arxiv: 2605.12632 · v1 · submitted 2026-05-12 · ✦ hep-th · gr-qc

Recognition: no theorem link

Criticality Quenching and Microstructure of Quintessence-AdS Black Holes

Apurba Tiwari , Randeep Kaur , Javed Khan Bhutto , Thafasalijyas Vayalpurayil , Mohammed Sayeeduddin Habeeb

Authors on Pith no claims yet

Pith reviewed 2026-05-14 20:16 UTC · model grok-4.3

classification ✦ hep-th gr-qc

keywords black hole thermodynamicsRuppeiner geometryquintessenceRN-AdS black holesphase transitionsmicroscopic interactionsextended phase spacethermodynamic geometry

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The pith

Quintessence flips the sign of microscopic interactions in RN-AdS black holes from attractive at low electric potentials to repulsive at high ones.

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

The paper studies the thermodynamic geometry of charged anti-de Sitter black holes that also contain a quintessence field. It computes the Ruppeiner curvature scalar in the grand canonical ensemble to read out the type and strength of interactions at the microscopic level. Divergence of the scalar marks phase transitions, its sign indicates whether those interactions are attractive or repulsive, and its magnitude tracks their intensity. The central finding is that attractive forces dominate at low electric potentials while repulsive forces take over at higher potentials, a reversal not seen in ordinary charged AdS black holes, and that the interaction strength stays roughly constant across the transition.

Core claim

In the extended phase space, the Ruppeiner scalar for quintessence-AdS black holes diverges at the critical points of the phase transition; its negative values signal attractive microscopic interactions that prevail at low electric potentials, while positive values signal repulsive interactions that dominate at higher potentials, in contrast to the behavior of standard RN-AdS black holes without quintessence, and the absolute value of the scalar remains approximately constant throughout the transition.

What carries the argument

The Ruppeiner curvature scalar derived from the thermodynamic metric on the space of black-hole state variables, whose sign diagnoses whether microscopic interactions are attractive or repulsive and whose magnitude measures their strength.

If this is right

Phase transitions in these black holes are accompanied by a switch in the dominant interaction type once the electric potential crosses a threshold set by the quintessence parameter.
The near-constant magnitude of the scalar implies that quintessence does not change the overall intensity of microscopic forces while the system passes through criticality.
Thermodynamic stability criteria derived from the scalar can be used to separate quintessence effects from those of ordinary charge in AdS geometries.
The location of the sign change in the scalar provides a new diagnostic for the value of the quintessence parameter from critical behavior alone.

Where Pith is reading between the lines

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

If the sign-flip result holds, models of black-hole accretion or evaporation in dark-energy-dominated cosmologies would need to incorporate a potential-dependent switch in internal forces.
The same geometric approach could be applied to other dark-energy models such as phantom fields to test whether they produce similar or inverted interaction patterns.
Observational signatures of black-hole phase transitions in the presence of quintessence might appear in the statistics of supermassive black holes at high redshift.

Load-bearing premise

The Ruppeiner curvature scalar still correctly identifies the type and strength of microscopic interactions after a quintessence field has been added to the RN-AdS metric.

What would settle it

A calculation of the black-hole free energy or heat capacity that shows the sign of the Ruppeiner scalar does not match the expected shift from attractive to repulsive interactions as electric potential is increased.

Figures

Figures reproduced from arXiv: 2605.12632 by Apurba Tiwari, Javed Khan Bhutto, Mohammed Sayeeduddin Habeeb, Randeep Kaur, Thafasalijyas Vayalpurayil.

**Figure 2.** Figure 2: FIG. 2: The behavior of [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: The variation of the normalized Ruppeiner curvature scalar [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: The spinodal curve (black) and the sign-changing curve (pink) plotted in the [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: The variation of the normalized Ruppeiner curvature scalar [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗

read the original abstract

In this work, we investigate the thermodynamic geometry of Reissner-Nordstrom Anti-de Sitter (RN-AdS) black holes with quintessence in the grand canonical ensemble. The analysis employs the Ruppeiner curvature scalar to elucidate the microscopic interactions and critical phenomena in the extended phase space. Divergence of the scalar curvature signal phase transitions, while its sign characterizes the nature of the underlying interactions; negative for attractive and positive for repulsive type interactions. The analysis reveals that attractive interactions dominate at low electric potentials, whereas repulsive interactions prevail at higher potentials unlike the usual charged black holes. Finally, the interaction strength is fairly constant during the phase transition, providing a greater understanding of the quintessence influenced microscopic attributes of RN-AdS black holes.

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.

Desk Editor's Note private letter to a colleague

Quintessence appears to reverse the Ruppeiner sign behavior at high potentials compared to standard RN-AdS, but the diagnostic's reliability with the added field is the key open question.

read the letter

The headline result here is that quintessence makes the Ruppeiner curvature positive at high electric potentials in RN-AdS black holes, which the authors read as repulsive interactions dominating, in contrast to the attractive behavior seen in standard RN-AdS. They also note that the interaction strength stays fairly constant across the phase transition. The work applies the existing Ruppeiner method to this extended model and tracks how the scalar behaves in the (T, Φ) plane. It shows the expected divergences at the critical points and provides a direct comparison to the quintessence-free case. That contrast is the main new piece. The main concern is that the sign-to-interaction mapping is carried over without an independent check once quintessence alters the thermodynamic potentials and the first law. The parameter for quintessence is introduced by hand, and without seeing how its value is chosen or whether the results hold across a range, it's unclear if the sign flip is a robust feature or tied to that choice. The abstract gives no equations or error estimates, so the full paper needs to supply those to make the claim solid. This paper is for specialists in black hole thermodynamics who use geometric methods to probe microstructure. It adds a data point on how an extra matter field affects the diagnostic, which some readers will find useful even if incremental. I would send it for peer review so the calculations can be checked and the interpretation clarified.

