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Black hole charge dominates Joule-Thomson cooling in f(R,T)+NLED AdS black holes; modified-gravity and nonlinear-electrodynamics corrections stay weak outside the near-horizon region.

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2026-07-10 23:02 UTC pith:XGCVLN64

load-bearing objection Competent incremental JT + geodesic calculation on a published f(R,T)+NLED metric; charge ranking is real within their window but not scale-invariant. the 3 major comments →

arxiv 2607.06704 v1 pith:XGCVLN64 submitted 2026-07-07 gr-qc astro-ph.HE

Joule-Thomson Effect and Geodesic Structure of Charged AdS Black Holes in f(R,T) Coupled with Nonlinear Electrodynamics

Shyamalee Bora , Dhruba Jyoti Gogoi , Pralay Kumar Karmakar This is my paper
classification gr-qc astro-ph.HE
keywords Joule-Thomson expansioncharged AdS black holesf(R,T) gravitynonlinear electrodynamicsgeodesicsinversion temperaturephoton sphereblack hole thermodynamics
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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 the geodesic motion of a charged AdS black hole that arises when f(R,T) gravity is coupled to a power-law nonlinear electrodynamics source. The central claim is that electric charge is the parameter that most strongly controls the inversion temperature, the size of the cooling domain, and the shape of isenthalpic curves, while the nonlinear-electrodynamics strength and the f(R,T) coupling only supply milder corrections. At the same time, the geodesic analysis shows that the same charge raises the effective-potential barrier and shifts the photon sphere inward, yet the higher-order corrections fall off so rapidly that, at ordinary astrophysical distances, the spacetime is essentially indistinguishable from an ordinary Reissner-Nordström-AdS black hole. The result matters because it shows that the singularity-regularising ingredients needed inside the horizon leave the exterior thermodynamics and orbital dynamics largely intact, so classical tests remain valid probes of these quantum-inspired models.

Core claim

In the extended phase space of a charged AdS black hole obtained from linear f(R,T)=R+βT gravity plus a p=6 nonlinear electrodynamics source, the electric charge produces the largest shifts in inversion temperature, cooling-region size, and isenthalpic peaks; the NLED and f(R,T) parameters supply only secondary corrections, and the exterior geodesic structure (stable circular orbits, precessing bound orbits, unstable photon sphere) reproduces the Reissner-Nordström-AdS pattern at astrophysically relevant radii.

What carries the argument

The explicit metric function A(r) that encodes mass, charge, effective cosmological constant, and the O(r^{-22}) NLED/f(R,T) correction terms; every thermodynamic response function (temperature, heat capacity, JT coefficient, inversion curve) and every geodesic effective potential is obtained by differentiating this single function.

Load-bearing premise

All conclusions rest on the specific metric that follows from fixing the gravity model to the linear form f(R,T)=R+βT and the nonlinear-electrodynamics power to p=6; if that functional choice does not faithfully represent the underlying theory, the thermodynamic and orbital results do not apply.

What would settle it

Compute or measure the inversion temperature versus pressure for a sequence of increasing charges while holding the NLED and f(R,T) couplings fixed; if the cooling domain does not enlarge systematically with charge, or if exterior photon-sphere and precession observables deviate strongly from the Reissner-Nordström-AdS prediction once the higher-order terms are included, the central claim is false.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The manuscript studies the extended-phase-space thermodynamics, Joule–Thomson expansion, and equatorial geodesic structure of a static charged AdS black hole in linear f(R,T)=R+βT gravity coupled to a p=6 power-law NLED source, taking the metric of Róis et al. as given. After deriving mass, Hawking temperature, entropy (area law), Gibbs free energy, heat capacity, and verifying the first law and Smarr relation, the authors analyse global/local stability via G(T) swallowtails and the Hessian of M(S,Q). They then compute the JT coefficient, inversion curves Ti(Pi), and isenthalpic trajectories, concluding that charge Q most strongly enlarges the cooling domain while α and β supply milder corrections. The geodesic section constructs the effective potential for timelike and null motion, identifies ISCOs, precessing bound orbits, and the photon sphere, and argues that at astrophysically relevant distances the geometry and orbits closely reproduce RN-AdS behaviour because the NLED/f(R,T) corrections fall as r^{-22}.

