The instability of a black hole with $f(R)$ global monopole under extended uncertainty principle

Hongbo Cheng; Yue Zhong

REVIEW 4 major objections 4 minor 2 cited by

The instability of a black hole with $f(R)$ global monopole under extended uncertainty principle

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper argues that extended-uncertainty corrections make an f(R)-global-monopole black hole thermodynamically unstable, fragmenting for any mass split and altering its tunneling radiation.

desk verdict The paper's abstract promises stronger radiation under EUP, but its own Section II concludes the opposite, and the fragmentation result rests entirely on an unexamined sign in the EUP ansatz. read the letter →

arxiv 1908.08201 v1 pith:Z4CQW6YM submitted 2019-08-22 hep-th gr-qc

Hongbo Cheng , Yue Zhong This is my paper · ORCID

classification hep-thgr-qc PACS 03.65.Bz03.65.Ta04.60.Bc

keywords EUPextendeduncertaintyprinciplef(R)gravityglobalmonopoleblackholeentropyHawkingtunnelingradiationfragmentationinstability

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 asks whether a black hole carrying an $f(R)$-global-monopole defect stays thermodynamically stable when the Heisenberg relations are replaced by the Extended Uncertainty Principle (EUP), a large-distance correction that shrinks measurable position intervals. The authors derive the entropy difference for two channels of evolution: Parikh-Kraus-Wilczek tunneling radiation and spontaneous fragmentation into two black holes. They find that the EUP makes the fragmentation entropy difference positive for every mass split $0\le \varepsilon_M\le 1$, so the black hole should divide spontaneously; the global monopole parameter and the $f(R)$ gravity parameter shift the size of the effect but not its sign. For tunneling radiation, the body of the paper concludes that stronger EUP corrections reduce the entropy difference and retard emission (the abstract says the opposite). If the calculation holds, the EUP would be a general destabilizer of this class of black holes, with modified gravity and topological defects only moderating the process.

What carries the argument

The load-bearing device is the EUP distance-uncertainty relation $\Delta x'=\Delta x/(1+\alpha\Delta x^2/L_*^2)$, translated into a corrected horizon radius $r_H'=r_H/(1+4\alpha r_H^2/L_*^2)$. Because the denominator grows with $r_H$, the effective horizon shrinks sharply for large black holes, which is what makes the entropy difference for fragmentation positive and drives the spontaneous division. All of the paper's temperature, entropy, radiation, and fragmentation results route through this single ansatz.

What would settle it

Numerically evaluate the full entropy-difference integral in Eq. (12) over the parameter ranges used in Figures 1-3; if $\Delta S'$ is negative for any mass split $0\le\varepsilon_M\le1$, or if $d\Delta S'/d\alpha$ changes sign, the paper's claims fail. A second check is to recompute the fragmentation entropy difference using a different large-scale uncertainty ansatz in place of Eq. (6) and see whether it remains positive.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that the EUP removes the stability that the same black hole possesses under the ordinary Heisenberg principle. The corrected horizon $r_H'=r_H/(1+4\alpha r_H^2/L_*^2)$ follows from the EUP distance rule, and the entropy built from that horizon gives $\Delta S'>0$ for the final two-black-hole state at all mass fractions, so the second law admits and even favors fragmentation. The same corrected entropy also enters the tunneling probability $\Gamma'\sim e^{\Delta S'}$; the paper's Section II calculation shows $\Delta S'$ decreasing as $\alpha$ grows, which suppresses radiation, while the abstract asserts the opposite sign. The monopole and $f(R)$ parameters modulate the magnitude but cannot overturn the EUP-driven instability, which the paper states as its final conclusion.

Load-bearing premise

The entire calculation rests on the EUP rule $\Delta x'=\Delta x/(1+\alpha\Delta x^2/L_*^2)$ being the correct large-distance uncertainty correction; if that rule is wrong, the shrinking effective horizon, and with it both the predicted fragmentation and the modified radiation, disappears.

