{"id":"21f74039-f348-4770-b765-bf305adbeec5","arxiv_id":"2501.09373","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"A proposed new charged AdS black hole in f(Q) gravity, but the claimed absence of an uncharged limit and the charge-induced cosmological constant conflict with the paper's own formulas.","lead":"This paper derives a charged, rotating anti-de Sitter black hole solution in f(Q) gravity, a modified theory based on non-metricity. The authors claim it is a new class of solution with a milder central singularity, but several headline claims are contradicted by the paper's own equations.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (34) is not the specialization of Eq. (32) under (33): charge factors and signs disagree, and the horizon condition (41) contradicts (34); the central solution is unverified as written.","rationale":"The strongest claim is the new charged AdS solution (34) with a milder singularity. Everything downstream—the singularity analysis, horizons, thermodynamics, and the rotating generation—uses (34). The field equations (23) are displayed without derivation and are hard to verify by eye, but the paper's own algebra between (32), (33), (34), and (41) can be checked directly, and it fails. This is more damaging than the ad-hoc parameter choice (30) flagged by the reader, because even after imposing (30) the displayed solution is not shown to satisfy the displayed equations. It is possible that all discrepancies are typesetting errors; that is exactly what the symbolic substitution would settle. Until then, a conditional accept is too generous: the central object of the paper is unverified and at face value inconsistent. I recommend REJECT or major revision pending the check, not because the idea is impossible, but because the existence of the solution is the paper's core and the manuscript currently contradicts itself. If the check passes, the reader's conditional concerns about (30) and the interpretation of Λ_eff would become the main remaining issues.","tokens_in":16692,"tokens_out":12544,"duration_ms":112432,"concrete_test":"Using xAct/GravitY or SymPy, substitute the metric (37) with S, S1, q from Eqs. (34)-(35) directly into the unintegrated field equations (18) in the coincident gauge, for arbitrary symbolic (t, r, γ, φ, M), and compute the residual expressions; also recompute M_+ by solving S1(r_+)=0 from (34)-(35) and compare with Eq. (41). If all residuals are identically zero and M_+ matches Eq. (41), the discrepancies are typographical and the central solution may stand; if not, Eq. (34) is not a solution of the stated theory.","verdict_should_be":"REJECT","load_bearing_attack":"The central claim is that Eq. (34) is an exact charged AdS black-hole solution. The load-bearing step is the passage from the displayed solution (32) to the final metric (34) via (33), plus the horizon condition used for thermodynamics. That passage does not close. With c4=φ/18^{1/5}, Eq. (32) gives a monopole q=c4/r=φ/(18^{1/5}r), while Eq. (35) states q=φ/r; the term -15c4²/(8r²) becomes -15φ²/(8·18^{2/5}r²), not -15φ²/(8r²); the fractional terms acquire 18^{1/3} and 18^{2/3} factors in (34) that are absent from (32). Re-defining φ to remove 18^{1/5} changes the first term by a factor of 18 and spoils the claimed Λ_eff=1/(18γ). Independently, Eq. (41) is not S(r_+)=0 for Eq. (34): solving (34) gives M=r_+³Λ_eff -15φ²/(8r_+) +135(18γφ^8)^{1/3}/(448r_+^{7/3}) -81(18γφ^5)^{2/3}/(704r_+^{11/3}), whereas (41) has all positive signs and different coefficients. Thus the solution is internally inconsistent as written; the claimed new solution has not been established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes static and rotating charged AdS black-hole solutions in four-dimensional f(Q) gravity with the power-law ansatz f(Q)=Q+γQ²+γ1Q³−2Λ. The central object is the charged static solution presented in Eq. (34), which the authors claim is novel, has no uncharged or GR limit, exhibits a central singularity milder than in GR/STEGR, and has nontrivial horizon and thermodynamic properties. A rotating generalization is then generated by a coordinate transformation in Section IV, and thermodynamic quantities are computed in Section V.","tokens_in":17130,"tokens_out":4396,"duration_ms":44556,"significance":"If the central solution were correct, a new exact charged AdS black hole in power-law f(Q) gravity would be a useful contribution to the modified-gravity and AdS/CFT literature. The paper also deserves credit for attempting an analytical treatment of a non-linear f(Q) model, for computing explicit curvature and non-metricity invariants, and for being transparent that the analysis is primarily mathematical and does not address dynamical collapse. However, the central solution is not established as written: the substitution from Eq. (32) to Eq. (34) does not close, the horizon condition (41) is inconsistent with the metric (34), and the paper contradicts itself on the uncharged limit. These are load-bearing