{"id":"c9a8378a-583a-4b3e-95a3-52491af1503b","arxiv_id":"2501.00060","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"The paper derives effective potentials and GUP-modified Hawking thermodynamics for cylindrical black holes in f(R) and Ricci-Inverse gravity, but the advertised quasinormal mode analysis is absent.","lead":"This paper studies cylindrical black holes in two modified theories of gravity and writes down effective potentials for scalar and electromagnetic waves around them. It also computes corrections to Hawking temperature and entropy from quantum uncertainty, but it does not actually compute the quasinormal mode frequencies it claims to analyze.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (5.23) misidentifies the Hawking temperature: for the Lemos metric T_H = Δ'(r_h)/(4π), not sqrt(Δ'(r_h))/(4π); the GUP temperatures (5.25)-(5.26) and entropies (5.38)-(5.39) inherit this error.","rationale":"The reader's weakest assumption (the reliability of the imported effective cosmological constants from ref. [77]) is real, but it is not the most decisive problem: even granting Λ_m, Sec. 5 contains an internal, checkable mistake. Eq. (5.8) defines Δ'(r_h) = 2κ, which together with κ = 2π T_H implies T_H = Δ'(r_h)/(4π). Eq. (5.23) instead writes T_H = sqrt(Δ'(r_h))/(4π), and Eq. (5.24) inherits the square root. This is not a convention difference; it changes the scaling of the temperature with M and Λ. Tracing back, the WKB radial momentum in Eqs. (5.6)-(5.16) has an incorrect metric factor: for g_tt = -F and g_rr = 1/F, the radial spatial term in the KG equation is g^{rr}(W')^2 = F(W')^2, and W' ~ 1/(F sqrt(...)) near the horizon, giving Im W ∝ 1/Δ' rather than 1/sqrt(Δ'). Thus the square-root error is systematic. The entropy section is also internally inconsistent: Eq. (5.33) states A = 2π z r_h, but Eq. (5.34) substitutes dA = 2π z r_h dr_h and integrates to S ∝ r_h^2, whereas A/4 = π z r_h/2. Since the GUP-corrected entropy is obtained by integrating the same wrong temperature, the central thermodynamic claims fail independently of Λ_m. Recomputing the GR limit (Λ_m → Λ, α_GUP → 0) against the textbook definition suffices to confirm the problem. The rest of the paper, including the effective potentials, also depends on quantities from a self-cited preprint, but the thermodynamic error alone is enough to invalidate the advertised results.","tokens_in":22021,"tokens_out":15275,"duration_ms":130544,"concrete_test":"Recompute the GR limit by hand: for f(r) = α^2 r^2 - 4M/(α r) with α = sqrt(-Λ/3), the horizon is r_h = (4M)^{1/3}/α and f'(r_h) = sqrt(-3Λ)(4M)^{1/3}. Then the standard Hawking temperature is T_H = f'(r_h)/(4π). Evaluate Eq. (5.24) at α2 = α3 = α4 = 0 and compare: the paper gives sqrt(f'(r_h))/(4π), which is not the Hawking temperature. Then redo the entropy integration in Eqs. (5.29)-(5.35) using dM = κ dA/(8π) and A = 2π z r_h; the result should be S_GUP = (π z r_h/2)/sqrt(1 - 2m_p^2 α_GUP), not Eq. (5.36). If these checks fail, the thermodynamic claims collapse.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Sec. 5, the GUP tunneling calculation mishandles the radial momentum. For the metric (2.22) with g_tt = -F and g_rr = 1/F, the leading-order KG/WKB equation is g^{tt}E^2 + g^{rr}(W')^2 + m_p^2[...] = 0, i.e. -E^2/F + F(W')^2 + ... = 0, so W' = ± sqrt(E^2 - F m_p^2(1 - 2m_p^2 α_GUP)) / (F sqrt(1 - 2m_p^2 α_GUP)). The paper's Eq. (5.6) instead uses g_rr(W')^2 in place of g^{rr}(W')^2 and effectively obtains W' ~ 1/sqrt(F). Near the horizon this gives Im W ∝ 1/sqrt(Δ'(r_h)) rather than 1/Δ'(r_h). Consequently Eq. (5.23) asserts T_H = sqrt(Δ'(r_h))/(4π), but the standard definition κ = Δ'/2 gives T_H = Δ'(r_h)/(4π). This square-root error propagates into Eqs. (5.24)-(5.26) and into the entropies (5.38)-(5.39). The entropy derivation is independently inconsistent: Eq. (5.33) sets A = 2π z r_h, yet Eq. (5.34) integrates 2π z r_h dr_h, yielding S ∝ r_h^2 rather than S ∝ r_h; the Bekenstein-Hawking limit would be A/4 = π z r_h/2. Both errors are internal and do not depend on the imported Λ_m.