Editorial extensions

If this is right

Under the EUP, an isolated f(R) global monopole black hole is thermodynamically unstable to fragmentation into two black holes for every mass fraction $0\le\varepsilon_M\le1$.
The body's calculation says stronger EUP corrections lower the entropy difference for tunneling radiation, making the black hole emit less; this is opposite to the GUP case, where stronger corrections enhance emission.
The global monopole parameter $8\pi G\eta^2$ and the $f(R)$ parameter $\psi_0$ adjust the magnitude of the entropy differences but cannot change the sign, so the EUP remains the controlling instability.
Without EUP corrections, the same black hole does not split under the Heisenberg principle; the EUP is thus the element that opens the fragmentation channel.

Reading between the lines

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

Editorial inference: because the denominator in Eq. (6) makes the corrected horizon shrink with mass, the entropy eventually becomes a decreasing function of $M$ for large black holes; the fragmentation conclusion is a direct symptom of that behavior, and a different large-distance uncertainty law would likely remove it.
Editorial inference: the body's claim that stronger EUP retards radiation and the abstract's claim that it promotes radiation cannot both be right; recomputing the full integral rather than the leading-order expression (13) would settle which sign is correct.
Editorial inference: if the fragmentation claim is right, EUP corrections would predict that black holes of this type are short-lived with respect to splitting, which would have observable consequences for astrophysical black holes if the EUP scale $L_*$ is not astronomically large, but the paper does not estimate timescales or rates.

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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

The thing to know: this manuscript has a load-bearing contradiction between the abstract and the body. The abstract says EUP corrections make the entropy difference larger and encourage radiation; Section II and the conclusion say the stronger EUP effect leads to smaller Delta S' and retards radiation. That is not a wording slip. The radiation claim is inverted, and any referee would trip on it immediately.

The novel part is narrow but legitimate: the authors take the known f(R) global monopole black hole, apply the EUP-corrected distance ansatz from Mureika, and recompute the entropy difference for tunneling and fragmentation. The method is borrowed, but the combination is new and the question - whether EUP behaves differently from GUP here - is a fair one. They also compare to their own earlier GUP papers, which is appropriate.

The soft spots are serious. The integral from Eq. (12) to Eq. (13) is asserted, not shown; it is not a trivial step. The figures use 8 pi G eta^2 = 0.1 while the text says the standard value is about 1e-5, and epsilon_eta appears in captions without definition. More importantly, both headline results pass through Eq. (6), the EUP distance relation. That relation makes the corrected horizon r'_H decrease like 1/r_H for large black holes, so the entropy becomes a decreasing function of mass. That decreasing branch is exactly what makes Delta S' positive for arbitrary fragmentation. The paper never derives Eq. (6) from Eq. (2); if the physically correct EUP correction had the opposite sign, both conclusions would reverse. This is not a peripheral concern; it is the load-bearing input.

The paper is a reasonable exercise in parameter scanning once you grant the ansatz, but it does not support its stated claims. The contradiction alone is a desk-reject level problem.

For a reader already working on GUP/EUP black hole thermodynamics, it is a cautionary example of how sign choices in the uncertainty relation control the result. I would not cite it or bring it to reading group in its current form, and I would not send it to referees. If the authors fix the abstract, justify or replace Eq. (6), show the integral, and correct the figures, the fragmentation part might be salvageable as a modest paper, but that is for a resubmission.

Referee Report

4 major / 4 minor

Summary. The manuscript studies the thermodynamic instability of a black hole with an f(R) global monopole under the extended uncertainty principle (EUP). The authors compute the entropy difference for Parikh-Kraus-Wilczek tunneling radiation in Section II and for fragmentation in Section III. The body of the paper concludes that EUP corrections reduce the entropy difference and therefore retard tunneling radiation, and that EUP makes the black hole fragment spontaneously into two parts with arbitrary mass distribution. The abstract, however, states that EUP corrections make the entropy difference larger and encourage the black hole to radiate more greatly, and that EUP causes the black hole's division.

