pith. sign in

arxiv: 2605.15005 · v1 · pith:37LE6G4Xnew · submitted 2026-05-14 · 🌀 gr-qc

An Exact Single-Rotating Near-Horizon Geometry in Einstein-Gauss-Bonnet Gravity

U. Can \c{C}elik , Kamal Hajian , Jutta Kunz This is my paper

Pith reviewed 2026-06-30 20:02 UTC · model grok-4.3

classification 🌀 gr-qc
keywords Einstein-Gauss-Bonnet gravitynear-horizon geometrysingly rotatingfive dimensionscurvature singularityblack hole thermodynamics
0
0 comments X

The pith

Five-dimensional singly rotating near-horizon solution in Einstein-Gauss-Bonnet gravity has finite curvature invariants for subcritical rotation.

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

The paper constructs an exact five-dimensional singly rotating near-horizon geometry in Einstein-Gauss-Bonnet gravity. It shows that the Gauss-Bonnet term eliminates the local curvature singularity that appears in pure Einstein gravity, resulting in finite curvature invariants throughout the spacetime when the rotation parameter is below a threshold determined by the Gauss-Bonnet coupling. This marks the first analytic example of such a regular singly rotating solution in this theory over a range of parameters. The analysis covers regular, singular, and marginal regimes in parameter space and examines thermodynamic properties, revealing that higher-derivative corrections regularize curvature but pose challenges to standard thermodynamic descriptions of Killing horizons.

Core claim

We construct a five-dimensional singly rotating near-horizon solution in Einstein-Gauss-Bonnet gravity. We show that the Gauss-Bonnet term removes the local curvature singularity, yielding finite curvature invariants throughout the spacetime, provided the rotation parameter remains below a certain value set by the Gauss-Bonnet coupling. To our knowledge, this is the first analytic example of a singly rotating five-dimensional solution in this framework with finite curvature invariants over a nontrivial region of parameter space. We analyze the geometry across this space, identifying regular, singular, and marginal regimes. Finally, we study the thermodynamic properties, finding that while hi

What carries the argument

The five-dimensional singly rotating near-horizon metric ansatz in Einstein-Gauss-Bonnet gravity, which permits an exact solution where the Gauss-Bonnet term cancels the curvature singularity for rotation parameters below a critical value.

If this is right

  • The spacetime exhibits finite curvature invariants when the rotation parameter is less than the value set by the Gauss-Bonnet coupling.
  • The parameter space divides into regular, singular, and marginal regimes based on the curvature behavior.
  • Higher-derivative corrections regularize local curvature but create challenges for the thermodynamic description of the Killing horizon.

Where Pith is reading between the lines

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

  • Similar regularization effects may appear in other higher-curvature theories if the same near-horizon ansatz applies.
  • The noted thermodynamic challenges point toward possible revisions in how entropy is defined for horizons in higher-derivative gravity.
  • Adding charge or additional rotation parameters could reveal whether the finite-curvature regime persists more generally.

Load-bearing premise

The construction assumes a specific metric ansatz for the singly rotating near-horizon geometry in five dimensions that allows an exact solution in the presence of the Gauss-Bonnet term.

What would settle it

Direct computation of curvature invariants for a rotation parameter value just below the critical threshold set by the Gauss-Bonnet coupling, checking whether the invariants stay finite everywhere.

read the original abstract

We construct a five-dimensional singly rotating near-horizon solution in Einstein-Gauss-Bonnet gravity. We show that the Gauss-Bonnet term removes the local curvature singularity, yielding finite curvature invariants throughout the spacetime, provided the rotation parameter remains below a certain value set by the Gauss-Bonnet coupling. To our knowledge, this is the first analytic example of a singly rotating five-dimensional solution in this framework with finite curvature invariants over a nontrivial region of parameter space. We analyze the geometry across this space, identifying regular, singular, and marginal regimes. Finally, we study the thermodynamic properties, finding that while higher-derivative corrections regularize the local curvature behavior, they also introduce unique challenges to the standard thermodynamic description of Killing 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

2 major / 1 minor

Summary. The paper constructs an exact five-dimensional singly rotating near-horizon solution in Einstein-Gauss-Bonnet gravity. It claims that the Gauss-Bonnet term removes the local curvature singularity, producing finite curvature invariants throughout the spacetime when the rotation parameter lies below a bound determined by the Gauss-Bonnet coupling. The work analyzes regular, singular, and marginal regimes in parameter space and examines thermodynamic properties of the resulting Killing horizons.