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies scalar and vector perturbations of Lemos-type cylindrical black holes embedded in f(R) and Ricci-Inverse gravity, and derives GUP-corrected Hawking temperatures and entropies via a tunneling calculation. The modified-gravity dependence enters only through effective cosmological constants Lambda_m^{f(R)} and Lambda_m^{RI} imported from the authors' earlier preprint [77]. The main results are the effective potentials (3.9) and (4.5) and the thermodynamic formulas (5.25)-(5.26) and (5.38)-(5.39), all obtained by substituting Lambda -> Lambda_m into known expressions for the Lemos metric.","tokens_in":22458,"tokens_out":12617,"duration_ms":117694,"significance":"If correct, the paper would provide explicit modified-gravity corrections to the perturbation potentials and to the Hawking radiation of cylindrical black holes, with the f(R) and Ricci-Inverse coupling constants controlling the deviations. The manuscript is transparent about the substitution structure and presents clear plots of the potentials and thermodynamic quantities. However, the advertised quasinormal-mode analysis is not actually performed, and the Hawking-temperature and entropy derivations contain internal, load-bearing errors. Because the central formulas of Section 5 are wrong as written, the contribution in its present form does not constitute a reliable quantitative result.","major_comments":[{"comment":"The tunneling calculation uses the wrong metric components. For the metric (2.22), the Hamilton-Jacobi equation from the Klein-Gordon equation is g^{tt}E^2 + g^{rr}(W')^2 + ... = 0, i.e. -E^2/f + f(W')^2 + ... = 0. Equation (5.4) instead writes 1/g_{tt}E^2 = g_{rr}(W')^2 + ..., which effectively uses g_{rr} in place of g^{rr}. This leads to W' ~ 1/sqrt(f) near the horizon rather than W' ~ 1/f, and consequently Eq. (5.23) gives T_H = sqrt(Delta'(r_h))/(4 pi) instead of the standard T_H = Delta'(r_h)/(4 pi) following from kappa = Delta'/2. The error propagates into the explicit temperatures (5.24)-(5.28) and into the entropy formulas (5.38)-(5.39).","section":"Sec. 5, Eqs. (5.33)-(5.39)"},{"comment":"The entropy derivation is internally inconsistent. Equation (5.33) sets A = 2 pi z r_h, which implies dA = 2 pi z dr_h, but Eq. (5.34) integrates 2 pi z r_h dr_h and yields S proportional to r_h^2. Moreover, for the metric (2.22) with g_phi phi = r^2 and g_zz = alpha^2 r^2, the horizon area for an axial length z is A = 2 pi alpha z r_h^2, not 2 pi z r_h. Thus both the area expression and its integration in Eqs. (5.34)-(5.36) are wrong, and the final GUP entropies (5.38)-(5.39) do not follow from the stated first-law integration.","section":"Sec. 5, Eqs. (5.33)-(5.39)"},{"comment":"The abstract and section titles promise an analysis of quasinormal modes, but no quasinormal frequencies or damping times are computed anywhere. Sections 3 and 4 reduce the perturbation equations to the Schrodinger-type form (3.8) and (4.3) and plot the effective potentials, but they never impose QNM boundary conditions, solve the eigenvalue problem, or list any omega values. The claim that QNMs are analyzed is therefore unsupported by the content of the paper.","section":"Secs. 3 and 4"},{"comment":"Every modified-gravity result in the paper depends on the effective cosmological constants Lambda_m^{f(R)} and Lambda_m^{RI} taken from ref. [77], a preprint by two of the present authors. The manuscript does not re-derive these constants or check them against an independent calculation, so the potentials, temperatures, and entropies inherit any error in [77]. Since this dependence is the sole channel through which the modified-gravity parameters enter the final formulas, the authors should either verify these constants within the present manuscript or state explicitly that the results are conditional on the correctness of [77].","section":"Sec. 2, Eqs. (2.8), (2.12), (2.21)"}],"minor_comments":[{"comment":"The displayed determinant is sqrt(-g) = r sqrt(-Lambda_m/3), but for the metric (3.3) the correct value is sqrt(-g) = r^2 sqrt(-Lambda_m/3). The subsequent radial equation (3.5) appears consistent with the r^2 factor, so this is likely a typographical error that should be corrected.","section":"Eq. (3.4)"},{"comment":"The metric functions are typeset ambiguously, e.g. expressions like '4 M q - Lambda/3 r' should clearly indicate whether the square-root factor is in the numerator or denominator. Please use explicit notation such as 4M/sqrt(-Lambda/3) r or 4M sqrt(-3/Lambda)/r.","section":"Eqs. (2.13), (2.22), (2.23), (3.3)"},{"comment":"There are several typographical and referencing issues: 'Feyman' should be 'Feynman'; the factor-of-two discussion around Eqs. (5.17)-(5.20) is described but the cited method in refs. [103,104] is not applied explicitly; and Eq. (5.10) contains the square root of a negative quantity without specifying that it is sqrt(-3/Lambda) for Lambda < 0.","section":"Sec. 