Significance. If the conclusions were reliable, the paper would establish a qualitative contrast between GUP and EUP effects on black hole stability, a topic of current interest in quantum-gravity phenomenology. The manuscript does follow a standard tunneling framework and provides explicit formulas for the entropy differences, which is a useful starting point. However, the central claim is not robust: the abstract and Section II state opposite signs for the EUP correction to radiation, and the fragmentation result depends entirely on an unverified EUP distance ansatz whose large-distance behavior drives the sign of the effect. These issues undermine the headline results as presented.

major comments (4)

[Abstract and Section II (Eq. (13), Figure 1)] The abstract states that "EUP corrections make the entropy difference larger to encourage the black hole to radiate more greatly," but Section II concludes the opposite: Eq. (13) and Figure 1 show that Delta S' decreases with increasing alpha, and the text explicitly says that "the stronger influence from EUP leads the value of Delta S' smaller, which retards the radiation of the black hole." This is a direct and load-bearing contradiction in the central claim of the paper.
[Section II, Eq. (6) and Section III, Eq. (17)] The EUP-corrected distance interval in Eq. (6) is imported from Ref. [19] without derivation, and the corrected horizon radius in Eq. (17) falls as L*^2/(4 alpha r_H) for r_H much larger than L*/sqrt(alpha). This large-mass behavior makes the EUP-corrected entropy a decreasing function of mass, which is what produces Delta S' > 0 for arbitrary fragmentation in Figures 2 and 3 and also controls the sign of Eq. (13). The manuscript does not test or justify this large-distance behavior; if the physically correct EUP correction grows the effective distance instead of shrinking it, both headline conclusions reverse. Since the central results are sign-dependent, this assumption requires independent support.
[Section II, Eqs. (12)-(13)] The integral leading to Eq. (13) is not shown, and the claim that Eq. (12) reduces to Eq. (9) for alpha = 0 is not demonstrated. The denominator in Eq. (12) has a nontrivial structure, and the jump from the integral to the closed-form ratio in Eq. (13) is not transparent. The reader cannot verify the sign or magnitude of the claimed EUP correction without redoing the calculation independently.
[Figure captions and parameter definitions] Figure 1 uses 8 pi G eta^2 = 0.1, while the text states that in a typical grand unified theory 8 pi G eta^2 is approximately 10^-5. Figures 2 and 3 introduce epsilon_eta = 0.5, which is never defined anywhere in the manuscript. These inconsistencies make the quantitative results impossible to reproduce and raise doubts about whether the plotted behavior reflects the physical parameter regime.

minor comments (4)

[Abstract] The abstract contains a typo: "ra diation" should be "radiation."
[Introduction] The sentence "it was found th at the parameter subject to the modification of gravity provides stable circular orbits" has a spacing error and would benefit from rewording.
[Figures 1-3] The axis labels in all figures are garbled (e.g., "'S1 D i" instead of a clear label for Delta S'). The figures should be redrawn with clean labels and a legend identifying the curves.
[References] Several references are incomplete or improperly formatted, including Ref. [39], which lists multiple papers under one number without individual citation keys.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the calculation is self-contained once the EUP ansatz in Eq. (6) is granted, and the authors' self-citations are only comparative, not load-bearing.

full rationale

The paper's derivation chain is: take the f(R) global monopole metric (3)-(4) from prior external literature, import the EUP position-uncertainty rule Eq. (6) from Mureika's Ref. [19], use it to obtain the corrected horizon and temperature, integrate to get an entropy difference for tunneling radiation, and compute the fragmentation entropy difference from the corrected horizon formula Eq. (17). No parameter is fitted to the target conclusions and no equation assumes the sign of Delta S'. The fragmentation result is a computed consequence of the monotonicity of r'_H(M) implied by Eq. (17); it is not inserted as an input. The references to the authors' own earlier GUP papers [73,74,78] are used to compare the EUP results with the GUP case and to state previously obtained results, but those statements are not needed to derive the EUP claims. The EUP ansatz Eq. (6) is an external input with an explicit citation and does not itself contain the paper's conclusions. The abstract/body contradiction about whether EUP enlarges or reduces the entropy difference is a sign error or wording inconsistency rather than circular reasoning, and the sensitivity of both headline results to the sign of Eq. (6) is a legitimate physical-assumption risk, not a circularity. Accordingly, the paper receives a score of 0.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

No new particles, forces, or conserved quantities are introduced. The only new object is the EUP-modified horizon radius, which is a reparameterization of the input uncertainty relation rather than an independently testable entity.

