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arxiv: 2508.00203 · v2 · submitted 2025-07-31 · 🌀 gr-qc · hep-th

Quantum-Corrected Thermodynamics of Conformal Weyl Gravity Black Holes: GUP Effects and Phase Transitions

Erdem Sucu , Suat Dengiz , \.Izzet Sakall{\i} This is my paper

Pith reviewed 2026-05-19 01:16 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords Conformal Weyl GravityBlack Hole ThermodynamicsGeneralized Uncertainty PrincipleQuantum CorrectionsPhase TransitionsJoule-Thomson ExpansionMannheim-Kazanas Solution
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The pith

Quantum corrections from GUP and modified entropy change the thermodynamic phase structure of Mannheim-Kazanas black holes in conformal Weyl gravity.

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

The paper studies black hole thermodynamics in conformal Weyl gravity by applying the Mannheim-Kazanas solution and adding quantum corrections that matter near the Planck scale. It derives the Hawking temperature via the Hamilton-Jacobi tunneling method, which now carries explicit dependence on the conformal parameters beta, gamma, and k. The generalized uncertainty principle is used to suppress thermal radiation at small scales, while an exponentially corrected entropy supplies the full set of thermodynamic potentials. Heat capacity is shown to diverge at critical points that mark stable and unstable regions, and Joule-Thomson expansion displays inversion points separating cooling and heating regimes. These phase-transition features are controlled by the scale-dependent parameter gamma and do not appear in the corresponding general-relativity case.

Core claim

In the Mannheim-Kazanas geometry of conformal Weyl gravity, the combination of GUP-modified tunneling and exponentially corrected entropy produces a Hawking temperature with explicit conformal-parameter dependence, systematic suppression of radiation in the near-Planckian regime, diverging heat capacity that separates thermodynamic phases, and Joule-Thomson inversion points that shift with gamma, none of which occur for the Schwarzschild solution.

What carries the argument

GUP-modified Hamilton-Jacobi tunneling for temperature together with the exponentially corrected entropy model applied to the Mannheim-Kazanas black-hole solution.

If this is right

  • Heat capacity diverges at radii set by gamma, separating stable and unstable thermodynamic regions.
  • Joule-Thomson expansion exhibits distinct cooling and heating regimes whose inversion points move with the conformal parameters.
  • Thermal radiation is suppressed relative to the classical case once the black-hole mass approaches the Planck scale.
  • Gravitational redshift acquires a more complex radial profile than in the Schwarzschild geometry.

Where Pith is reading between the lines

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

  • The same correction scheme could be applied to rotating or charged solutions in conformal gravity to check whether the phase-transition pattern persists.
  • If the suppression of radiation survives in a more complete quantum treatment, it would affect estimates of black-hole lifetimes in any modified-gravity setting.
  • The absence of direct observational signals noted in the paper implies that the main value lies in providing controlled theoretical laboratories for quantum-gravity effects rather than in immediate astrophysical tests.

Load-bearing premise

The exponentially corrected entropy together with the GUP-modified Hamilton-Jacobi tunneling method correctly captures the leading quantum-gravitational corrections to Mannheim-Kazanas black-hole thermodynamics.

What would settle it

A recomputation of heat capacity or Joule-Thomson coefficient that yields no divergence or no parameter-dependent inversion points when the exponential entropy correction is removed would falsify the claimed modification of phase structure.

Figures

Figures reproduced from arXiv: 2508.00203 by Erdem Sucu, \.Izzet Sakall{\i}, Suat Dengiz.

Figure 1
Figure 1. Figure 1: FIG. 1. Density plot of the inertial energy [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Helmholtz free energy [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Gibbs free energy [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Heat capacity [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: presents a comprehensive visualization of the JTE coefficient µJ as a function of the event horizon radius rh for various values of the scale-dependent parameter γ, with fixed parameters β = 2 and k = 1. This plot elegantly illustrates the BH thermal response under isenthalpic expan￾sion conditions, where the sign of µJ serves as the crucial diagnostic: positive values indicate cooling phases during ex￾pan… view at source ↗
Figure 8
Figure 8. Figure 8: presents a comprehensive visualization of the gravitational redshift behavior in CWGBH geometry, illus￾trating how the redshift parameter z varies as a function of radial distance and the various CWG parameters. The plot reveals several distinctive features that distinguish CWG redshift from its GR counterpart: the presence of oscillatory behavior at intermediate distances due to the linear γr term, the mo… view at source ↗
read the original abstract

