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arxiv: 2606.18432 · v2 · pith:QKR74ZWJnew · submitted 2026-06-16 · ✦ hep-th · gr-qc

Thermodynamic Stability and Fluctuations of the (2+1)-dimensional GMG Warped Black Hole

Tsvetan Vetsov This is my paper

Pith reviewed 2026-06-26 23:10 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords thermodynamic stabilitywarped black holeGeneral Massive Gravitythermal fluctuationsDavies phase transitionRuppeiner geometryangular momentum trajectories
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The pith

The (2+1)-dimensional GMG warped black hole is thermodynamically unstable, with its heat capacities revealing Davies phase-transition curves and its angular momentum changing continuously during relaxation processes.

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

This paper examines the thermodynamic properties of the warped black hole solution in three-dimensional General Massive Gravity. It establishes that the black hole is unstable by analyzing the sign changes and divergences in its admissible heat capacities, which also mark the locations of Davies phase-transition curves. The analysis then moves to stochastic fluctuations by applying a modified finite-time nonequilibrium version of Ruppeiner's theory to isentropic and isoenergetic processes. From this framework the paper derives exact on-shell trajectories for the black hole's angular momentum in thermodynamic state space and computes the associated thermodynamic lengths that characterize relaxation between macrostates. The geodesic equations in this space admit no constant-angular-momentum solutions, implying that the black hole's angular momentum must vary continuously throughout any such relaxation process.

Core claim

We demonstrate that the black hole is thermodynamically unstable and identify the nontrivial Davies phase-transition curves from the behavior of its admissible heat capacities. Going beyond the classical stability analysis, we study thermal fluctuations within a modified finite-time nonequilibrium extension of Ruppeiner's Hessian-based fluctuation theory. For a class of isentropic and isoenergetic processes, we derive exact on-shell angular momentum trajectories in the thermodynamic state space and compute the corresponding thermodynamic lengths. These quantities characterize relaxation processes between macrostates and provide an estimate of the associated relaxation times. Furthermore, we

What carries the argument

Modified finite-time nonequilibrium extension of Ruppeiner's Hessian-based fluctuation theory, used to obtain on-shell angular momentum trajectories and thermodynamic lengths in the state space.

If this is right

  • The black hole is thermodynamically unstable.
  • Nontrivial Davies phase-transition curves appear from the admissible heat capacities.
  • Exact on-shell angular momentum trajectories exist for isentropic and isoenergetic processes.
  • Thermodynamic lengths supply estimates of the associated relaxation times.
  • Angular momentum changes continuously because the geodesic equations lack constant-angular-momentum solutions.

Where Pith is reading between the lines

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

  • The same modified fluctuation framework could be tested on other three-dimensional black hole solutions whose metrics reduce to the warped AdS3 limit.
  • Continuous angular-momentum variation during relaxation may impose additional constraints when matching thermodynamic lengths to dynamical timescales in the spacetime.
  • The derived relaxation-time estimates offer a concrete quantity that could be compared against numerical evolution of perturbed GMG geometries.

Load-bearing premise

The modified finite-time nonequilibrium extension of Ruppeiner's fluctuation theory applies to the GMG warped black hole and yields physically meaningful thermodynamic lengths and relaxation times.

What would settle it

Explicit computation of the heat capacities showing no sign changes or divergences at the claimed Davies curves, or direct solution of the geodesic equations admitting constant-angular-momentum paths, would falsify the instability and trajectory results.

read the original abstract

We investigate the thermodynamic stability and the stochastic thermal fluctuations of the warped black hole solution in three-dimensional General Massive Gravity. We demonstrate that the black hole is thermodynamically unstable and identify the nontrivial Davies phase-transition curves from the behavior of its admissible heat capacities. Going beyond the classical stability analysis, we study thermal fluctuations within a modified finite-time nonequilibrium extension of Ruppeiner's Hessian-based fluctuation theory. For a class of isentropic and isoenergetic processes, we derive exact on-shell angular momentum trajectories in the thermodynamic state space and compute the corresponding thermodynamic lengths. These quantities characterize relaxation processes between macrostates and provide an estimate of the associated relaxation times. Furthermore, we show that the thermodynamic geodesic equations do not admit constant-angular-momentum solutions, suggesting a continuous change of the black hole's angular momentum. Our results consistently reproduce the warped AdS$_3$ black hole limit of Topological Massive Gravity.

