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arxiv: 2605.17476 · v1 · pith:3G3ZKWTYnew · submitted 2026-05-17 · 🌀 gr-qc · hep-th

Joule-Thomson effect and Efficiency of deformed AdS-Schwarzschild black hole in presence of quintessence

Dhruba Jyoti Gogoi , Ronit Karmakar , Jyatsnasree Bora , Pohar Buragohain , Chandika Gogoi This is my paper

Pith reviewed 2026-05-19 23:17 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords Joule-Thomson expansionblack hole thermodynamicsquintessencedeformed AdS-Schwarzschildheat engine efficiencyinversion temperatureextended phase space
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The pith

Deformed AdS-Schwarzschild black holes with quintessence shift temperature minima and raise inversion temperatures via parameters α and β.

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

This paper studies the Joule-Thomson expansion and heat-engine efficiency of a modified AdS-Schwarzschild black hole that incorporates a deformation parameter α, a control parameter β, and a quintessence parameter σ. The analysis of Hawking temperature, Joule-Thomson coefficient, inversion curves, and isenthalpic trajectories shows that α and β shift the temperature minimum, enlarge the cooling region, and increase the inversion temperature, while σ exerts a milder but consistent effect. In the heat-engine context, α raises efficiency, whereas larger values of β and σ lower it. These modifications arise within the standard extended-phase-space thermodynamics that obeys the first law and Smarr relation.

Core claim

The central claim is that the deformation parameter α, control parameter β, and quintessence parameter σ jointly modify the Hawking temperature and Joule-Thomson coefficient of the black hole, shifting the temperature minimum, enlarging the cooling region, and raising the inversion temperature, with σ producing a weaker influence; the same parameters also control heat-engine efficiency, which increases with α and decreases with higher β and σ.

What carries the argument

The modified black hole metric defined by the three parameters α, β, and σ, which determines the thermodynamic quantities (temperature, pressure, volume) and their derivatives in extended phase space.

If this is right

  • The cooling region in isenthalpic processes expands as α or β increases.
  • Inversion temperatures rise with larger α and β, extending the range where cooling occurs.
  • Black-hole heat-engine efficiency improves with the deformation parameter α but declines with increases in β or σ.
  • Thermal stability regions change according to the combined influence of the three parameters.

Where Pith is reading between the lines

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

  • If deformed metrics of this form arise in realistic gravitational theories, their altered inversion curves could provide indirect signatures in cosmological or astrophysical settings.
  • The parameter dependence suggests testable extensions to other thermodynamic processes, such as phase transitions or critical phenomena in the same black-hole family.
  • Connections to quintessence models may allow these results to inform broader studies of dark-energy effects on black-hole thermodynamics.

Load-bearing premise

The modified metric with parameters α, β, and σ is assumed to describe a physically realizable black hole whose thermodynamic quantities obey the standard first law and Smarr relation of extended phase space without additional constraints from the underlying field equations.

What would settle it

A direct computation showing that the first law of thermodynamics fails to hold for the given metric parameters, or numerical evaluation of inversion curves that exhibit no shift when α or β is varied.

Figures

Figures reproduced from arXiv: 2605.17476 by Chandika Gogoi, Dhruba Jyoti Gogoi, Jyatsnasree Bora, Pohar Buragohain, Ronit Karmakar.

Figure 1
Figure 1. Figure 1: FIG. 1: Variation of Hawking temperature with horizon radius of the black hole. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: JT coefficient vs event horizon radius of the black hole. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Inversion curves of the black hole. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Isenthalpic and inversion curves of the black hole. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Isenthalpic and inversion curves of the black hole. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: A schematic figure of the working of a heat engine is shown. On the right, we have the Carnot engine P-V cycle. [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: The efficiency of a deformed AdS-Schwarzschild black hole in the presence of quintessence field is shown in the plots. [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: The efficiency of a deformed AdS-Schwarzschild black hole in the presence of quintessence field is shown in the plot. [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: The efficiency of a deformed AdS-Schwarzschild black hole in the presence of quintessence field is shown in the plots. [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Ratio of efficiency to Carnot efficiency of a deformed AdS-Schwarzschild black hole in the presence of quintessence [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
read the original abstract

We study the Joule-Thomson expansion and extended thermodynamics of a modified black hole characterised by the parameters $\alpha$, $\beta$, and $\sigma$. Analysis of the Hawking temperature, Joule-Thomson coefficient, inversion curves, and isenthalpic trajectories shows that these parameters significantly modify the heating-cooling behaviour and thermal stability of the system. The deformation parameter $\alpha$ and control parameter $\beta$ shift the temperature minimum, enlarge the cooling region, and raise the inversion temperature, while $\sigma$ produces a weaker but consistent influence. The heat-engine analysis reveals that $\alpha$ enhances efficiency, whereas higher $\beta$ and $\sigma$ reduce it. Overall, the results demonstrate that geometric deformation and quintessence jointly govern the unified thermodynamic structure of the black hole.

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 / 2 minor

Summary. The paper examines the Joule-Thomson expansion and heat engine efficiency for a deformed AdS-Schwarzschild black hole in the presence of quintessence, with deformation parameters α, β, and σ. Using the standard extended-phase-space dictionary, it computes the Hawking temperature T = f'(r_+)/4π, entropy S = π r_+², and pressure P = −Λ/8π, then derives the Joule-Thomson coefficient μ_JT = (∂T/∂P)_H, inversion curves, isenthalpic trajectories, and heat-engine efficiency η = 1 − Q_C/Q_H. The central claims are that α and β shift the temperature minimum, enlarge the cooling region, and raise the inversion temperature (with σ exerting a weaker but consistent effect), while α increases efficiency and higher β, σ decrease it.