5"}],"recommendation":"reject","confidential_remarks":"The manuscript's central thermodynamic derivation is internally inconsistent (wrong metric components in the WKB equation, square-root Hawking temperature, and an area/integration mismatch in the entropy), and the QNM analysis promised in the title and abstract is absent. These are not local presentation issues: correcting them requires redoing Section 5 and adding a substantial QNM computation. For a journal report, reject is appropriate. I would also note that the reliance on ref. [77], a preprint by two of the present authors, for all modified-gravity input deserves an independent check before any resubmission."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The honest headline: this is a substitution exercise with a broken thermodynamics section. The scalar and vector potentials are the standard cylindrical black hole potentials with Λ swapped for Λ_m, imported from ref. [77] by two of the present authors. No QNM frequencies or damping rates are computed, despite the abstract and conclusion advertising a QNM analysis.\n\nWhat the paper does well is modest but real. The scalar perturbation derivation in Sec. 3 is algebraically consistent, and the potential (3.9) plus its f(R)/RI special cases reduce properly to the GR limit when the coupling constants vanish. The plots comparing potentials for different coupling strengths are clear and might be useful to someone working on these specific models. The paper also honestly states that the effective cosmological constants come from ref. [77], which is a preprint by two of the authors; that is not by itself a flaw, but it is an unchecked input on which every modified-gravity result depends.\n\nThe soft spots are serious. First, the advertised QNM analysis is absent: the paper stops at effective potentials and never computes ω, so the stability claims are unsupported. Second, the GUP tunneling derivation in Sec. 5 has a load-bearing error. The Klein-Gordon/WKB equation should use g^{rr}(W')^2, not g_{rr}(W')^2; the paper uses the wrong component, which leads to Eq. (5.23) asserting T_H = sqrt(Δ'(r_h))/(4π). The correct surface-gravity relation is T_H = Δ'(r_h)/(4π). This square-root mistake propagates into Eqs. (5.24)-(5.28) and into the GUP temperatures. The entropy section is internally inconsistent on its own terms: Eq. (5.33) sets A = 2π z r_h, but Eq. (5.34) integrates 2π z r_h dr_h, yielding S ∝ r_h^2 instead of S ∝ r_h. These are not minor typos; they invalidate the central thermodynamic claims.\n\nThe stress-test note holds up on reading. I would not send this paper to a referee: the advertised QNM result is missing and the thermodynamics needs to be redone. The effective-potential part could become a short, useful note if the authors compute actual QNM frequencies and redo the GUP calculation properly, but as submitted it is not a reliable source for modified black hole thermodynamics.","headline":"The perturbation potentials are standard cylindrical black hole results with Λ replaced by Λ_m from the authors' own preprint, and the Hawking-temperature derivation has a square-root error that propagates into all thermodynamic formulas.","tokens_in":22993,"tokens_out":6475,"would_cite":false,"duration_ms":61129,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["04.70.Dy","04.50.Kd"],"model":"deepseek-v4-flash","headline":"For a cylindrical black hole, modified gravity changes the effective cosmological constant, and all perturbation and thermodynamic results follow from that replacement.","keywords":["cylindrical black holes","f(R) gravity","Ricci-inverse gravity","effective cosmological constant","quasinormal modes","Hawking radiation","generalized uncertainty principle","black hole remnants"],"falsifier":"Take the cylindrical metric (2.1) with f(r)=α²r²−4M/(α r), plug it together with f(R)=R+α1R²+...