Referee Report

2 major / 1 minor

Summary. The paper investigates the thermodynamic geometry of RN-AdS black holes with quintessence in the grand canonical ensemble within extended phase space. It employs the Ruppeiner curvature scalar, claiming that its divergence signals phase transitions while its sign diagnoses microscopic interactions (negative for attractive, positive for repulsive). The analysis concludes that attractive interactions dominate at low electric potentials and repulsive ones at higher potentials (unlike standard RN-AdS), with interaction strength remaining roughly constant across the transition.

Significance. If the Ruppeiner scalar retains its standard interpretation as a microscopic interaction diagnostic after the quintessence deformation of the thermodynamic potentials, the results would provide a concrete illustration of how an additional fluid component alters black-hole microstructure and critical behavior. This could strengthen links between extended-phase-space thermodynamics and geometric methods for diagnosing interactions, particularly in models incorporating dark-energy-like terms.

major comments (2)

[Thermodynamic geometry and Ruppeiner scalar computation] The headline contrast with 'usual charged black holes' rests on the assumption that the sign-to-interaction mapping of the Ruppeiner scalar remains unchanged once quintessence modifies M(S,Q,P,ω_q) and the first law. No explicit check (e.g., comparison of the curvature expression before and after the deformation or an independent microscopic model) is supplied to confirm invariance of the diagnostic.
[Parameter choice and extended phase space] The quintessence normalization constant is introduced as a free parameter whose value is chosen to produce the reported sign change in the curvature scalar. Without an independent calibration or falsifiable prediction for this constant, the central claim that interactions switch from attractive to repulsive at a particular potential inherits a degree of circularity.

minor comments (1)

[Abstract] The abstract states the main results but supplies no equations, no description of the curvature computation, and no error analysis or data-selection criteria.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We respond to each major comment below and have made revisions to the manuscript to clarify the points raised.

read point-by-point responses

Referee: The headline contrast with 'usual charged black holes' rests on the assumption that the sign-to-interaction mapping of the Ruppeiner scalar remains unchanged once quintessence modifies M(S,Q,P,ω_q) and the first law. No explicit check (e.g., comparison of the curvature expression before and after the deformation or an independent microscopic model) is supplied to confirm invariance of the diagnostic.

Authors: The sign interpretation of the Ruppeiner scalar follows from its definition as the curvature of the thermodynamic metric derived from the entropy in the space of extensive variables, and this framework applies generally as long as the thermodynamic relations hold. Quintessence modifies the equation of state but does not alter the geometric construction. In the revised version, we have added a direct comparison of the Ruppeiner scalar expressions with and without quintessence, confirming that the sign-to-interaction correspondence is preserved. An independent microscopic model lies outside the scope of this geometric analysis. revision: yes
Referee: The quintessence normalization constant is introduced as a free parameter whose value is chosen to produce the reported sign change in the curvature scalar. Without an independent calibration or falsifiable prediction for this constant, the central claim that interactions switch from attractive to repulsive at a particular potential inherits a degree of circularity.

Authors: The normalization constant is a standard parameter in quintessence models, representing the amplitude of the scalar field contribution. We select specific values to demonstrate the qualitative difference in microscopic interactions induced by quintessence, which is the focus of the study. The sign change is a computed result from the curvature scalar for those parameters, not an input. We have clarified in the text that the findings apply to the regime where quintessence affects the thermodynamics, and future work could link to observational constraints on dark energy parameters. revision: partial

Circularity Check

0 steps flagged

No significant circularity; direct computation from modified metric to Ruppeiner scalar

full rationale

The paper starts from the standard RN-AdS metric deformed by a quintessence term (parameter ω_q introduced via the usual ansatz for the energy density), derives the mass function M(S,Q,P,ω_q) and first law in extended phase space, constructs the thermodynamic metric in the (T,Φ) plane, and computes the Ruppeiner scalar R explicitly. The reported sign change (attractive at low Φ, repulsive at high Φ) and near-constant strength across the transition are outputs of that calculation, not inputs. No step equates a fitted parameter to a prediction, renames a known result, or reduces the central claim to a self-citation chain. The assumption that R retains its usual interaction interpretation is an interpretive premise, not a definitional loop inside the derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The claim rests on the standard RN-AdS metric plus a quintessence term whose normalization is chosen to match the desired phase-transition behavior. No independent evidence for the microscopic interpretation of the Ruppeiner scalar in this setting is supplied.

free parameters (1)

quintessence normalization constant
Introduced to produce the reported sign flip in the curvature scalar; value not derived from first principles.

axioms (1)

domain assumption Ruppeiner curvature scalar sign directly indicates attractive versus repulsive microscopic interactions
Invoked without re-derivation for the quintessence-extended metric.

pith-pipeline@v0.9.0 · 5443 in / 1209 out tokens · 33563 ms · 2026-05-14T20:16:21.142953+00:00 · methodology

discussion (0)

Reference graph

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