We investigate the thermodynamic properties of black holes in Conformal Weyl Gravity (CWG) using the Mannheim-Kazanas solution, with particular emphasis on quantum corrections that become significant near the Planck scale. Our analysis employs the Hamilton-Jacobi tunneling formalism to derive the Hawking temperature, revealing explicit contributions from the conformal parameters $\beta$, $\gamma$, and $k$ that lead to substantial deviations from the behavior of a Schwarzschild black hole. We incorporate quantum gravitational effects through the Generalized Uncertainty Principle, demonstrating systematic suppression of thermal radiation in the near-Planckian regime. Using an exponentially corrected entropy model, we compute the complete spectrum of QC thermodynamic potentials, including internal energy, pressure, heat capacity, and free energies. Our heat capacity analysis shows divergence behavior that separates stable and unstable regions, indicating possible thermodynamic transitions controlled by the scale-dependent parameter $\gamma$. The Joule-Thomson expansion analysis shows distinct cooling and heating regimes with inversion points that shift systematically with CWG parameters, capturing QC phase transitions absent in general relativity. We also examine gravitational redshift in CWG geometry, finding complex radial dependence that highlights modifications compared to the Schwarzschild case, although redshift alone cannot observationally distinguish CWG from Einstein's theory. Our results demonstrate that CWG offers a consistent framework for studying black hole thermodynamics beyond general relativity, with quantum corrections modifying phase structures in the near-Planckian regime, though these effects are not expected to yield direct observational consequences.

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 investigates thermodynamic properties of Mannheim-Kazanas black holes in Conformal Weyl Gravity, deriving a GUP-corrected Hawking temperature that includes explicit dependence on conformal parameters β, γ, and k. It adopts an exponentially corrected entropy model to compute internal energy, pressure, heat capacity, and free energies, reporting divergences in heat capacity that separate stable and unstable phases and Joule-Thomson inversion points that shift with the CWG parameters. Gravitational redshift is also examined, with the overall claim that quantum corrections modify phase structures in the near-Planckian regime within a consistent framework beyond general relativity.

Significance. If the central derivations hold after addressing the foundational assumptions, the work would extend black-hole thermodynamics to conformal gravity with controlled quantum corrections, providing concrete expressions for how scale-dependent parameters alter stability and expansion behavior near the Planck scale. The explicit inclusion of GUP suppression and parameter-dependent inversion points offers falsifiable predictions within the model, though the paper itself notes the absence of direct observational signatures.

major comments (2)
  1. [Abstract / entropy model] Abstract and the section introducing the entropy model: the exponentially corrected entropy S = A/4 + exp(−A/4) together with the GUP-modified Hamilton-Jacobi temperature are inserted directly into the thermodynamic potentials for the Mannheim-Kazanas metric. No re-derivation from the Wald Noether charge of the Weyl-squared action is provided; such a charge generally yields additional terms proportional to β and γ that would shift the locations of heat-capacity divergences and Joule-Thomson points, making this assumption load-bearing for the reported phase-transition structure.
  2. [Heat capacity and Joule-Thomson analysis] Heat-capacity and Joule-Thomson sections: the temperature formula already contains β, γ, k and the GUP parameter; the subsequent divergences and inversion points are then expressed in terms of the same parameters. This raises the possibility that the claimed 'phase transitions' largely re-express the input parameter dependence rather than constituting independent emergent phenomena, which must be clarified by explicit limiting-case checks against the Schwarzschild or pure Mannheim-Kazanas thermodynamics.
minor comments (1)
  1. [Redshift discussion] The abstract states that redshift 'cannot observationally distinguish CWG from Einstein's theory' yet reports 'complex radial dependence'; a brief quantitative comparison of the redshift factor to the Schwarzschild case would improve clarity without altering the central claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below, indicating the revisions we will incorporate.

read point-by-point responses

  1. Referee: [Abstract / entropy model] Abstract and the section introducing the entropy model: the exponentially corrected entropy S = A/4 + exp(−A/4) together with the GUP-modified Hamilton-Jacobi temperature are inserted directly into the thermodynamic potentials for the Mannheim-Kazanas metric. No re-derivation from the Wald Noether charge of the Weyl-squared action is provided; such a charge generally yields additional terms proportional to β and γ that would shift the locations of heat-capacity divergences and Joule-Thomson points, making this assumption load-bearing for the reported phase-transition structure.

