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arxiv: 2606.13167 · v1 · pith:UABNSTYEnew · submitted 2026-06-11 · 🌀 gr-qc · hep-th

Thermodynamics of polymerized vacuum regular black holes in anti-de Sitter spacetime

Sepideh Bakhoda , Ioannis Soranidis This is my paper

Pith reviewed 2026-06-27 06:25 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords regular black holesanti-de Sitter spacetimeHawking-Page transitionextended phase spacethermodynamicsvacuum solutionsde Sitter coreanti-de Sitter core
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The pith

Regular black holes in anti-de Sitter space undergo Hawking-Page transitions set by how each core deforms the outer horizon.

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

This paper derives a family of vacuum regular black holes in asymptotically anti-de Sitter spacetime by reducing the dynamics to independent radial shells. It establishes that the static geometry is uniquely fixed by the mass parameter for a given reconstruction function. The thermodynamic analysis shows that the free energy of these black holes crosses that of thermal anti-de Sitter space at a transition point whose location depends on the core type. The differences between de Sitter-core and anti-de Sitter-core models trace to how each core alters the physical outer-horizon branch rather than to regularity in general. In the limit of large anti-de Sitter radius the de Sitter-core solutions reach the transition at higher temperature.

Core claim

Within the deparameterized formulation the dynamics factorizes across radial shells, yielding a Birkhoff-type uniqueness theorem: for fixed reconstruction function and cosmological constant the static solution is determined solely by its mass. Several explicit regular geometries are constructed, some possessing de Sitter cores and others anti-de Sitter cores. Their extended-phase-space thermodynamics are computed, revealing that the dominant phase transition occurs when the black-hole free energy equals the free energy of the thermal anti-de Sitter background. The regularization modifies the quantitative value of this transition temperature through its effect on the outer-horizon branch and

What carries the argument

The factorized shell Hamiltonian arising from the deparameterized dynamics, which enforces a Birkhoff-type uniqueness property for the static geometry given fixed reconstruction function and cosmological constant.

If this is right

  • The Hawking-Page transition remains the dominant transition for all models in the class.
  • The transition temperature is shifted quantitatively by the core-induced deformation of the outer-horizon branch.
  • In the large anti-de Sitter radius regime, de Sitter-core solutions reach the transition at higher temperature than anti-de Sitter-core solutions.
  • The relative ordering of the two classes can reverse when the anti-de Sitter radius approaches its lower admissible value.

Where Pith is reading between the lines

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

  • Thermodynamic observables may distinguish different choices of regularization function through their effect on horizon-branch endpoints.
  • The same core-deformation mechanism could be examined in asymptotically flat or de Sitter settings to test whether the Hawking-Page dominance persists.
  • Comparison of free-energy curves across multiple reconstruction functions would map how internal structure controls global thermodynamic behavior.

Load-bearing premise

The auxiliary dust field is used exclusively to define an internal time coordinate and does not contribute any stress-energy to the spacetime.

What would settle it

A direct computation for one of the explicit models in which the black-hole free energy never crosses the thermal anti-de Sitter free energy would falsify the claim that the dominant transition is of Hawking-Page type.

Figures

Figures reproduced from arXiv: 2606.13167 by Ioannis Soranidis, Sepideh Bakhoda.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p024_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗
read the original abstract

We derive a class of vacuum regular black holes inspired by effective loop quantum gravity dynamics and extend the construction to asymptotically anti-de Sitter spacetimes. The derivation is based on a deparameterized Lema\^itre--Tolman--Bondi formulation, where an auxiliary dust field is introduced only to define an internal time and does not act as a matter source. In spherical symmetry, the dynamics reduces to a set of independent radial shells, giving rise to a factorized shell Hamiltonian and to a Birkhoff-type property: for a fixed reconstruction function and cosmological constant, the static geometry is uniquely determined by the mass. Within this framework, we construct several regular black hole models with de Sitter cores and corresponding models with anti-de Sitter cores. We then study their thermodynamics in the extended phase space, with particular emphasis on the Hawking--Page transition. For the class of models considered, the dominant transition is of Hawking--Page type, determined by the crossing of the black hole free energy with the corresponding thermal-AdS background. The regularization affects the quantitative transition temperature by deforming the physical outer-horizon branch, including its endpoint structure. In the large anti-de Sitter radius regime, the de Sitter core solutions exhibit a higher Hawking--Page temperature than their anti-de Sitter-core counterparts, while the ordering can be modified close to the lower admissible range of the AdS scale. Thus, the thermodynamic differences between the two classes are not a consequence of regularity alone, but arise from how the core deformation modifies the horizon branch relative to the thermal-AdS reference background.

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 manuscript derives a class of vacuum regular black holes in asymptotically anti-de Sitter spacetime from a deparameterized Lemaître-Tolman-Bondi formulation in which an auxiliary dust field defines an internal time but is asserted not to source stress-energy. In spherical symmetry the dynamics factorizes into independent radial shells, yielding a Birkhoff-type uniqueness property: for fixed reconstruction function and cosmological constant the static geometry is uniquely fixed by the mass. Several explicit models with de Sitter and anti-de Sitter cores are constructed and their thermodynamics are studied in the extended phase space, with the conclusion that the dominant transition is of Hawking-Page type set by the crossing of black-hole and thermal-AdS free energies; quantitative differences between the two core classes arise from how the core deformation modifies the outer-horizon branch rather than from regularity alone.

