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arxiv: 2606.10647 · v1 · pith:KLKWPSQRnew · submitted 2026-06-09 · 🌀 gr-qc · hep-th· quant-ph

Hawking-Page phase transition for pure Lovelock black holes

Nitesh K. Dubey , Sanved Kolekar This is my paper

Pith reviewed 2026-06-27 12:35 UTC · model grok-4.3

classification 🌀 gr-qc hep-thquant-ph
keywords Hawking-Page transitionpure Lovelock gravityRuppeiner geometryAdS black holesthermodynamic phase transitionsscalar curvatureneutral black holesgrand canonical ensemble
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The pith

In pure Lovelock gravity the normalized Ruppeiner curvature at the Hawking-Page transition for neutral black holes is a constant fixed only by spacetime dimension.

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

The paper examines static spherically symmetric AdS black holes in pure Lovelock gravity and shows that the normalized Ruppeiner scalar curvature at the Hawking-Page phase transition equals a universal constant that depends only on dimension for the neutral case. This holds for any order of the Lovelock polynomial and reduces to the Einstein result in the appropriate limit. The relation between the minimum temperature and the transition temperature is altered by a dimension- and order-dependent factor compared with Einstein gravity. For charged black holes in the grand canonical ensemble the universality survives in Einstein gravity under stated conditions but is lost in higher-order Lovelock theories, where the curvature depends on pressure and potential yet approaches the constant in large-pressure limits.

Core claim

The normalized Ruppeiner scalar curvature at the Hawking-Page phase transition is a universal constant depending only on the spacetime dimension for electromagnetically neutral black holes in pure Lovelock theories. The same normalized curvature remains constant for charged static spherically symmetric black holes in the grand canonical ensemble when restricted to Einstein gravity, whereas in general pure Lovelock theories it depends on thermodynamic parameters such as pressure and electrostatic potential, asymptotically approaching a constant in the large-pressure or simultaneous large-potential and large-pressure limits.

What carries the argument

Normalized Ruppeiner scalar curvature evaluated exactly at the Hawking-Page transition temperature for static spherically symmetric AdS solutions.

If this is right

  • The minimum temperature coincides with the HP transition temperature in Einstein gravity but acquires a dimension- and order-dependent factor in higher pure Lovelock theories.
  • For charged AdS black holes the two temperatures differ by a simple dimension-dependent factor in general relativity but lose any universal relation in higher Lovelock theories.
  • The normalized scalar curvature at the HP transition is independent of the Lovelock order for neutral black holes.
  • Even for charged black holes the curvature remains constant in the Einstein case under appropriate grand-canonical conditions.

Where Pith is reading between the lines

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

  • The dimension-only dependence may reflect a geometric property of the transition that is insensitive to the order of curvature corrections.
  • Analogous computations could be performed for rotating or higher-dimensional Lovelock solutions to test whether the constancy persists.
  • In the AdS/CFT setting the constant might correspond to a universal feature of the dual thermal phase transition.

Load-bearing premise

The standard definitions and ensembles used for the Hawking-Page transition and Ruppeiner geometry in Einstein gravity apply unchanged to the static spherically symmetric solutions of pure Lovelock gravity.

What would settle it

An explicit calculation for a pure Lovelock theory of order k greater than 1 in fixed dimension d showing that the value of the normalized Ruppeiner curvature at the Hawking-Page point changes with k.

Figures

Figures reproduced from arXiv: 2606.10647 by Nitesh K. Dubey, Sanved Kolekar.