    Authors: We appreciate the referee highlighting this foundational point. The exponentially corrected entropy is employed as a phenomenological model to capture quantum effects in the near-Planckian regime, consistent with prior literature on GUP-corrected thermodynamics. We acknowledge that a complete Wald Noether charge derivation for the Weyl-squared action would generally produce additional contributions involving β and γ. Our focus remains on the application of GUP and exponential corrections to the given Mannheim-Kazanas metric. In the revised manuscript we will add a clarifying discussion of this modeling choice, its scope, and relevant references to modified-gravity entropy calculations, while noting that the reported phase features result from the interplay of the metric parameters and the correction terms. revision: partial

  2. Referee: [Heat capacity and Joule-Thomson analysis] Heat-capacity and Joule-Thomson sections: the temperature formula already contains β, γ, k and the GUP parameter; the subsequent divergences and inversion points are then expressed in terms of the same parameters. This raises the possibility that the claimed 'phase transitions' largely re-express the input parameter dependence rather than constituting independent emergent phenomena, which must be clarified by explicit limiting-case checks against the Schwarzschild or pure Mannheim-Kazanas thermodynamics.

    Authors: We thank the referee for this observation. To establish that the divergences and inversion points reflect genuine emergent behavior arising from the quantum corrections rather than direct re-expression of the input parameters, we will include explicit limiting-case analyses in the revised manuscript. These will recover the Schwarzschild limit and the pure Mannheim-Kazanas thermodynamics (with and without GUP) and demonstrate the corresponding shifts or disappearance of the heat-capacity divergences and Joule-Thomson points, thereby clarifying the independent role of the quantum corrections. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard application of assumed corrections to given metric

full rationale

The paper takes the Mannheim-Kazanas solution as input, applies the GUP-modified Hamilton-Jacobi method to obtain temperature (with explicit β, γ, k dependence), adopts an exponentially corrected entropy model, and computes thermodynamic potentials and their derivatives to locate heat-capacity divergences and Joule-Thomson points. These calculations produce results that depend on the input parameters and assumed forms but are not equivalent to the inputs by construction. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations are exhibited in the abstract or described chain. The study of how conformal parameters control phase structure is the intended content rather than a tautology.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the Mannheim-Kazanas solution as the background geometry, the validity of the Hamilton-Jacobi tunneling method with GUP, and the choice of an exponentially corrected entropy; these are modeling inputs rather than derived quantities.

free parameters (2)
  • conformal parameters β, γ, k
    Parameters appearing in the Mannheim-Kazanas metric that control deviations from Schwarzschild geometry and enter all thermodynamic expressions.
  • GUP deformation parameter
    Parameter controlling the strength of quantum corrections in the generalized uncertainty principle; its value is not fixed by the paper.
axioms (2)
  • domain assumption The Mannheim-Kazanas metric solves the field equations of conformal Weyl gravity.
    Invoked at the outset to define the black-hole spacetime.
  • domain assumption The Hamilton-Jacobi tunneling formalism remains valid when supplemented by the generalized uncertainty principle.
    Used to obtain the quantum-corrected Hawking temperature.

pith-pipeline@v0.9.0 · 5801 in / 1499 out tokens · 50208 ms · 2026-05-19T01:16:55.365043+00:00 · methodology

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Lean theorems connected to this paper

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

    Relation between the paper passage and the cited Recognition theorem.

    We employ the Hamilton-Jacobi tunneling formalism to derive the Hawking temperature... incorporate quantum gravitational effects through the Generalized Uncertainty Principle... Using an exponentially corrected entropy model S = S0 + e^{-S0}

  • IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    heat capacity analysis shows divergence behavior that separates stable and unstable regions... Joule-Thomson expansion analysis shows distinct cooling and heating regimes with inversion points

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Reference graph

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