Significance. An analytic singly rotating near-horizon geometry with finite curvature invariants in EGB gravity would be a useful explicit example in higher-curvature gravity, especially if the regularity holds beyond a narrow ansatz. The thermodynamic analysis also highlights potential tensions between higher-derivative corrections and standard horizon thermodynamics. However, the significance is limited by the reliance on a fixed metric ansatz whose generality is not demonstrated.

major comments (2)
  1. [construction of the metric ansatz and solution] The central regularity claim (finite curvature invariants when rotation parameter < bound set by GB coupling) is obtained only inside the chosen metric ansatz for the singly rotating near-horizon geometry. No derivation is given showing that this ansatz is the most general form compatible with the isometries of a 5D singly rotating near-horizon geometry, nor is it shown that a more general ansatz (additional radial functions or cross terms allowed by the symmetries) would still admit regular solutions. This makes the statement that the GB term “removes the local curvature singularity” potentially ansatz-dependent rather than a property of the theory.
  2. [thermodynamic properties section] The thermodynamic analysis identifies challenges to the standard description of Killing horizons, but it is unclear how these challenges depend on the specific ansatz or whether they persist under a more general metric compatible with the same symmetries.
minor comments (1)
  1. [parameter space analysis] Clarify the precise range of the rotation parameter relative to the GB coupling for which invariants remain finite; explicit expressions or plots would help.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the detailed report and the recommendation for major revision. We address the two major comments below. We agree that our results are obtained within a specific metric ansatz and will revise the manuscript to state this limitation explicitly, without claiming generality beyond the ansatz used.

read point-by-point responses

  1. Referee: The central regularity claim (finite curvature invariants when rotation parameter < bound set by GB coupling) is obtained only inside the chosen metric ansatz for the singly rotating near-horizon geometry. No derivation is given showing that this ansatz is the most general form compatible with the isometries of a 5D singly rotating near-horizon geometry, nor is it shown that a more general ansatz (additional radial functions or cross terms allowed by the symmetries) would still admit regular solutions. This makes the statement that the GB term “removes the local curvature singularity” potentially ansatz-dependent rather than a property of the theory.

    Authors: We accept this observation. The metric ansatz was selected to be compatible with the isometries expected for a singly rotating near-horizon geometry (stationary, axisymmetric with the appropriate Killing vectors), following standard constructions in the literature for near-horizon limits. The solution and the finiteness of curvature invariants are demonstrated explicitly within this ansatz for rotation parameters below the bound set by the Gauss-Bonnet coupling. We do not provide a classification proving this is the most general ansatz allowed by the symmetries, nor do we solve the field equations for a broader family. We will revise the abstract, introduction, and conclusion to state clearly that the regularity result holds for the constructed family of solutions within the adopted ansatz, and that extension to more general metrics remains open. revision: partial

  2. Referee: The thermodynamic analysis identifies challenges to the standard description of Killing horizons, but it is unclear how these challenges depend on the specific ansatz or whether they persist under a more general metric compatible with the same symmetries.

    Authors: The thermodynamic quantities (surface gravity, entropy, etc.) and the identified tensions with standard horizon thermodynamics are computed directly from the Killing horizons of the explicit metric we obtained. Because the metric is tied to the ansatz, these features are specific to the solutions presented. We agree that a different metric ansatz satisfying the same isometries could yield different thermodynamic relations. We will add a clarifying paragraph in the thermodynamics section noting that the reported challenges apply to the geometries constructed here and may not be universal. revision: partial

standing simulated objections not resolved
  • Demonstrating that the chosen ansatz is the most general metric compatible with the isometries of a 5D singly rotating near-horizon geometry, or that regularity persists for arbitrary additional functions allowed by the symmetries.