+$α4R^{5}$ into the f(R) field equations (2.5) with zero stress-energy, and solve for the constant that makes the equations hold; if the resulting effective cosmological constant does not match Eq. (2.8), the paper's central substitution claim collapses.","tokens_in":21826,"feed_emoji":"🕳️","tokens_out":9618,"duration_ms":91022,"temperature":0.7,"pith_summary":"This paper claims that, for a cylindrical black hole, switching from general relativity to f(R) or Ricci-inverse gravity changes only one input: the cosmological constant Λ is replaced by an effective constant Λ_m built from the coupling constants of the modified action. Starting from that replacement, the authors derive closed-form effective potentials for scalar and vector perturbations, identify the quasinormal-mode equation they feed into, and then compute GUP-corrected Hawking temperatures and entropies. The payoff is a concrete dictionary: each coupling constant of the modified theory controls how much the potential, the evaporation temperature, and the entropy deviate from their general-relativity values. In the Ricci-inverse model the temperature stays finite as Λ→0, which the authors read as a sign of black-hole remnant formation. If the formulas are right, they give a direct way to test these modified gravities through ringdown or radiation signatures.","feed_headline":"Modified gravity couplings retune black hole spectra and heat","feed_subtitle":"Scalar and vector potentials, Hawking temperature, and entropy follow from one effective constant.","key_machinery":"The load-bearing object is the effective cosmological constant Λ_m, obtained in an earlier paper by the same authors [77]: $Λ_m^{{f(R)}}$=Λ+α_k(1−k)4^$kΛ^{{k+1}}$ for the polynomial f(R), and $Λ_m^{{RI}}$=Λ−16Λ³α2+3β1/Λ+16β2/Λ²+4γ/Λ² for the Ricci-inverse model. Every result in the paper is this constant inserted into the GR cylindrical black hole metric and into the perturbation and thermodynamic equations; all coupling constants of the modified actions enter only through Λ_m. The second essential piece is the GUP-deformed Klein-Gordon equation, which modifies the radial momentum by the factor (1−2α_GUP(...)) and ultimately multiplies the Hawking temperature and entropy by √(1−2m_p²α_GUP). The mechanism that carries the argument is therefore substitution: solve the modified field equations once to get Λ_m, then recycle the standard GR computation with Λ_m in place of Λ.","core_discovery":"The paper's central claim is that the cylindrical black hole solutions of f(R)-gravity and Ricci-inverse gravity are the same GR metric with Λ replaced by $Λ_m^{{f(R)}}$ or $Λ_m^{{RI}}$, and that every derived quantity follows from that single substitution. For f(R) with f=R+Σ α_i $R^{{i+1}}$, the effective constant is Λ + α_k(1−k)4^k $Λ^{{k+1}}$; for the Ricci-inverse Class III model f=R+α1R²+α2R³+β1A+β2A²+γA_{μν}$A^{{μν}}$, it is Λ−16Λ³α2+3β1/Λ+16β2/Λ²+4γ/Λ². Writing the metric with Λ_m, the authors reduce the Klein-Gordon equation for a massless scalar to a Schrödinger-type equation with effective potential V=(ι²/r²+f′/r)f, ι²=m²−3k²/Λ_m, and the Maxwell equation to a similar potential V_e=f ι²/r²; these potentials, with the modified constants, are the paper's predictions for scalar and electromagnetic quasinormal modes. For thermodynamics, solving the GUP-modified Klein-Gordon equation near the horizon gives a tunneling rate whose Boltzmann comparison yields T_GUP=T_H√(1−2m_p²α_GUP), with T_H=(−3Λ_m)^{1/4}(4M)^{1/6}/(4π), and the first law then gives S_GUP=(πz/4)√(1−2m_p²α_GUP) r_h². The coupling constants of both modified actions therefore control the deviations from GR in all these quantities.","pith_inferences":["Since the paper's derivation stops at the potentials, a direct numerical computation of the quasinormal frequencies would be the obvious next step; if the potentials take negative values in the plotted ranges, the stability conclusion may not follow without checking the sign of the imaginary part.","The same Λ_m substitution should apply to other observables of this metric family, such as photon orbits, shadows, and geodesic precession, so the two modified theories predict a full parametric family of deviations from GR that could be tested with horizon-scale imaging.","The temperature formula T_GUP=T_H√(1−2m_p²α_GUP) is real only for 2m_p²α_GUP≤1; the paper does not discuss this bound, but it implies a maximum particle mass or GUP parameter beyond which the semiclassical temperature is undefined.","The remnant behavior in RI-gravity could be sharpened by computing the heat capacity: a change of sign in C=dM/dT near the minimum temperature would tell whether the remnant is thermodynamically stable."],"forward_implications":["For both modified theories, the scalar and vector perturbation potentials reduce exactly to the GR form when the coupling constants vanish, so any observational difference from GR ringdown is controlled by the strengths of the higher-curvature and anti-curvature terms.","The GUP correction factor √(1−2m_p²α_GUP) lowers the Hawking temperature and entropy for every model, slowing evaporation, and the same factor appears in the f(R) and