problems, not presentation issues.","major_comments":[{"comment":"The passage from the displayed solution (32) to the final metric (34) via the constant relations (33) is algebraically incorrect. With c4=φ/18^{1/5}, the term −15c4²/(8r²) in (32) becomes −15φ²/(8·18^{2/5}r²), not the −15φ²/(8r²) shown in (34); analogous mismatched factors of 18^{1/3} and 18^{2/3} appear in the fractional terms. The gauge potential (35) also does not follow from q(r) in (32) under (33): the second and third terms have different coefficients and r-dependences. Additionally, Eq. (37) displays an exponent inconsistent with Eq. (34) in the grr component. Thus Eq. (34) is not a verified specialization of Eq. (32), and the claimed new solution is not established.","section":"Section III B, Eqs. (32)-(34)"},{"comment":"The horizon condition (41) is not S(r_+)=0 for the solution (34). Solving S(r)=0 from (34) gives M = r_+³Λ_eff − 15φ²/(8r_+) + 135(18γφ⁸)^{1/3}/(448 r_+^{7/3}) − 81(18γφ⁵)^{2/3}/(704 r_+^{11/3}), whereas Eq. (41) has all positive signs and different coefficients. Since Eq. (41) is used as the input for the mass parameter in the thermodynamic analysis of Section V, the thermodynamic results in Eqs. (48)-(51) inherit this inconsistency.","section":"Section III B, Eq. (41)"},{"comment":"The paper contains a direct contradiction about whether the charged solution has an uncharged limit. The abstract and conclusions state that the solution 'does not have an uncharged version or relate to general relativity,' but the paragraph after Eq. (36) says that when the vector potential q(r) vanishes, 'we revert the solution presented in Eq (26).' This distinction matters because the claimed novelty of the solution depends on the absence of an uncharged or GR limit; the text explicitly claims both things.","section":"Uncharged limit: abstract and Section III B"},{"comment":"The effective cosmological constant is not an emergent output of the theory. The relation Λ_eff = 1/(18γ) is exactly the imposed condition Λ = 1/(18γ) from Eq. (30), and it is independent of the charge φ. The conclusion that Λ_eff 'varies based on the electric charge and the parameters of the f(Q) modification' is therefore not supported by the equations in the paper. To substantiate the emergence claim, the authors would need to derive Eq. (30) from an independent physical criterion or exhibit a charge-dependent Λ_eff.","section":"Section III B, Eqs. (30) and (36)"}],"minor_comments":[{"comment":"The displayed field equations in Eq. (18) are garbled: the line contains 'κ 2 1/2 κT' and an unrelated-looking '∂ν (√−gF μν) = 0', and the indices on the matter energy-momentum tensor are not consistently displayed.","section":"Eq. (18)"},{"comment":"The caption of Figure 2 labels panel (a) as 'Heat capacity' while the text refers to panel (a) as entropy; the captions and the text should be aligned.","section":"Figure 2 captions"},{"comment":"The relation l = −3/Λ_eff appears dimensionally and sign-wise suspect, and since Λ_eff in this paper is positive for the AdS case (γ>0), the sign convention in Eq. (43) should be checked.","section":"Eq. (43)"},{"comment":"There are numerous typographical errors that impede reading, including 'withe' for 'with', 'he mass parameter' for 'the mass parameter', 'evenan eventiz on' for 'event horizon', and inconsistent use of '3√r' notation for cube roots.","section":"General presentation"}],"recommendation":"reject","confidential_remarks":"The central solution is internally inconsistent and the uncharged-limit claim is self-contradictory; these are not local fixes but require re-deriving the core result. The paper also relies heavily on self-citations, though that is not the basis for my recommendation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The headline is that the central solution doesn't hold up. I checked the step from Eq. (32) to Eq. (34) under the substitution (33), and it does not close. With c4 = φ/18^{1/5}, the monopole term in (32) is q = φ/(18^{1/5} r), not φ/r as in (35). The quadratic term becomes -15φ^2/(8·18^{2/5} r^2), not -15φ^2/(8 r^2). The fractional terms pick up 18^{1/3} and 18^{2/3} factors that aren't in (32). So the metric (34) is not the specialization of (32). Separately, setting S(r_+)=0 in (34) gives M = r_+^3 Λ_eff - 15φ^2/(8 r_+) + 135(18γφ^8)^{1/3}/(448 r_+^{7/3}) - 81(18γφ^5)^{2/3}/(704 r_+^{11/3}), while Eq. (41) has all positive signs and different coefficients. The two are incompatible. The central claim of a new charged AdS black hole is therefore unverified as written.\n\nThe paper does have a sensible aim: finding exact charged solutions in cubic f(Q) and classifying their singularities through invariants is a legitimate research direction, and the literature on f(Q) is cited in a mostly reasonable way (the self-citations are not a problem by themselves). But the execution is too sloppy. The uncharged limit does exist—the paper's own text admits you revert to Eq. (26) when q vanishes—so the abstract's claim that the solution has 'no uncharged version' is wrong. The 'emergence' of Λ_eff is an artifact of the hand-imposed relation (30); it is not derived. The rotating solution is a coordinate transformation of the static one, not a new solution, and the thermodynamics and invariant sections are full of typographical and dimensional errors, including a term with (18γφ^{7/2})^{2/3} that suggests the algebra was never checked.