Significance. The work supplies a systematic JT and geodesic analysis for a relatively recent regular charged AdS solution in f(R,T)–NLED gravity, filling a documented gap. The algebraic consistency of the thermodynamic identities (first law, Smarr, µ_JT from CP and the equation of state) and of the effective-potential formulae is a clear strength, as is the explicit correlation drawn between horizon thermodynamics (A, A') and exterior orbital conditions. The finding that short-scale regularisation terms decouple from large-scale kinematics and thermodynamics is useful for observational tests. The contribution remains incremental: the metric is imported, the methods are standard, and the strongest ranking claim (dominance of Q) is not yet placed on a scale-invariant footing. If that claim is properly qualified or re-established with dimensionless measures, the paper will be a solid, citable addition to black-hole chemistry in modified gravity.

major comments (3)
  1. Abstract and §V (Figs. 3–5, inversion and isenthalpic discussion): the central claim that “the black hole charge has the most pronounced impact on the JT behaviour” rests on visual comparison of curves obtained by varying Q, α and β over comparable O(0.1–0.9) intervals. For p=6 the NLED coupling α multiplies a Q^{12}/r^{22} term and therefore carries dimensions of length^{10} (or equivalent), while β is dimensionless only after the linear f(R,T) model is fixed; the chosen numerical windows are therefore not scale-invariant. A different choice of units or of the natural NLED/matter-curvature scale can reverse the apparent hierarchy of shifts in Ti(Pi) and in the isenthalpic peaks. The ranking should be re-established with dimensionless combinations (e.g. αQ^{10}/r_+^{10}, β relative to a fixed curvature scale) or explicitly qualified as holding only inside the plotted window; otherwise th
  2. §I and §VI: the introduction correctly notes that non-minimal matter–curvature coupling in f(R,T) implies ∇_µT^{µν}≠0 and an extra force, so that test-particle motion “deviates from geodesic trajectories.” Section VI nevertheless adopts the standard geodesic Lagrangian (Eq. 43) and the usual effective-potential formalism without the extra force. Because the geodesic conclusions (stable circular orbits, precession rates, photon-sphere location, and the claim of RN-AdS recovery at large r) are load-bearing for the second half of the paper, either (i) the extra-force term must be shown to be negligible for the adopted linear model and parameter ranges, or (ii) the orbital equations must be recomputed with the non-geodesic force. Leaving the tension unaddressed undermines the kinematic half of the central narrative.
  3. §II, Eq. (20) and subsequent thermodynamics: all results are obtained for the single power p=6 and the linear model f(R,T)=R+βT taken from Róis et al. The abstract and conclusions present the JT and geodesic findings as characteristic of “f(R,T) coupled with nonlinear electrodynamics.” At minimum the text should state clearly that the hierarchy of parameter influence and the r^{-22} decoupling are specific to this functional choice, and indicate whether the qualitative picture (single inversion branch, RN-AdS recovery) is expected to survive for the other powers (p=2,4) already examined in the source paper.
minor comments (6)
  1. Several figure panels reuse the same subplot label “(a)” (e.g. Fig. 3 has two panels labelled (a); Fig. 1 insets are hard to read). Renumber consistently and enlarge insets or move them to separate panels.
  2. Notation: the charge is written both q and Q; the cosmological constant appears as Λ, Λ_eff and f_0. Unify symbols after Eq. (18).
  3. Eq. (24) for TH still contains an unsimplified mix of αβ and α terms; a single factor α(10β−1) would match the metric and improve readability.
  4. Metric signature is stated as (+,−,−,−) while the geodesic normalisation uses g_µνẋ^µẋ^ν=−ϵ with ϵ=1 for massive particles; a one-sentence clarification of the sign convention for ϵ would avoid confusion.
  5. Typos: “inf(R, T)” spacing in the title and several headings; “R’oiset al.” / “Róis et al.” inconsistent; “Mod(A)Max-AdS” left unexplained on first use.
  6. §VII claims a “direct physical correlation” between thermodynamic phase boundaries and orbital dynamics; the shared dependence on A and A' is correctly noted, but the language could be toned down to “common geometric origin” unless a quantitative map (e.g. between Ti and r_ph) is supplied.