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 / 0 minor

Summary. The manuscript investigates the thermodynamic stability and stochastic thermal fluctuations of the warped black hole in (2+1)-dimensional General Massive Gravity (GMG). It demonstrates thermodynamic instability, identifies nontrivial Davies phase-transition curves from admissible heat capacities, and extends the analysis using a modified finite-time nonequilibrium extension of Ruppeiner's Hessian-based fluctuation theory. For isentropic and isoenergetic processes, exact on-shell angular momentum trajectories in thermodynamic state space are derived, thermodynamic lengths are computed to characterize relaxation, and it is shown that the thermodynamic geodesic equations admit no constant-angular-momentum solutions. Results consistently reproduce the warped AdS3 black hole limit of Topological Massive Gravity (TMG).

Significance. If the modified Ruppeiner extension is rigorously justified for this system, the work strengthens understanding of classical thermodynamic stability in 3D massive gravity models and introduces concrete nonequilibrium quantities (trajectories, lengths, relaxation times) that could inform fluctuation dynamics. The reproduction of the TMG limit supplies a useful internal consistency check. The Davies-curve analysis appears comparatively robust, while the fluctuation claims depend critically on the validity of the extension.

major comments (1)
  1. [Abstract (and associated methods section on the extension)] The fluctuation results (exact on-shell angular momentum trajectories, thermodynamic lengths, relaxation times, and absence of constant-J geodesic solutions) rest on a modified finite-time nonequilibrium extension of Ruppeiner geometry whose applicability to the GMG warped black hole is not independently derived or bounded beyond the TMG reproduction; this directly affects whether the Hessian structure and finite-time effects remain controlled without hidden approximations.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript investigating the thermodynamic stability and fluctuations of the GMG warped black hole. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract (and associated methods section on the extension)] The fluctuation results (exact on-shell angular momentum trajectories, thermodynamic lengths, relaxation times, and absence of constant-J geodesic solutions) rest on a modified finite-time nonequilibrium extension of Ruppeiner geometry whose applicability to the GMG warped black hole is not independently derived or bounded beyond the TMG reproduction; this directly affects whether the Hessian structure and finite-time effects remain controlled without hidden approximations.

    Authors: The modified finite-time nonequilibrium extension is formulated at the level of the thermodynamic potentials and the Hessian of the entropy, using only the first law and the general structure of Ruppeiner geometry; it does not rely on model-specific features of GMG. The exact reproduction of all TMG warped AdS3 results (trajectories, lengths, and absence of constant-J solutions) constitutes a strong internal consistency check that would fail in the presence of uncontrolled approximations or hidden model dependence. Because the extension is applied identically to both theories and recovers the known TMG case without adjustment, we regard the applicability to the GMG warped black hole as justified by the same general thermodynamic framework. revision: no

Circularity Check

0 steps flagged

No significant circularity; derivations apply external framework to new metric

full rationale

The paper computes heat capacities, Davies curves, on-shell trajectories, thermodynamic lengths and relaxation times by direct substitution of the GMG warped metric into the (modified) Ruppeiner Hessian and geodesic equations. These steps are algebraic applications of the stated framework rather than redefinitions or fits that recover the inputs by construction. Reproduction of the TMG limit supplies an independent consistency check. No self-definitional equations, fitted-input predictions, or load-bearing self-citations that reduce the central claims to unverified prior results are present in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; the paper relies on the standard thermodynamic relations for black holes and the validity of the modified Ruppeiner framework, but no explicit free parameters, axioms, or invented entities are identifiable without the full text.

pith-pipeline@v0.9.1-grok · 5686 in / 1213 out tokens · 23422 ms · 2026-06-26T23:10:18.906806+00:00 · methodology

discussion (0)

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Reference graph

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