a_min equals 3 sqrt(3) M over 8 appears and the branch is bounded.
  • An internal point exists where the rotation parameter and the AdS curvature scale become comparable.
  • Electric charge extends the allowed branch while reducing the minimal rotation to M over 4 at the maximum charge.
  • In the de Sitter case the branch shows an ultra-extremal maximum followed by decay to the non-rotating limit.

Where Pith is reading between the lines

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

  • The explicit parametrization makes it straightforward to compute thermodynamic quantities or quasinormal modes along the entire extremal curve without numerical root-finding.
  • The qualitative difference between the AdS termination and the richer dS structure indicates that the sign of the cosmological constant controls whether extremality is limited by a geometric endpoint or by an internal maximum.
  • Because the results rely only on the constant-curvature property, they apply to any f(R) model that admits such solutions without requiring the explicit functional form of f.

Load-bearing premise

Kerr-Newman-AdS metrics of general relativity remain exact solutions of f(R) gravity whenever the curvature scalar is constant.

What would settle it

An explicit calculation showing a real horizon root that survives after the algebraic mass constraint is imposed would falsify the claim that the constraint removes all physical horizons.

Figures

Figures reproduced from arXiv: 2605.23090 by Alikram N. Aliev.

Figure 1
Figure 1. Figure 1: FIG. 1: The left panel shows the dependence of the squared ext [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The left panel displays the behavior of the squared ex [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Comparison of the extremal structure in the AdS and dS [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
read the original abstract

Exploiting the correspondence between Kerr-Newman-(A)dS black hole solutions in general relativity and their constant-curvature counterparts in $f(R)$ gravity, we employ a unified framework to investigate the horizon structure and extremal configurations of these black holes, focusing primarily on the anti-de Sitter case. By solving the extremality conditions with respect to the squared rotation parameter $a^2$ and the inverse curvature scale $l^{-2}$, we obtain closed analytic relations that provide a transparent parametrization of the extremal branch in the $(a^2,\, l^{-2})$ parameter space. We determine the physically admissible extremal domain and derive an upper bound on the electric charge, $q_{\max}=M/2$, corresponding to the point at which the metric becomes singular and the extremal branch terminates. For vanishing electric charge, the rotation parameter decreases monotonically along the extremal branch and remains bounded from below, implying the existence of a minimal rotation, $a_{\min}=3\sqrt{3}M/8$. The extremal branch also exhibits a distinguished internal scale-matching point at which the rotation parameter and the AdS curvature scale become comparable. The inclusion of electric charge introduces an additional competing scale, extending the extremal branch while lowering the minimal rotation to $a_{\min}=M/4$ at the maximal allowed charge $q_{\max}=M/2$. Comparing these results with the corresponding de Sitter case, we show that extremality in AdS is constrained by a geometric endpoint, whereas the dS branch exhibits a considerably richer structure characterized by an ultra-extremal maximum and a subsequent decay toward the non-rotating limit. Finally, we demonstrate that the algebraic mass constraint associated with the quartic horizon equation completely removes the real-root structure, yielding a class of solutions without physical horizons.

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 / 3 minor

Summary. The manuscript claims that, exploiting the standard correspondence between Kerr-Newman-(A)dS solutions of general relativity and constant-curvature solutions of f(R) gravity, closed analytic relations for a² and l^{-2} are obtained by directly solving the extremality conditions on the quartic horizon equation. This furnishes a transparent parametrization of the extremal branch in the (a², l^{-2}) plane, determines the admissible domain, yields q_max = M/2 (at which the metric becomes singular), gives a_min = 3√3 M/8 for q = 0 and a_min = M/4 at q_max, identifies an internal scale-matching point, contrasts the geometric endpoint of the AdS branch with the richer ultra-extremal structure of the dS branch, and shows that an algebraic mass constraint on the quartic eliminates all real roots.

Significance. If the algebraic derivations are correct, the work supplies an explicit, closed-form parametrization of extremal Kerr-Newman-AdS configurations in f(R) gravity together with sharp bounds on charge and rotation. The comparison between AdS and dS extremal branches and the observation that the mass constraint removes physical horizons are useful additions to the literature on black-hole thermodynamics and parameter-space structure in modified gravity.

minor comments (3)
  1. The abstract and introduction state that the metric satisfies the f(R) field equations by the constant-curvature correspondence, but a short explicit substitution of R = -12/l² into the f(R) equations (or a reference to the standard result) would make the transfer of the horizon polynomial fully self-contained.
  2. Notation for the quartic horizon function and the extremality conditions (presumably Eqs. (X)–(Y) in §3) should be introduced with a single compact display equation before the solving steps begin.
  3. The statement that the algebraic mass constraint “completely removes the real-root structure” would benefit from a brief remark on whether this holds only for the extremal slice or for the full parameter space.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive evaluation of our manuscript, including the recommendation for minor revision. The referee summary accurately captures the central results: the closed-form parametrization of the extremal branch via direct solution of the extremality conditions, the bounds q_max = M/2 and a_min = 3√3 M/8 (q=0), the internal scale-matching point, the AdS versus dS comparison, and the effect of the algebraic mass constraint.

Circularity Check

0 steps flagged

No significant circularity; derivations are direct algebraic solutions

full rationale

The paper's central results follow from solving the extremality conditions (double roots of the horizon polynomial) directly for a² and l^{-2} in the standard Kerr-Newman-AdS metric. This metric is imported via the well-known constant-curvature correspondence between GR and f(R) gravity, which is an external mathematical fact independent of the present work and does not depend on any fitted parameters or self-citations from the author. The derived bounds (q_max = M/2, a_min expressions) are algebraic consequences of the quartic metric function becoming singular or losing real roots; they are not renamed fits or self-referential. No load-bearing step reduces to a prior result by the same authors or to an ansatz smuggled via citation. The analysis is self-contained against the metric equations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the mathematical correspondence between GR and constant-curvature f(R) solutions together with the assumption that the quartic horizon equation can be solved analytically for extremality without further restrictions on f(R).

axioms (1)
  • domain assumption Kerr-Newman-(A)dS solutions of general relativity are constant-curvature solutions of f(R) gravity
    This correspondence is invoked at the outset to transfer the metric and horizon structure to the f(R) case.

pith-pipeline@v0.9.0 · 5874 in / 1411 out tokens · 27102 ms · 2026-05-25T05:11:39.387595+00:00 · methodology

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