{"id":"eda3c2db-eb58-41c6-8231-49db1cf99ddf","arxiv_id":"1908.08201","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":6,"one_line_summary":"The paper claims EUP corrections make a black hole with an f(R) global monopole unstable, but its abstract and body disagree about whether radiation is enhanced or suppressed.","lead":"This paper applies an extended uncertainty principle (EUP) to a black hole that carries an f(R) global monopole, and reports that the correction changes radiation and makes the black hole split spontaneously. The abstract says the EUP encourages radiation, while the main text says it retards radiation, so the paper's central message is internally contradictory.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The fragmentation claim rests entirely on Eq. (6), whose large-mass limit shrinks the EUP horizon and makes entropy decrease with mass; if this ansatz has the wrong sign, both headline results reverse.","rationale":"The reader's rejection is well supported. The contradiction between the abstract ('entropy difference larger ... radiate more greatly') and Section II ('stronger influence from EUP leads the value of Delta S' smaller, which retards the radiation') is unambiguous and would by itself make the paper unreliable. I nevertheless locate the load-bearing weakness in Eq. (6), because that single ansatz is the only input that generates both the EUP tunneling correction in Eqs. (12)-(13) and the fragmentation instability in Eqs. (17)-(20). The manuscript never derives Eq. (6) from the defining EUP relation Eq. (2); it imports the ansatz from Ref. [19]. Its large-mass behavior is suspicious: for r_H much larger than L*/sqrt(alpha), r'_H ~ L*^2 / (4 alpha r_H), so S' decreases with M. That is exactly the branch on which the universal fragmentation result depends. If the EUP correction instead grows the effective distance in the large-r limit, the sign of the denominator in Eq. (6) flips and both headline results reverse. The proposed recomputation with the alternative horizon is the minimal check that would show whether the claimed instability is robust or an artifact of an unverified sign convention. The verdict remains REJECT, unchanged from the reader.","tokens_in":9409,"tokens_out":17995,"duration_ms":180484,"concrete_test":"With the parameters of Figure 2 (8 pi G eta^2 = 0.1, psi_0 = 0.05, G = M = L* = 1, alpha = 2, 6, 10), recompute Delta S' from Eqs. (18)-(20) using the alternative EUP horizon r'_H = r_H (1 + 4 alpha r_H^2 / L*^2) in place of Eq. (17), and also evaluate S'(M) for M = 1, 10, 100. If Delta S' is not positive for every epsilon_M, or if S'(M) no longer decreases with M, the universal fragmentation result is an artifact of the sign of the denominator in Eq. (6).","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim has two legs: EUP enhances tunneling radiation, and EUP makes the black hole fragment for any mass split. Both legs pass through the same unproven input, Eq. (6): Delta x' = Delta x / (1 + alpha Delta x^2 / L*^2). Eq. (17) then gives r'_H = r_H / (1 + 4 alpha r_H^2 / L*^2). For r_H much larger than L*/sqrt(alpha), this corrected horizon falls as L*^2 / (4 alpha r_H), so the EUP-corrected entropy S' = pi r'_H^2 falls with mass. That decreasing-entropy branch is exactly what makes Delta S' > 0 for arbitrary fragmentation in Figures 2 and 3, and it also controls the sign of Eq. (13). The manuscript never derives Eq. (6) from Eq. (2); it imports the ansatz from Ref. [19] and does not test its large-distance behavior. If the physically correct EUP correction grows the effective distance rather than shrinking it, for example Delta x' = Delta x (1 + alpha Delta x^2 / L*^2), then both the sign of the radiation correction and the universal fragmentation instability reverse. The abstract/body contradiction about whether EUP helps or retards radiation is a separate symptom of the same uncontrolled sign in Eqs. (6) and (13).","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":9892,"tokens_out":3772,"duration_ms":36831,"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":[{"comment":"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":"Abstract and Section II (Eq. (13), Figure 1)"},{"comment":"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":"Section II, Eq. (6) and Section III, Eq. (17)"},{"comment":"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.","section":"Section II, Eqs. (12)-(13)"},{"comment":"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.","section":"Figure captions and parameter definitions"}],"minor_comments":[{"comment":"The abstract contains a typo: \"ra diation\" should be \"radiation.