free parameters (6)

alpha (EUP coefficient) = symbolic; figures use 2, 6, 10
Dimensionless strength of EUP correction; set by hand in plots, not constrained by data.
L* (EUP distance scale) = L* = 1 in figures
Large fundamental scale in EUP relation; inherited from prior literature, fixed to 1 for plotting.
psi_0 (f(R) parameter) = 0.01, 0.05, 0.08 in Figures 1 and 3
Deviation from general relativity; chosen by hand in plots, not fitted.
8 pi G eta^2 (monopole parameter) = 0.1 in figures; text says about 1e-5
Global monopole solid-angle deficit; figure value differs from quoted physical value by four orders of magnitude.
epsilon_M (mass fraction) = scanned over [0,1]
Mass split in fragmentation; it is the variable of the plot, not a fitted constant.
epsilon_eta = 0.5 in Figure 2 and 3 captions
Appears in figure captions but is never defined in the text.

assumptions (6)

domain assumption The spacetime of a black hole with f(R) global monopole is given by metric (3)-(4) with A(r)=1-8 pi G eta^2 - 2GM/r - psi_0 r.
Taken from refs [9,10,15]; the paper does not derive this solution and relies on its validity beyond GR.
ad hoc to paper EUP modifies the distance interval according to Eq. (6), Delta x' = Delta x / (1 + alpha Delta x^2 / L*^2).
Phenomenological ansatz from Mureika [19]; all quantitative results follow from this map, so the conclusions inherit any error in it.
ad hoc to paper The black hole horizon is identified with rH = r- in Eq. (5), the inner root, and the horizon radius is used in Delta x = 2 rH.
The text calls r- the black hole horizon without discussion of why the outer root r+ is not used; this choice affects the entropy formulas.
standard math Hawking temperature and entropy obey TH = dE/dS approximately equal to dM/dS and the tunneling probability is Gamma similar to e^{Delta S}.
Parikh-Wilczek tunneling formalism; standard within the semiclassical black hole literature.
domain assumption Fragmentation is allowed when the final entropy S_f exceeds the initial entropy S_i, with fragments of the same monopole type and conserved total mass.
Second-law criterion from refs [47,66,78]; the paper assumes the fragments are also f(R) global monopole black holes.
ad hoc to paper The EUP-corrected horizon radius r' = r / (1 + 4 alpha r^2 / L*^2) is the relevant length for the entropy area S = pi r'^2.
Eq. (17) assumes the entropy-area law survives with the corrected radius; no independent derivation is given.

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Cite this review

Pith. "Pith review of The instability of a black hole with $f(R)$ global monopole under extended uncertainty principle." pith.science (2026). https://pith.science/paper/Z4CQW6YM

@misc{pith2026190808201,
  author       = {Pith},
  title        = {Pith review of: The instability of a black hole with $f(R)$ global monopole under extended uncertainty principle},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z4CQW6YM}},
  note         = {Machine review of arXiv:1908.08201}
}

abstract

We consider the evolution of black hole involving an $f(R)$ global monopole based on the Extended Uncertainty Principle (EUP). The black hole evolutions refer to the instability due to the Parikh-Kraus-Wilczeck tunneling radiation or fragmentation. It is found that the EUP corrections make the entropy difference larger to encourage the black hole to radiate more greatly. We also show that the appearance of the EUP effects result in the black hole's division. The influence from global monopole and the revision of general relativity can also adjust the black hole evolution simultaneously, but can not change the final result that the black hole will not be stable because of the EUP's effects.

Figures

Figures reproduced from arXiv: 1908.08201 by the authors.

**Figure 2.** The solid, dotted and dashed curves of the dependence o [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗

**Figure 3.** The solid, dotted and dashed curves of the dependence o [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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A Godel-rotation-modified uncertainty principle is used to define a corrected black hole mass, producing enlarged horizon, shadow, and deflection with lower bounds a/M ~ 10^5 from EHT and PPN data.
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gr-qc 2024-11 reject novelty 3.0 of 10

The authors derive a black hole metric with a cosmological-constant-dependent effective mass and use EHT and VLBI data to put extremely weak bounds on a quantum parameter beta.

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Reviewed August 14, 2026 · model on record in the stance chip above.

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