Significance. If the metric satisfies the Einstein equations with the quintessence stress-energy, the results would provide concrete illustrations of how geometric deformations and a dark-energy-like component jointly modify black-hole thermodynamic processes in extended phase space. The work supplies explicit trends for the JT coefficient, inversion temperature, and efficiency as functions of the three parameters, which could serve as benchmarks for future studies of modified black-hole thermodynamics. The parameter-free limiting cases (α = β = σ = 0 recovering the standard AdS-Schwarzschild results) are a modest strength.

major comments (2)
  1. [§2 (metric ansatz)] §2 (metric ansatz): the line element is introduced as a phenomenological deformation of the AdS-Schwarzschild-quintessence metric without an explicit check that G_μν = 8π(T_μν^quintessence + T_μν^Λ) for w = −2/3. Because the thermodynamic potentials T, S, V, and P are read off directly from this f(r), any failure of the field equations would invalidate the first law and Smarr relation used throughout §§3–5; the reported shifts in T_min and the enlargement of the cooling region would then be artifacts of the ansatz rather than consequences of the Einstein equations.
  2. [§3.2 (Joule-Thomson coefficient)] §3.2 (Joule-Thomson coefficient): μ_JT is computed from the standard extended-phase-space identity without additional work terms that would arise if the deformation parameters α, β, σ introduce extra degrees of freedom. The claim that α and β enlarge the cooling region therefore rests on the unverified assumption that dM = T dS + V dP continues to hold exactly; a direct verification of the first law for the deformed metric is required before the inversion-curve results can be regarded as robust.
minor comments (2)
  1. [Abstract] The abstract states that σ produces a “weaker but consistent influence,” yet no quantitative measure (e.g., relative shift in T_min or Δη) is supplied; a short table comparing the magnitudes of the three parameters’ effects would improve clarity.
  2. [§2] Notation for the quintessence parameter σ is introduced without reference to the standard normalization in the literature (e.g., the usual Kiselev parameter); a brief comparison would help readers place the results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and insightful comments on our manuscript. We address each major comment in detail below and outline the revisions we plan to make.

read point-by-point responses

  1. Referee: [§2 (metric ansatz)] §2 (metric ansatz): the line element is introduced as a phenomenological deformation of the AdS-Schwarzschild-quintessence metric without an explicit check that G_μν = 8π(T_μν^quintessence + T_μν^Λ) for w = −2/3. Because the thermodynamic potentials T, S, V, and P are read off directly from this f(r), any failure of the field equations would invalidate the first law and Smarr relation used throughout §§3–5; the reported shifts in T_min and the enlargement of the cooling region would then be artifacts of the ansatz rather than consequences of the Einstein equations.

    Authors: We appreciate the referee highlighting this important point. The metric is constructed as a phenomenological extension incorporating the deformation parameters while reducing to the standard AdS-Schwarzschild-quintessence solution when α = β = σ = 0. To strengthen the foundation, we will include in the revised version an explicit calculation of the Einstein tensor components for the proposed metric and demonstrate that the resulting stress-energy tensor corresponds to a quintessence field with w = −2/3 plus the cosmological constant contribution. This verification will confirm the validity of the thermodynamic quantities and relations used in the subsequent sections. revision: yes

  2. Referee: [§3.2 (Joule-Thomson coefficient)] §3.2 (Joule-Thomson coefficient): μ_JT is computed from the standard extended-phase-space identity without additional work terms that would arise if the deformation parameters α, β, σ introduce extra degrees of freedom. The claim that α and β enlarge the cooling region therefore rests on the unverified assumption that dM = T dS + V dP continues to hold exactly; a direct verification of the first law for the deformed metric is required before the inversion-curve results can be regarded as robust.

    Authors: We agree that a direct verification of the first law is essential for the robustness of our results. In the revised manuscript, we will compute the differential dM explicitly in terms of dS and dP, treating α, β, and σ as fixed parameters, and show that dM = T dS + V dP holds without additional conjugate terms for these deformations. If any extra terms arise, we will incorporate them into the analysis of the Joule-Thomson coefficient and inversion curves. This will provide a solid basis for the reported effects on the cooling region and inversion temperature. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper introduces a phenomenological deformed metric with free parameters α, β, σ and applies the standard dictionary of extended black-hole thermodynamics (T = f'(r_+)/4π, S = π r_+², P = -Λ/8π) to compute the Joule-Thomson coefficient, inversion curves, and heat-engine efficiency. These quantities are direct functions of the input metric; the reported shifts in temperature minimum, cooling region, and efficiency are simply the numerical or analytic consequences of varying the parameters inside those expressions. No parameter is fitted to a subset of the same thermodynamic data and then re-labeled as a prediction, no load-bearing self-citation supplies a uniqueness theorem, and no ansatz is smuggled from prior work by the same authors. The derivation therefore remains self-contained within the usual first-law and Smarr relations applied to the given line element.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard extended black-hole thermodynamics dictionary and on the assumption that the given metric ansatz satisfies the Einstein equations with quintessence. No new free parameters are introduced beyond α, β, σ; these are treated as given inputs rather than fitted quantities in the abstract.

free parameters (1)
  • α, β, σ
    Three parameters that deform the metric and control quintessence; their specific values are chosen to illustrate the reported shifts but are not derived from first principles or external data.
axioms (2)
  • domain assumption The cosmological constant is identified with thermodynamic pressure in the extended phase space.
    Invoked implicitly when Joule-Thomson expansion and heat-engine cycles are defined.
  • domain assumption The modified metric with parameters α, β, σ yields a valid black-hole solution whose Hawking temperature and entropy obey the first law.
    Required for all thermodynamic quantities to be well-defined.

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