Infrared Extended Uncertainty Principle Corrections and Quintessence-Induced Topology of Reissner-Nordstr\"om AdS Black Holes

A.Baruah; G.G.Luciano; S.N.Gashti; Y. Sekhmani

REVIEW 3 major objections 3 minor 1 cited by

Infrared Extended Uncertainty Principle Corrections and Quintessence-Induced Topology of Reissner-Nordstr\"om AdS Black Holes

T0 review · 3 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper derives analytic EUP-corrected thermodynamics for charged AdS black holes with quintessence and shows that quintessence can split or merge photon spheres while preserving the total exterior topological charge of -1.

desk verdict Abstract-only verdict: plausible combination, but the first-law consistency question is unaddressed in the abstract, so I can't sign off on the physics yet. read the letter →

arxiv 2508.14953 v1 pith:OT62EPHY submitted 2025-08-20 gr-qc hep-th

Y. Sekhmani , G.G.Luciano , S.N.Gashti , A.Baruah This is my paper · ORCID

classification gr-qchep-th MSC 83C57 PACS 04.70.Dy

keywords extendeduncertaintyprincipleblackholethermodynamicsquintessenceReissner-NordströmAdSholesphotonspheretopologicalchargewindingnumberDuan'scurrent

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to show that adding infrared Extended Uncertainty Principle (EUP) corrections and a quintessence field to charged anti-de Sitter black holes produces a single, quantitative account of their thermodynamics and photon-sphere topology. It derives closed-form expressions for the Hawking temperature, entropy, and heat capacity in terms of the EUP deformation parameter. It then claims that the quintessence equation-of-state parameter controls the number of inflection points in the relaxation-time function, meaning the dark-energy equation of state determines how many thermodynamic phases the black hole can access. Applying Duan's topological current method, it assigns integer winding numbers to thermodynamic critical points and ±1 charges to individual photon spheres, with the total exterior charge remaining -1 even when quintessence splits or merges the spheres.

What carries the argument

The central machinery is an EUP-modified metric that introduces a minimal-momentum/maximal-length scale, together with a quintessence energy-momentum tensor characterized by a barotropic index. The relaxation-time function tau(r_h) serves as the phase-structure probe, and Duan's topological current method applied to the off-shell free energy converts thermodynamic critical points into integer winding numbers. The same topological technique is applied to photon spheres, assigning ±1 charges to light rings and making the total exterior topological charge an invariant.

What would settle it

Set the EUP deformation parameter to zero and the quintessence density to zero in the model; the total photon-sphere charge must reduce exactly to the standard Reissner-Nordström-AdS value of -1, and the corrected Hawking temperature must collapse to the known textbook expression. A numerical computation of Duan's current on a fine radial grid yielding any other integer would falsify the claim.

Watch

Extended reading notes

Core claim

The paper asserts that for charged AdS black holes surrounded by quintessence, incorporating EUP infrared corrections yields analytic expressions for Hawking temperature, entropy, and heat capacity parameterized by the EUP deformation parameter. It further claims that the quintessence barotropic index determines the number of inflection points of the relaxation-time function, that Duan's topological current assigns integer winding numbers to thermodynamic critical points, and that photon spheres carry ±1 topological charges whose total exterior charge remains -1 even when quintessence splits or merges the spheres.

Load-bearing premise

The fixed quintessence equation-of-state parameters and the specific EUP-modified metric ansatz are assumed without derivation, and every claimed topological and thermodynamic result follows from that ansatz.

Editorial extensions

If this is right

The corrected Hawking temperature and entropy depend explicitly on the EUP deformation parameter, so black hole evaporation rates and heat capacities become quantitative probes of infrared quantum-gravity effects.
The number of inflection points of tau(r_h) changes with the quintessence barotropic index, implying the dark-energy equation of state controls how many distinct thermodynamic phases the black hole can access.
Winding numbers computed via Duan's topological current give integer labels to thermodynamic critical points, providing a classification that is stable under continuous deformations of the off-shell free energy.
Photon spheres carry individual charges ±1 and can split or merge under quintessence, yet the total exterior charge of -1 is preserved, so the global topology of the shadow is robust even when the image structure changes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

One could test the universality of the total -1 charge by applying the same analysis to rotating or higher-dimensional black holes; a different total charge would indicate that the invariant depends on symmetry assumptions rather than being a universal feature.
The inflection-point count of tau(r_h) offers a potential observational handle: if relaxation time can be linked to quasinormal modes, the predicted dependence on omega_q might be compared with ringdown measurements.
The same Duan-current machinery could be applied to black hole shadows with plasma or accretion disks to see whether the splitting and merging of photon spheres survives in realistic astrophysical environments.
The results suggest that the EUP deformation parameter and the quintessence index act as two separable knobs: one controls the scale of thermodynamic corrections, while the other controls the number of available phases and the arrangement of light rings.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

I'm working from the abstract only, so this is a judgment about a summary, not the paper. What I can say: the combination of EUP corrections with quintessence-charged AdS black holes, plus Duan's topological method applied to both thermodynamics and photon spheres, is a plausible extension and not obviously nonsense. The abstract makes concrete, checkable claims: analytic T, S, C, integer winding numbers, and photon-sphere splitting/merging that preserves total exterior charge -1. That specificity is a real plus.