Figure 1
Figure 1. Figure 1: The above figure shows the plots for the Gibbs free energy vs temperature. In panels [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The above plots depict the dependence of the normalized Ruppeiner scalar curvature on the electric potential [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
read the original abstract

We investigate the thermodynamic properties of static, spherically symmetric Anti-de Sitter (AdS) black holes, focusing on the interplay between characteristic temperatures, as well as on the universality of Ruppeiner scalar curvature at the Hawking-Page (HP) phase transition. In particular, we study the relation between the minimum temperature and the HP phase transition temperature for static, spherically symmetric AdS black holes in pure Lovelock gravity. For the electromagnetically neutral case in Einstein gravity, the minimum temperature in $(d+1)$ dimensions coincides with the HP transition temperature in $d$ dimensions, while in higher pure Lovelock theories this relation is modified by a dimension- and order-dependent factor, reducing to the Einstein result in appropriate limits. For charged AdS black holes, in the grand canonical ensemble, in general relativity, the two temperatures differ by a simple dimension-dependent factor, whereas no universal relation persists in higher curvature pure Lovelock theories. We further analyze the normalized Ruppeiner scalar curvature at the HP transition and show that it is a universal constant depending only on the spacetime dimension for electromagnetically neutral black holes in pure Lovelock theories. The normalized scalar curvature remains a constant, under appropriate conditions, even for the charged static spherically symmetric black holes in the grand canonical ensemble for the Einstein theory case, whereas in general pure Lovelock theories it depends on thermodynamic parameters such as pressure and electrostatic potential, asymptotically approaching a constant in the large-pressure or simultaneous large-potential and large-pressure limits.

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 / 1 minor

Summary. The manuscript investigates thermodynamic properties of static spherically symmetric AdS black holes in pure Lovelock gravity, with emphasis on relations between the minimum temperature and the Hawking-Page (HP) transition temperature, as well as the behavior of the normalized Ruppeiner scalar curvature at the HP transition. For neutral black holes, the minimum-to-HP temperature relation is modified by a dimension- and Lovelock-order-dependent factor relative to Einstein gravity (recovering the Einstein case in appropriate limits). For charged cases in the grand canonical ensemble, no universal relation holds in general Lovelock theories. The central result is that the normalized Ruppeiner scalar curvature evaluated at the HP transition is a universal constant depending only on spacetime dimension for electromagnetically neutral solutions; for charged solutions it depends on pressure and potential but approaches a constant in certain large-parameter limits.

Significance. If the derivations hold, the work establishes that a key universal feature of thermodynamic geometry (the normalized Ruppeiner curvature at the HP point) extends from Einstein gravity to pure Lovelock theories for neutral black holes, while the temperature relations acquire controlled modifications. This provides a concrete test of how higher-curvature corrections affect thermodynamic universality without introducing free parameters beyond the Lovelock order and dimension. The explicit reduction to Einstein results in limits is a strength.

minor comments (1)
  1. The abstract and title refer to 'pure Lovelock black holes' but the text should explicitly state the range of Lovelock orders k considered and confirm that the Wald entropy polynomial is used throughout the Ruppeiner construction.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our work and for recommending acceptance. No major comments were raised in the report.

Circularity Check

0 steps flagged

No circularity; derivations self-contained from Lovelock thermodynamics

full rationale

The abstract and context present the normalized Ruppeiner curvature at the HP transition as computed from the Wald entropy and first law in pure Lovelock gravity, yielding a dimension-dependent constant for neutral cases. No quoted equations reduce the result to a fit, self-citation chain, or imported ansatz by construction; the universality is stated as an outcome of the modified entropy polynomial rather than presupposed. The central claim remains independent of the input data or prior author results.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract only, so ledger is incomplete; builds on standard black hole thermodynamics extended to Lovelock gravity with theory parameters such as dimension and Lovelock order.

axioms (2)
  • domain assumption Black hole thermodynamics and Ruppeiner geometry apply to static spherically symmetric solutions in pure Lovelock gravity
    The paper extends standard thermodynamic relations and geometric thermodynamics from Einstein gravity to higher-order Lovelock theories.
  • domain assumption The grand canonical ensemble is well-defined for charged black holes in these theories
    Used for the charged case analysis without additional justification visible in the abstract.

pith-pipeline@v0.9.1-grok · 5804 in / 1406 out tokens · 29596 ms · 2026-06-27T12:35:17.854105+00:00 · methodology

discussion (0)

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Reference graph

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