Circularity Check

0 steps flagged

No circularity: direct construction from assumed ansatz yields independent solution properties.

full rationale

The paper constructs an exact solution by adopting a specific metric ansatz for the singly rotating near-horizon geometry and solving the Einstein-Gauss-Bonnet field equations within it. The regularity of curvature invariants for rotation parameters below a GB-coupling bound follows directly from the resulting explicit metric functions and their curvature scalars, without any reduction of the output to fitted parameters, self-definitions, or load-bearing self-citations. The ansatz is an explicit modeling choice (standard for exact solutions in modified gravity), and the thermodynamic analysis likewise derives from the obtained geometry. No step equates a claimed prediction or uniqueness result to its own input by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Based on the abstract only. The theory is Einstein-Gauss-Bonnet, which is a standard extension, but the specific solution is new. No new entities postulated. The GB coupling acts as a free parameter setting the regularity threshold.

free parameters (2)
  • Gauss-Bonnet coupling
    Sets the threshold value for the rotation parameter below which curvature invariants remain finite.
  • rotation parameter
    Must remain below a value determined by the coupling for the solution to be regular.
axioms (1)
  • domain assumption Existence of an exact solution to the field equations under the near-horizon singly rotating ansatz in 5D EGB gravity
    The paper constructs the solution assuming such an ansatz works.

pith-pipeline@v0.9.1-grok · 5661 in / 1347 out tokens · 34625 ms · 2026-06-30T20:02:29.841693+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

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

  1. Off-shell Hessian thermodynamic stability of higher-curvature black holes

    gr-qc 2026-06 unverdicted novelty 6.0

    An off-shell Hessian criterion H = S'_W(r_h) T'(r_h) governs thermodynamic stability of higher-curvature black holes, recovering the temperature-slope rule on physical branches and producing mean-field critical exponents.

Reference graph

Works this paper leans on

30 extracted references · 18 linked inside Pith · cited by 1 Pith paper

  1. [1]

    The Einstein tensor and its generalizations,

    D. Lovelock, “The Einstein tensor and its generalizations,” J. Math. Phys.12, 498 (1971)

    1971

  2. [2]

    The four-dimensionality of space and the einstein tensor,

    D. Lovelock, “The four-dimensionality of space and the einstein tensor,” J. Math. Phys. 13, 874 (1972)

    1972

  3. [3]

    Curvature Squared Terms and String Theories,

    B. Zwiebach, “Curvature Squared Terms and String Theories,” Phys. Lett. B156, 315 (1985)

    1985

  4. [4]

    String Generated Gravity Models,

    D. G. Boulware and S. Deser, “String Generated Gravity Models,” Phys. Rev. Lett.55, 2656 (1985)

    1985

  5. [5]

    Gauss-Bonnet black holes in AdS spaces,

    R. G. Cai, “Gauss-Bonnet black holes in AdS spaces,” Phys. Rev. D65, 084014 (2002), [arXiv:hep-th/0109133 [hep-th]]

    Pith/arXiv arXiv 2002

  6. [6]

    Black Holes in Higher Dimensional Space-Times,

    R. C. Myers and M. J. Perry, “Black Holes in Higher Dimensional Space-Times,” Annals Phys.172, 304 (1986)

    1986

  7. [7]

    Rotating black holes with equal- magnitude angular momenta ind= 5 Einstein-Gauss-Bonnet theory,

    Y. Brihaye, B. Kleihaus, J. Kunz and E. Radu, “Rotating black holes with equal- magnitude angular momenta ind= 5 Einstein-Gauss-Bonnet theory,” JHEP11, 098 (2010), [arXiv:1010.0860 [hep-th]]

    Pith/arXiv arXiv 2010

  8. [8]