Significance. If the vacuum property and Birkhoff uniqueness hold, the construction supplies a controlled, parameter-light framework for comparing the thermodynamics of regular black holes with qualitatively different cores against a common thermal-AdS reference. The explicit factorization into shells and the ability to vary the core while preserving the vacuum character are genuine strengths that permit falsifiable statements about how horizon-branch deformations shift the Hawking-Page temperature.

major comments (2)
  1. [Deparameterized LTB formulation and Hamiltonian reduction] The central claim that the solutions remain vacuum (and therefore obey the stated Birkhoff-type uniqueness) rests on the auxiliary dust contributing identically zero stress-energy after deparameterization and shell factorization. The abstract asserts this, yet the load-bearing step—whether the Hamiltonian reduction and conjugate-momentum constraints enforce T_{\mu\nu}^{dust}=0 identically—requires an explicit derivation; without it the vacuum character, the uniqueness property, and the controlled comparison to thermal AdS are not secured.
  2. [Thermodynamic analysis] § on thermodynamic analysis: the assertion that the dominant transition is Hawking-Page type for the entire class, together with the ordering of transition temperatures in the large-AdS-radius regime, is stated without reported error estimates, convergence checks against the Schwarzschild-AdS limit, or tabulated free-energy crossings; these omissions make the quantitative claims difficult to assess.
minor comments (1)
  1. Notation for the reconstruction function and the auxiliary dust momentum should be introduced once with a clear table of symbols; repeated redefinitions in different sections hinder readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of the framework's strengths and for the constructive major comments. We address each point below, indicating where the manuscript will be revised to strengthen the presentation.

read point-by-point responses

  1. Referee: [Deparameterized LTB formulation and Hamiltonian reduction] The central claim that the solutions remain vacuum (and therefore obey the stated Birkhoff-type uniqueness) rests on the auxiliary dust contributing identically zero stress-energy after deparameterization and shell factorization. The abstract asserts this, yet the load-bearing step—whether the Hamiltonian reduction and conjugate-momentum constraints enforce T_{\mu\nu}^{dust}=0 identically—requires an explicit derivation; without it the vacuum character, the uniqueness property, and the controlled comparison to thermal AdS are not secured.

    Authors: We agree that an explicit derivation of T_{\mu\nu}^{dust}=0 from the Hamiltonian reduction and constraints is necessary to secure the vacuum character and Birkhoff-type uniqueness. While the deparameterized LTB setup and shell factorization are presented in the manuscript, the step showing that the dust stress-energy vanishes identically under the conjugate-momentum constraints is not derived in sufficient detail. We will add a dedicated subsection in the revised manuscript that carries out this derivation from the reduced Hamiltonian and constraints, thereby making the vacuum property fully explicit. revision: yes

  2. Referee: [Thermodynamic analysis] § on thermodynamic analysis: the assertion that the dominant transition is Hawking-Page type for the entire class, together with the ordering of transition temperatures in the large-AdS-radius regime, is stated without reported error estimates, convergence checks against the Schwarzschild-AdS limit, or tabulated free-energy crossings; these omissions make the quantitative claims difficult to assess.

    Authors: We accept that the thermodynamic claims would be strengthened by the inclusion of error estimates, convergence checks against the Schwarzschild-AdS limit, and tabulated free-energy crossings. The manuscript currently presents the free-energy comparisons and transition temperatures through analytic expressions and representative plots, but does not report numerical error estimates or explicit tables of crossings. In the revision we will add these elements: (i) tabulated values of the free-energy crossing points for representative parameter choices, (ii) convergence checks of the outer-horizon branch and transition temperatures as the regularization parameter approaches the Schwarzschild-AdS limit, and (iii) brief error estimates on the numerically located transition temperatures. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses external mass/Λ inputs and computes transitions from geometry

full rationale

The paper's chain starts from the deparameterized LTB setup with the auxiliary dust introduced by assumption (explicitly stated not to source stress-energy), reduces to shell Hamiltonians, obtains the Birkhoff-type uniqueness as a derived consequence for fixed reconstruction function and Λ, then constructs explicit regular models and computes free energies and Hawking-Page crossings directly from the resulting horizon radii. Mass and cosmological constant enter as external parameters; transition temperatures are obtained by comparing on-shell actions rather than by fitting any output to itself. No self-citation is invoked for load-bearing uniqueness, no ansatz is smuggled, and no prediction is renamed from a fit. The derivation remains self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the deparameterized LTB reduction, the auxiliary-dust time choice, spherical symmetry, and the existence of a reconstruction function that produces regular cores while preserving the Birkhoff property. No new particles or forces are postulated.

free parameters (2)
  • reconstruction function
    Chosen to produce a regular center; its specific form determines the core type (dS or AdS) and is not derived from first principles in the abstract.
  • cosmological constant
    Treated as a free parameter in the extended phase space; its value sets the AdS radius and affects the ordering of transition temperatures.
axioms (2)
  • domain assumption Auxiliary dust field defines internal time but carries no stress-energy
    Stated in the abstract as the basis for the vacuum character of the solutions.
  • standard math Spherical symmetry and factorized shell Hamiltonian
    Invoked to obtain the Birkhoff-type uniqueness for fixed reconstruction function and cosmological constant.

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Forward citations

Cited by 1 Pith paper

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Reference graph

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