Circularity Check

0 steps flagged

No significant circularity: metric imported from independent prior work; thermodynamics and geodesics are standard forward calculations with no definitional loops or fitted-as-prediction steps.

full rationale

The load-bearing input is the metric function A(r) of Eq. (20), taken directly from the independent solution of Róis et al. [107] (different author set) after fixing the linear f(R,T)=R+eta T model and the p=6 NLED power. All subsequent quantities—M(r+), TH, S= ho r+^{2}, G, CP, ho JT, Ti(Pi), isenthalpic T(P)|M, Veff, circular-orbit conditions, ISCO, and photon-sphere loci—are obtained by ordinary differentiation and algebraic rearrangement of that fixed A(r) (Eqs. 21–54). No free parameter is fitted to any thermodynamic or geodesic observable and then re-used as a “prediction”; the numerical curves simply evaluate the same closed-form expressions at chosen O(1) values of Q, ho, eta. Self-citations (e.g. Gogoi et al. [63] on JT methods) appear only as comparative references and do not supply uniqueness theorems or ansatzes that force the present results. Consequently the derivation chain is self-contained and non-circular.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 0 invented entities

The paper inherits the entire spacetime metric and the linear f(R,T)+power-law NLED action from prior work, then applies textbook extended-phase-space thermodynamics and geodesic analysis. Free parameters are the usual black-hole charges and the two model couplings; no new dynamical entities are postulated.

free parameters (5)
  • Q (electric/magnetic charge)
    Scanned freely in all thermodynamic and geodesic plots; controls the dominant shifts in inversion temperature and potential barrier height.
  • α (NLED coupling)
    Dimensionless strength of the F^p term; varied by hand to produce families of curves.
  • β (f(R,T) coupling)
    Linear matter-curvature coupling constant; scanned independently of α.
  • Λ_eff (or f_0)
    Effective cosmological constant fixed by the vacuum term in the action; treated as a free AdS scale.
  • p=6 (NLED power)
    Fixed by hand to the representative value chosen in the source paper; higher powers generate the r^{-22} correction that is later declared negligible.
axioms (4)
  • domain assumption The metric function A(r) of Eq. (20) is an exact solution of the f(R,T)+NLED field equations for p=6.
    Taken verbatim from Róis et al. (2025); every subsequent thermodynamic and geodesic quantity is derived from this A(r).
  • domain assumption Black-hole mass M is identified with enthalpy in the extended phase space, so constant-M curves are isenthalpic.
    Standard assumption of AdS black-hole chemistry (Kastor-Ray-Traschen, Kubizňák-Mann); used without re-derivation to define the JT process.
  • domain assumption Entropy remains the Bekenstein-Hawking area law S=π r_+^{2} even after the f(R,T) and NLED modifications.
    Stated after Eq. (25) and justified by the linear form of f(R,T); if the entropy formula acquired extra terms the entire thermodynamic analysis would change.
  • ad hoc to paper Test-particle motion is governed by the standard geodesic equation of the metric (no extra force from non-conservation of T_µν).
    f(R,T) theories generically produce non-geodesic motion; the paper ignores that force when writing the effective potential (Eq. 46).

pith-pipeline@v1.1.0-grok45 · 32904 in / 3195 out tokens · 37763 ms · 2026-07-10T23:02:20.367093+00:00 · methodology

0 comments
read the original abstract

We herein study both the Joule-Thomson (JT) expansion process and the geodesic properties of a charged anti-de Sitter (AdS) black hole arising in modified gravity with nonlinear electrodynamic (NLED) sources. Our thermodynamic study reveals that the black hole charge has the most pronounced impact on the JT behaviour. The nonlinear electromagnetic sector together with the modified gravity parameters introduces further corrections to the inversion temperature and the associated cooling characteristics. At astrophysically relevant distances, the geometry closely reproduces expected outcomes.

Figures

Figures reproduced from arXiv: 2607.06704 by Dhruba Jyoti Gogoi, Pralay Kumar Karmakar, Shyamalee Bora.

Figure 1
Figure 1. Figure 1: FIG. 1. Gibbs free energy variation with temperature for different indicated parameter values. [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Behaviour of stability functions [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Variation of Joule-Thomson coefficient with respect to the horizon radius. [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Joule-Thomson inversion curves [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Joule-Thomson isenthalpic curves in the [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Influence of model parameters on the effective potential for massive particles. [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Parameter dependence of the effective potential for massless particles. [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Geodesic structure for massive particles. [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Geodesic structure for massive particles. [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Geodesic structure for massive particles. [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Geodesic structure for massive particles. [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Geodesic structure for massless particles. [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Geodesic structure for massless particles. [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Geodesic structure for massless particles. [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Geodesic structure for massless particles. [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗

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