    Phases of Rotating Black Objects ind= 5 Ein- stein–Gauss–Bonnet Theory,

    B. Kleihaus, J. Kunz and E. Radu, “Phases of Rotating Black Objects ind= 5 Ein- stein–Gauss–Bonnet Theory,” Universe9, 156 (2023), [arXiv:2303.12471 [gr-qc]]

    arXiv 2023

  9. [9]

    The Extreme Kerr throat geometry: A Vacuum analog of AdS(2) x S**2,

    J. M. Bardeen and G. T. Horowitz, “The Extreme Kerr throat geometry: A Vacuum analog of AdS(2) x S**2,” Phys. Rev. D60, 104030 (1999), [arXiv:hep-th/9905099 [hep-th]]

    Pith/arXiv arXiv 1999

  10. [10]

    Near-horizon symmetries of extremal black holes,

    H. K. Kunduri, J. Lucietti and H. S. Reall, “Near-horizon symmetries of extremal black holes,” Class. Quant. Grav.24, 4169 (2007), [arXiv:0705.4214 [hep-th]]

    Pith/arXiv arXiv 2007

  11. [11]

    A Classification of near-horizon geometries of extremal vacuum black holes,

    H. K. Kunduri and J. Lucietti, “A Classification of near-horizon geometries of extremal vacuum black holes,” J. Math. Phys.50(2009) 082502, [arXiv:0806.2051 [hep-th]]

    Pith/arXiv arXiv 2009

  12. [12]

    Classification of near-horizon geometries of extremal black holes,

    H. K. Kunduri and J. Lucietti, “Classification of near-horizon geometries of extremal black holes,” Living Rev. Rel.16, 8 (2013), [arXiv:1306.2517 [hep-th]]

    Pith/arXiv arXiv 2013

  13. [13]

    Single-rotating five-dimensional near-horizon extremal geometry in general relativity,

    K. Hajian, “Single-rotating five-dimensional near-horizon extremal geometry in general relativity,” Phys. Rev. D109, no.4, 4, (2024) [arXiv:2307.16534 [gr-qc]]

    arXiv 2024

  14. [14]

    Black hole entropy function and the attractor mechanism in higher derivative gravity,

    A. Sen, “Black hole entropy function and the attractor mechanism in higher derivative gravity,” JHEP09, 038 (2005), [arXiv:hep-th/0506177 [hep-th]]

    Pith/arXiv arXiv 2005

  15. [15]

    Black Holes in String Theory,

    C. G. Callan, Jr., R. C. Myers and M. J. Perry, “Black Holes in String Theory,” Nucl. Phys. B311, 673 (1989)

    1989

  16. [16]

    The Kerr/CFT Correspondence,

    M. Guica, T. Hartman, W. Song, A. Strominger, “The Kerr/CFT Correspondence,” Phys. Rev.D80, 124008 (2009), [arXiv:0809.4266 [hep-th]]

    Pith/arXiv arXiv 2009

  17. [17]

    NHEG Mechanics: Laws of Near Horizon Extremal Geometry (Thermo)Dynamics,

    K. Hajian, A. Seraj and M. M. Sheikh-Jabbari, “NHEG Mechanics: Laws of Near Horizon Extremal Geometry (Thermo)Dynamics,” JHEP03, 014 (2014), [arXiv:1310.3727 [hep- th]]. 11

    Pith/arXiv arXiv 2014

  18. [18]

    Near Horizon Extremal Geometry Pertur- bations: Dynamical Field Perturbations vs. Parametric Variations,

    K. Hajian, A. Seraj and M. M. Sheikh-Jabbari, “Near Horizon Extremal Geometry Pertur- bations: Dynamical Field Perturbations vs. Parametric Variations,” JHEP10, 111 (2014), [arXiv:1407.1992 [hep-th]]

    Pith/arXiv arXiv 2014

  19. [19]

    Black hole entropy is Noether charge

    R. M. Wald, “Black hole entropy is Noether charge”, Phys. Rev. D48, 3427 (1993), [arXiv:gr-qc/9307038 [gr-qc]]

    Pith/arXiv arXiv 1993

  20. [20]