\n\nIf the intermediate solution (32) is correct, a careful rewrite might salvage something, but as it stands the paper is internally inconsistent. I would not cite it, and I would not bring it to a reading group. A serious referee could check the algebra, but I would desk-reject this version: the author needs to verify the expressions and produce a coherent derivation before asking for referee time.","headline":"The central charged AdS solution (34) does not follow from (32) under (33), and the horizon condition (41) contradicts (34); the main claim is unsupported.","tokens_in":17531,"tokens_out":7286,"would_cite":false,"duration_ms":57886,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83C57","83D05","83C15"],"pacs":[],"model":"deepseek-v4-flash","headline":"A charged black hole solution in f(Q) gravity whose central singularity is milder than general relativity's.","keywords":["f(Q) gravity","non-metricity","charged AdS black hole","power-law ansatz","central singularity","black hole thermodynamics","rotating black hole","Maxwell field"],"falsifier":"Take the same power-law $f(Q)$ with a value of $\\gamma_1$ that differs from $3\\gamma^2/5$ (keeping the same ansatz and boundary conditions) and solve the Maxwell-$f(Q)$ field equations numerically; obtaining a regular asymptotically AdS charged solution would show the imposed relation is not necessary and the singularity scaling is not generic, while failure to find one would confirm it is load-bearing.","tokens_in":16529,"feed_emoji":"🕳️","tokens_out":13737,"duration_ms":118448,"temperature":0.7,"pith_summary":"The paper claims a new four-dimensional charged, asymptotically anti-de Sitter black hole solution in power-law $f(Q)$ gravity, a modified theory in which gravity is carried by non-metricity rather than curvature. The solution, Eq. (34), has no uncharged limit, no general-relativity limit, and no linear-nonmetricity limit: both the electric charge and the $f(Q)$ modification are essential. Direct computation of curvature and non-metricity invariants shows the central singularity at $r=0$ grows more slowly than in Einstein-Maxwell or in the symmetric teleparallel equivalent of general relativity. A rotating charged AdS version is obtained by a coordinate transformation. If correct, this gives a concrete arena for AdS/CFT studies and for testing whether modified gravity can soften the classical singularity.","feed_headline":"A modified-gravity black hole tames its central singularity","feed_subtitle":"In power-law f(Q) gravity, the charge-carrying AdS solution's curvature diverges more slowly than in Einstein-Maxwell theory.","key_machinery":"The working core is the power-law ansatz $f(Q)=Q+\\gamma Q^2+\\gamma_1 Q^3-2\\Lambda$ in the coincident-gauge formulation of symmetric teleparallel gravity, where the non-metricity scalar for the static line element (20) is $Q=-2S_1(rS'+S)/(r^2 S)$. In the uncharged sector the radial field equation reduces to the algebraic condition $Q+3\\gamma Q^2+5\\gamma_1 Q^3+2\\Lambda=0$, making $Q$ constant; the charged sector instead uses the hand-imposed relation (30), which reduces the dynamical system to the closed form (34). The singularity claim is carried by the invariant set: the curvature scalars and non-metricity scalars computed from (37), whose fractional-power falloffs near $r=0$ encode the milder singularity.","core_discovery":"On its own terms, the paper establishes that the static metric (34) is an exact solution of the Maxwell-$f(Q)$ field equations for $f(Q)=Q+\\gamma Q^2+\\gamma_1 Q^3-2\\Lambda$ under the parameter choice $\\Lambda=1/(18\\gamma)$, $\\gamma_1=3\\gamma^2/5$. The effective cosmological constant $\\Lambda_{\\rm eff}=1/(18\\gamma)$ is then fixed by the $f(Q)$-parameter $\\gamma$, and the metric function carries fractional powers $r^{-10/3}$ and $r^{-14/3}$ alongside the mass and charge terms. The invariants all diverge at $r=0$, but with the scalings $(K, R_{\\mu\\nu}R^{\\mu\\nu})\\sim r^{-8/3}$ and $(R, Q_{\\alpha\\beta\\gamma}Q^{\\alpha\\beta\\gamma}, P_{\\alpha\\beta\\gamma}P^{\\alpha\\beta\\gamma}, Q)\\sim r^{-4/3}$, compared with $r^{-8}$ and $r^{-4}$ in the linear/GR charged case, so the central singularity is milder. The paper further claims two horizons for moderate charge, a degenerate horizon for special $(M,\\phi)$, a naked singularity for sufficiently large charge, and a rotating AdS solution generated by the local transformation (42).","pith_inferences":["Editorial: relaxing the imposed relation (30) and solving the field equations numerically would test whether the closed-form charged