The soft spot is exactly what the stress-test note flags. The abstract doesn't say how the EUP correction enters. If they just replace T in the classical RN-AdS-quintessence metric, then S and C computed via standard thermodynamics won't satisfy the first law, and the quantitative claims collapse. This is a well-known pitfall in the GUP/EUP literature, and the abstract gives no indication that they've avoided it. Also, winding numbers from Duan's method depend on regularization choices, so the integers alone are not a strong diagnostic. And there's no citation to prior EUP black hole thermodynamics, so I can't tell if the novelty is just the topology or also the thermodynamics.

These are not failures I've found in the paper; they're gaps in the abstract. But given the subfield's track record, the first-law check is the one I'd want referees to enforce. If the full text derives T, S, C from a single consistent framework—say a deformed metric or a proper action—and shows dM = T dS holds, then this is a solid subfield contribution. If not, the central quantitative part fails.

As an editor, I'd send this to peer review rather than desk-reject. The claims are specific enough to check, and the combination is not obviously wrong. I'd expect a referee to demand the derivation and to verify the first law. Who's this for? People working on black hole thermodynamics, GUP/EUP phenomenology, and topological methods. I wouldn't cite it until I've seen the full text, but I'd read it if I had it.

My honest take: it's a plausible paper that could be either a legitimate extension or another example of the first-law pitfall; the abstract alone can't distinguish those.

Referee Report

3 major / 3 minor

Summary. The paper presents a combined topological and thermodynamic analysis of charged AdS black holes surrounded by quintessence, with corrections from the Extended Uncertainty Principle (EUP). The abstract claims analytic expressions for the EUP-corrected Hawking temperature, entropy, and heat capacity, together with a study of the relaxation-time function τ(r_h) and the identification of inflection points that depend on the quintessence barotropic index. It further applies Duan's topological current method to assign winding numbers to thermodynamic critical points and to photon spheres, reporting that quintessence can split or merge photon spheres while preserving a total exterior topological charge of -1.

Significance. If the derivations are correct, the paper would contribute to a growing literature on black hole thermodynamics and topology in modified uncertainty-principle frameworks. The combination of EUP corrections with quintessence is nontrivial, and the claimed preservation of total topological charge under splitting/merging is an interesting structural result. The abstract indicates that the analysis is analytic, which would be a strength if fully transparent. However, with only the abstract available, the central quantitative claims cannot be checked, and the physical consistency of the EUP-modified thermodynamic quantities is not yet established.

major comments (3)

[Abstract (EUP-corrected T, S, C)] The abstract states that analytic expressions for the corrected Hawking temperature, entropy, and heat capacity are derived in terms of the EUP deformation parameter, but it does not state how the EUP correction is implemented. If the correction is introduced by directly replacing T while keeping the classical RN-AdS-quintessence metric, then S=∫dM/T and C=T(dS/dT) generically violate the first law dM=T dS at fixed charge and quintessence parameter, and the entropy will not match the area law. The authors must either derive T, S, and C from a single consistent deformed metric (e.g., a modified lapse) or explicitly verify the first law and Smarr relation. Without this, the central quantitative claim is not secure.
[Abstract (quintessence barotropic indices)] The values ω_q = -2/3 and -1/3 are introduced without derivation or discussion of their provenance in the quintessence model. The claimed dependence of the number of inflection points, winding numbers, and photon-sphere splitting on the equation-of-state parameter is a central result; the reader needs to know whether these values are exhaustive, physically motivated, or merely illustrative. The authors should justify these choices and explain how the results depend on the allowed range of ω_q, including energy conditions and stability of the quintessence field.
[Abstract (topological charge -1)] The claim that quintessence can split or merge photon spheres while preserving the total exterior topological charge of -1 is stated without any expression or derivation. Since Duan's topological current method involves a normalization choice for the topological current, the integer values of the winding numbers are not unique unless that choice is specified. The authors should present the explicit computation of the winding numbers for the considered metric, including the contribution from any zero points at infinity, to demonstrate that the total charge is indeed -1 in the exterior region.

minor comments (3)