\"","section":"Abstract"},{"comment":"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.","section":"Introduction"},{"comment":"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.","section":"Figures 1-3"},{"comment":"Several references are incomplete or improperly formatted, including Ref. [39], which lists multiple papers under one number without individual citation keys.","section":"References"}],"recommendation":"reject","confidential_remarks":"The paper's central result is internally contradictory (abstract vs. Section II), and the fragmentation conclusion rests on an unverified sign choice in the EUP ansatz. These are not presentation issues that a moderate revision could address; the authors would need to rework the physics or substantially reframe the claims. The paper also has parameter inconsistencies in the figures. I recommend rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nThe 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.\n\nThe 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.\n\nThe 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.\n\nFor 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.","headline":"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.","tokens_in":10262,"tokens_out":3551,"would_cite":false,"duration_ms":31416,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.65.Bz","03.65.Ta","04.60.Bc"],"model":"deepseek-v4-flash","headline":"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.","keywords":["EUP","extended uncertainty principle","f(R) gravity","global monopole","black hole entropy","Hawking tunneling radiation","black hole fragmentation","black hole instability"],"falsifier":"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.","tokens_in":9235,"feed_emoji":"🕳️","tokens_out":8962,"duration_ms":81441,"temperature":0.7,"pith_summary":"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.","feed_headline":"EUP makes an f(R)-monopole black hole spontaneously divide","feed_subtitle":"Entropy changes show the black hole fragments for any mass split; monopole and f(R) terms only adjust the rate.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the EUP distance-uncertainty rule and the prescription for using it to correct black hole horizons and entropy.","marker":"[19]"},{"why":"Provides the f(R) global monopole metric and horizon roots that define the black hole background being studied.","marker":"[9]"},{"why":"Supplies the Parikh-Kraus-Wilczek tunneling framework and the identification of tunneling probability with e raised to the entropy difference.","marker":"[46]"},{"why":"Gives the thermodynamic criterion that a black hole can fragment when the final entropy exceeds the initial entropy.","marker":"[47]"},{"why":"Earlier GUP treatment of tunneling for the same f(R) global monopole black hole, used as the comparison case.","marker":"[73]"},{"why":"Earlier result that the same black hole does not split under the Heisenberg principle but does under GUP, the baseline the EUP result is compared with.","marker":"[78]"}],"fun_headline_variants":["EUP makes black holes fragment, f(R) monopole no shield","Extended uncertainty principle destabilizes f(R)-monopole black hole","Black hole with f(R) monopole splits under EUP effects","EUP-induced instability drives black hole spontaneous division","Uncertainty principle extension forces black hole to divide"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["EUP makes black holes fragment, f(R) monopole no shield","Extended uncertainty principle destabilizes f(R)-monopole black hole","Black hole with f(R) monopole splits under EUP effects","EUP-induced instability drives black hole spontaneous division","Uncertainty principle extension forces black hole to divide"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.0006,"raw_usage":{"total_tokens":2751,"prompt_tokens":842,"completion_tokens":1909,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":458,"completion_tokens_details":{"reasoning_tokens":1824}},"tokens_in":458,"tokens_out":1909,"duration_ms":13111,"temperature":1.0,"reasoning_tokens":1824,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:46:39.202350+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the f(R) global monopole metric and horizon roots that define the black hole background being studied."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Parikh-Kraus-Wilczek tunneling framework and the identification of tunneling probability with e raised to the entropy difference."},{"cited_title":"Emparan, R","cited_arxiv_id":null,"evidence_quote":"Gives the thermodynamic criterion that a black hole can fragment when the final entropy exceeds the initial entropy."}],"review_version":1}