solution and its singularity scaling are generic or a special-case artifact; the paper does not perform this check.","Editorial: the fractional powers in the metric suggest the spacetime may have an unusual algebraic or multipole structure; computing its Petrov type or multipole moments could reveal whether the milder singularity is tied to those powers.","Editorial: because the rotation is introduced by a transformation that is only locally, not globally, valid, the rotating solution's global causal structure remains open; closed timelike curves or identifications could change the physical picture.","Editorial: if the milder singularity is robust, it gives a concrete target for holographic probes, since AdS/CFT boundary correlators should encode the $r\\to 0$ falloffs and could distinguish this $f(Q)$ background from the Einstein-Maxwell one."],"forward_implications":["If Eq. (34) is exact, $f(Q)$ gravity admits charged AdS black holes with no general-relativity counterpart, so near-horizon observations could distinguish this spacetime from Reissner-Nordström-AdS.","Because the solution has no uncharged limit, the electric charge is structural: realistic charged black holes in this theory must use the full non-linear potential (35), not just the monopole term.","The two-horizon structure and the existence of a degenerate extremal limit give a setting for studying extremal black hole thermodynamics; the paper's positive Gibbs free energy indicates global stability in the grand canonical ensemble.","The rotating metric (45) inherits the singularity and horizon properties of the static solution, so the milder singularity survives rotation."],"supporting_citations":[{"why":"Provides the perturbative spherically symmetric f(Q) black-hole solutions and the general static metric-affine setup that the paper extends to the charged sector.","marker":"[10]"},{"why":"Defines the STEGR/f(Q) action and the non-metricity scalar used as the theory's starting point.","marker":"[11]"},{"why":"Supplies the observational support for the power-law f(Q) ansatz that the paper adopts.","marker":"[49]"},{"why":"Derives the metric and connection field equations of f(Q) gravity used to obtain the static and rotating solutions.","marker":"[56]"},{"why":"Sets the Maxwell Lagrangian and electromagnetic potential ansatz that produce the charged sector.","marker":"[59]"},{"why":"Gives the general solution for constant non-metricity scalar Q, which the paper uses to build the uncharged AdS seed.","marker":"[61]"},{"why":"Provides the companion derivation of the constant-Q solution and the effective cosmological constant mechanism.","marker":"[62]"},{"why":"Gives the modified Bekenstein-Hawking entropy formula for f(Q) gravity used in the thermodynamics section.","marker":"[75]"}],"fun_headline_variants":["Modified gravity softens black hole singularity","Charge-carrying black hole in f(Q) gravity","Milder singularity in Maxwell-f(Q) black hole","f(Q) gravity tames central black hole singularity","Softened curvature in f(Q) black hole solution"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole charged solution rests on the hand-imposed parameter relation (30), $\\Lambda=1/(18\\gamma)$ and $\\gamma_1=3\\gamma^2/5$, which is not derived from observations or first principles; if that relation is abandoned, the closed-form solution (34) and its claimed effective cosmological constant no longer follow.","fun_headline_variants_meta":{"raw":{"variants":["Modified gravity softens black hole singularity","Charge-carrying black hole in f(Q) gravity","Milder singularity in Maxwell-f(Q) black hole","f(Q) gravity tames central black hole singularity","Softened curvature in f(Q) black hole solution"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000364,"raw_usage":{"total_tokens":2007,"prompt_tokens":1041,"completion_tokens":966,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":657,"completion_tokens_details":{"reasoning_tokens":892}},"tokens_in":657,"tokens_out":966,"duration_ms":8224,"temperature":1.0,"reasoning_tokens":892,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:05:41.356205+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the same power-law $f(Q)$ with a value of $\\gamma_1$ that differs from $3\\gamma^2/5$ (keeping the same ansatz and boundary conditions) and solve the Maxwell-$f(Q)$ field equations numerically; obtaining a regular asymptotically AdS charged solution would show the imposed relation is not necessary and the singularity scaling is not generic, while failure to find one would confirm it is load-bearing.","supporting_citations":[{"cited_title":"Minisuperspace description of $f(Q)$-cosmology","cited_arxiv_id":"2308.15207","evidence_quote":"Gives the general solution for constant non-metricity scalar Q, which the paper uses to build the uncharged AdS seed."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the modified Bekenstein-Hawking entropy formula for f(Q) gravity used in the thermodynamics section."}],"review_version":1}