[Abstract] The term 'infrared gravitational corrections' is somewhat vague; EUP is associated with a minimal momentum/maximal length scale, and it would be helpful to state the specific uncertainty relation used.
[Abstract] The relaxation-time function τ(r_h) is mentioned but not defined in the abstract. If this is a standard quantity, a brief definition or reference would aid the reader.
[Abstract] The notation ω_q for the barotropic index is used without explicitly connecting it to the quintessence energy-momentum tensor; a one-line definition of the quintessence equation of state would improve clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular step identifiable from the abstract; the derivations are model-internal consequences.

full rationale

The abstract describes a model in which the EUP deformation parameter and quintessence barotropic indices are inputs to a modified black-hole metric (or thermodynamic framework). From that framework, it computes corrected Hawking temperature, entropy, heat capacity, inflection points, and winding numbers. Computing outputs from assumed inputs is not circular: the outputs are not used to define the inputs. No equation is shown in which the EUP parameter or quintessence index is defined in terms of the derived temperature or winding numbers, and no fitted data are renamed as predictions. The observation that the total exterior topological charge of photon spheres remains -1 is a consistency statement of the topological method (sum of local winding numbers equals boundary charge), not a fitted prediction. The first-law concern raised in the skeptic note is a physical consistency issue requiring the explicit deformation of the metric; it is not evidence of circularity. Because the full text is unavailable, no self-citation load-bearing chains can be evaluated, but nothing in the abstract exhibits the required reduction to inputs.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central results depend on two free parameters (EUP deformation and quintessence barotropic index) and three background assumptions about the correct effective spacetime model and the applicability of the topological method. No new particles or forces are introduced; the EUP and quintessence are drawn from prior literature.

free parameters (2)

EUP deformation parameter
Introduced as a modification parameter in the uncertainty relation; no value or prior constraint given in the abstract; all corrected quantities (temperature, entropy, capacity) depend on it.
Quintessence barotropic index ω_q = -2/3 and -1/3
Chosen as two representative values; the phase structure and photon-sphere topology depend on this choice.

assumptions (3)

domain assumption The extended uncertainty principle modifies the Heisenberg relation by introducing a minimal momentum/maximal length scale.
Abstract states this modification as the starting point; it is not derived in the abstract and is assumed to be the correct effective quantum-gravity correction for the black hole spacetime.
domain assumption Quintessence is modeled as a barotropic perfect fluid with p_q = ω_q ρ_q that contributes a specific term to the metric.
The abstract states that inclusion of quintessence modifies the black hole metric function; the specific Kiselev-type solution is assumed without derivation.
standard math Duan's topological current method yields integer winding numbers for off-shell free energy critical points and photon spheres.
The method is a standard mathematical tool, but its physical application here depends on the chosen off-shell free energy definition.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Infrared Extended Uncertainty Principle Corrections and Quintessence-Induced Topology of Reissner-Nordstr\"om AdS Black Holes." pith.science (2026). https://pith.science/paper/OT62EPHY

@misc{pith2026250814953,
  author       = {Pith},
  title        = {Pith review of: Infrared Extended Uncertainty Principle Corrections and Quintessence-Induced Topology of Reissner-Nordstr\"om AdS Black Holes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OT62EPHY}},
  note         = {Machine review of arXiv:2508.14953}
}

abstract

We present a unified topological and geometric analysis of charged Anti-de Sitter (AdS) black holes immersed in a quintessence field, incorporating infrared gravitational corrections arising from the Extended Uncertainty Principle (EUP). The latter modifies the standard Heisenberg uncertainty relation by introducing a minimal momentum/maximal length scale, which effectively captures long-wavelength quantum gravitational effects relevant to black hole thermodynamics in curved spacetimes. We derive analytic expressions for the corrected Hawking temperature, entropy and heat capacity in terms of the EUP deformation parameter. Furthermore, the inclusion of quintessence, characterized by barotropic indices $\omega_q = -\frac{2}{3}$ and $\omega_q = -\frac{1}{3}$, modifies the black hole metric function. By studying the relaxation-time function $\tau(r_h)$, we identify a number of inflection points that depends sensitively on the equation of state parameter of quintessence, indicating a nontrivial impact of the latter on the black hole phase structure. Applying Duan's topological current method to the off-shell free energy, we compute integer-valued winding numbers associated with each thermodynamic critical point. A parallel topological analysis of the photon sphere assigns charges $ \pm 1 $ to individual light rings, showing that quintessence effects can trigger the splitting or merging of photon spheres, while preserving the total exterior topological charge of $-1$.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Topological Signatures and Geometrothermodynamics of Critical Phenomena in Regularized Maxwell Black Holes
gr-qc 2025-10 conditional novelty 5.0 of 10

For RegMax-AdS black holes, the dimensionless combination α²|Q| separates a stable small-black-hole regime with an intermediate phase (α²|Q| > 1) from an unstable small-black-hole regime with simple first-order coexis...

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.