    Some properties of Noether charge and a proposal for dynamical black hole entropy

    V. Iyer, R. M. Wald, “Some properties of Noether charge and a proposal for dynamical black hole entropy”, Phys. Rev. D50, 846 (1994), [arXiv:gr-qc/9403028 [gr-qc]]

    Pith/arXiv arXiv 1994

  21. [21]

    A Comparison of Noether charge and Euclidean methods for computing the entropy of stationary black holes,

    V. Iyer and R. M. Wald, “A Comparison of Noether charge and Euclidean methods for computing the entropy of stationary black holes,” Phys. Rev. D52, 4430 (1995), [gr- qc/9503052 [gr-qc]]

    arXiv 1995

  22. [22]

    Solution Phase Space and Conserved Charges: A General Formulation for Charges Associated with Exact Symmetries,

    K. Hajian and M. M. Sheikh-Jabbari, “Solution Phase Space and Conserved Charges: A General Formulation for Charges Associated with Exact Symmetries,” Phys. Rev. D93, no.4, 044074 (2016), [arXiv:1512.05584 [hep-th]]

    arXiv 2016

  23. [23]

    Revisiting Conserved Charges in Higher Cur- vature Gravitational Theories,

    M. Ghodrati, K. Hajian and M. R. Setare, “Revisiting Conserved Charges in Higher Cur- vature Gravitational Theories,” Eur. Phys. J. C76, no.12, 701 (2016), [arXiv:1606.04353 [hep-th]]

    Pith/arXiv arXiv 2016

  24. [24]

    First law of black hole thermodynamics and Smarr formula with a cosmological constant,

    K. Hajian, H. ¨Oz¸ sahin and B. Tekin, “First law of black hole thermodynamics and Smarr formula with a cosmological constant,” Phys. Rev. D104, no.4, 044024 (2021), [arXiv:2103.10983 [gr-qc]]

    arXiv 2021

  25. [25]

    A Universal Smarr Formula via Coupling Constants,

    K. Hajian, B. Tekin and O. Ucanok, “A Universal Smarr Formula via Coupling Constants,” [arXiv:2511.22558 [gr-qc]]

    Pith/arXiv arXiv

  26. [26]

    On Thermodynamics and Phase Space of Near Horizon Extremal Geometries,

    K. Hajian, “On Thermodynamics and Phase Space of Near Horizon Extremal Geometries,” [arXiv:1508.03494 [gr-qc]]

    Pith/arXiv arXiv

  27. [27]

    Extremal Rotating Black Holes in the Near-Horizon Limit: Phase Space and Symmetry Algebra,

    G. Comp` ere, K. Hajian, A. Seraj and M. M. Sheikh-Jabbari, “Extremal Rotating Black Holes in the Near-Horizon Limit: Phase Space and Symmetry Algebra,” Phys. Lett. B 749, 443-447 (2015), [arXiv:1503.07861 [hep-th]]

    Pith/arXiv arXiv 2015

  28. [28]

    Wiggling Throat of Extremal Black Holes,

    G. Comp` ere, K. Hajian, A. Seraj and M. M. Sheikh-Jabbari, “Wiggling Throat of Extremal Black Holes,” JHEP10, 093 (2015), [arXiv:1506.07181 [hep-th]]

    Pith/arXiv arXiv 2015

  29. [29]

    Extreme Kerr black hole microstates with horizon fluff,

    K. Hajian, M. M. Sheikh-Jabbari and H. Yavartanoo, “Extreme Kerr black hole microstates with horizon fluff,” Phys. Rev. D98, no.2, 026025 (2018), [arXiv:1708.06378 [hep-th]]

    Pith/arXiv arXiv 2018

  30. [30]

    Coupling Constants as Conserved Charges in Black Hole Ther- modynamics,

    K. Hajian and B. Tekin, “Coupling Constants as Conserved Charges in Black Hole Ther- modynamics,” Phys. Rev. Lett.132, no.19, 191401 (2024), [arXiv:2309.07634 [gr-qc]]. 12

    arXiv 2024