RI cases because the derivation is metric-independent once Λ_m is substituted.","In the Ricci-inverse model the Hawking temperature remains nonzero as Λ→0, implying that evaporation stops at a remnant, whereas the f(R) model in the GR limit instead shows complete evaporation as Λ→0.","Because the effective potentials V and V_e are explicit functions of the coupling constants, quasinormal frequencies computed from them would shift with α2, α3, α4 (f(R)) and α2, β1, β2, γ (RI), providing a parameter-dependent ringdown signature."],"supporting_citations":[{"why":"Supplies the effective cosmological constants Λ_m^{f(R)} and Λ_m^{RI} that are substituted into every perturbation and thermodynamic formula.","marker":"[77]"},{"why":"Provides the GR cylindrical black hole metric that is the seed solution for both modified theories.","marker":"[78]"},{"why":"Supplies the covariant Klein-Gordon equation used to derive the scalar perturbation potential.","marker":"[79]"},{"why":"Supplies the tetrad formalism used to set up the Maxwell/vector perturbation equations.","marker":"[80]"},{"why":"Supplies the tunneling-rate and Boltzmann-factor comparison used to identify the Hawking temperature from the tunneling probability.","marker":"[84]"},{"why":"Gives the GUP-modified Klein-Gordon equation from which the corrected temperature is derived.","marker":"[100]"},{"why":"Fixes the factor-two problem in the tunneling-rate derivation and justifies normalizing the ingoing probability to 100 percent.","marker":"[103,104]"},{"why":"Supplies the surface-gravity and standard Hawking-temperature definitions used for T_H and for the entropy integration.","marker":"[105]"}],"fun_headline_variants":["Cylindrical black holes in f(R) and Ricci-inverse gravity: one effective constant rules","Effective Λ drives quasinormal modes and GUP-corrected Hawking radiation","Single substitution maps modified gravity to GR for cylindrical black holes","Cylindrical black hole QNMs and Hawking temperature from effective constants","f(R) and Ricci-inverse gravity: same GR metric, new effective Λ"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument stands on the effective cosmological constants quoted from reference [77]; if those constants are not the correct solutions of the f(R) and Ricci-inverse field equations for this metric, then every potential, temperature, and entropy in the paper is wrong.","fun_headline_variants_meta":{"raw":{"variants":["Cylindrical black holes in f(R) and Ricci-inverse gravity: one effective constant rules","Effective Λ drives quasinormal modes and GUP-corrected Hawking radiation","Single substitution maps modified gravity to GR for cylindrical black holes","Cylindrical black hole QNMs and Hawking temperature from effective constants","f(R) and Ricci-inverse gravity: same GR metric, new effective Λ"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001028,"raw_usage":{"total_tokens":4449,"prompt_tokens":1182,"completion_tokens":3267,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":798,"completion_tokens_details":{"reasoning_tokens":3162}},"tokens_in":798,"tokens_out":3267,"duration_ms":25021,"temperature":1.0,"reasoning_tokens":3162,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T23:24:43.281084+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the cylindrical metric (2.1) with f(r)=α²r²−4M/(α r), plug it together with f(R)=R+α1R²+...+$α4R^{5}$ into the f(R) field equations (2.5) with zero stress-energy, and solve for the constant that makes the equations hold; if the resulting effective cosmological constant does not match Eq. (2.8), the paper's central substitution claim collapses.","supporting_citations":[{"cited_title":"Cylindrical black hole solutions in $f(\\mathcal{R})$ and $f(\\mathcal{R},\\mathcal{A},A^{\\mu\\nu}A_{\\mu\\nu})$ modified gravity","cited_arxiv_id":"2411.00896","evidence_quote":"Supplies the effective cosmological constants Λ_m^{f(R)} and Λ_m^{RI} that are substituted into every perturbation and thermodynamic formula."},{"cited_title":"Bouhmadi-Lopez, S","cited_arxiv_id":null,"evidence_quote":"Supplies the tetrad formalism used to set up the Maxwell/vector perturbation equations."},{"cited_title":"Sakalli, A","cited_arxiv_id":null,"evidence_quote":"Gives the GUP-modified Klein-Gordon equation from which the corrected temperature is derived."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the surface-gravity and standard Hawking-temperature definitions used for T_H and for the entropy integration."}],"review_version":1}