{"id":"c6f17498-a4ce-45d9-9a46-4c4ac5cf8029","arxiv_id":"1908.07381","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"New charged AdS black hole solutions are constructed for quadratic f(T) gravity with a specific nonlinear electrodynamics source, generalizing earlier Maxwell solutions and producing entropy that deviates from the area law.","lead":"This paper constructs new charged black hole solutions in quadratic f(T) gravity, a modified theory of gravity based on torsion, coupled to a nonlinear generalization of electromagnetism. It generalizes the authors' earlier Maxwell-field solutions, reproduces them when the new parameter vanishes, and finds that black hole entropy is not proportional to horizon area.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The exact solution (33) rests on the diagonal vielbein (17) without a good-tetrad check, so the central claim may be frame-dependent in f(T) gravity.","rationale":"The reader's weakest assumption identifies the same load-bearing premise: the diagonal vielbein (17) is adopted without a good-tetrad justification in a theory that is not local-Lorentz invariant. The manuscript itself flags this issue in the introduction by citing Refs. [59,60], and the solution derivation only reports the diagonal field equations (21)-(24). Because the full field equations (13) are frame-dependent, the truth of the central claim requires that (33) satisfies every component of those equations for the specific vielbein (17). This is not a matter of disagreeing with a consensus; it is a concrete correctness risk in the construction. I do not recommend rejecting the paper outright, because the issue is checkable by direct symbolic substitution and may be resolved in the authors' notebooks. The current conditional verdict is therefore appropriate, with the added condition that the full-component substitution and a good-tetrad comparison be provided. Other internal issues, such as the q1→0 limit of the mass parameter in (33) and the normalization mismatch between the entropy definitions in (42) and (43), are secondary and correctable, but they reinforce rather than replace the need for a frame-level verification.","tokens_in":20024,"tokens_out":9297,"duration_ms":104436,"concrete_test":"Use a computer algebra system (xAct or Cadabra) to contract the full field equations (13) for f(T)=a0+a1T+a2T^2 and insert the vielbein (17) with A(r), g(r), q(r), ℵ(r) taken from the exact expressions (31) and (33), for d=4 and d=5. Print every independent component of ζ^ν_μ and ∂_ν(√-g P^{μν}); require all residuals to vanish identically, including the mixed (t,η_i) and (η_i,η_j) components. Then repeat the same substitution using the local-Lorentz rotated 'good tetrad' of the type used in Ref. [61]. If the residual is nonzero for (17) but zero after a frame rotation that leaves the metric (18) unchanged, the solution is frame-dependent and the central claim fails; if both frames pass, the tetrad concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the unverified use of the diagonal vielbein (17). In f(T) gravity the action is not invariant under local Lorentz transformations of the tetrad, so (17) is not merely a coordinate choice: different vielbeins representing the same metric can satisfy different field equations. The paper's introduction explicitly cites Refs. [59,60] stating that diagonal ansätze are unsuitable in spherically symmetric f(T) settings, and Ref. [61] uses a non-diagonal 'good tetrad'. Section III nevertheless adopts (17) and reports only the diagonal field-equation components (21)-(24), without demonstrating that the off-diagonal components of the full system (13) vanish for the resulting A(r), g(r), q(r), ℵ(r). If (17) is a 'bad tetrad' in the sense of [59,60], then the metric (18) with (33) is not a solution of the same f(T) theory, and the claimed new solution, the milder-singularity conclusion, and the entropy formula (43) would be frame artifacts rather than properties of a spacetime. The paper needs an explicit check of all components of the field equations for the proposed tetrad before the central claim can be accepted.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies d-dimensional static charged AdS black holes in f(T) = a0 + a1 T + a2 T^2 teleparallel gravity coupled to nonlinear electrodynamics. Starting from a diagonal vielbein in cylindrical coordinates, the authors derive a formal solution (31) and then impose constraints N = 0 and 2 a2 c1^2 c2 = a1 P to obtain the simplified metric (33), whose asymptotic expansion contains an effective cosmological term, a mass term, a monopole term Q^2, and higher-order terms Q14 and Q24. The electric field (34) reduces to the Maxwell-field result of Ref. [1] when q1 -> 0. The paper also constructs a rotating counterpart by the coordinate transformation (35), computes invariants near r = 0, and studies entropy, Hawking temperature, heat capacity, and Gibbs free energy, concluding that the entropy is not proportional to the horizon area and can be negative.","tokens_in":20316,"tokens_out":11931,"duration_ms":111189,"significance":"Charged AdS black hole families in quadratic f(T) gravity coupled to nonlinear electrodynamics are of interest for modified-gravity phenomenology, and this paper provides explicit formulas together with a direct reduction to the known Maxwell solution of Ref. [1]. If the central solution is genuine, the q1 parameter gives a tunable nonlinear-electrodynamics correction and the thermodynamic analysis is a concrete extension of earlier work. However, the physical claims are presently conditional: the use of a diagonal vielbein is not justified in a theory that is not local-Lorentz invariant, the singularity comparison is internally inconsistent, and the thermodynamic formulas contain coefficient and topology inconsistencies. These issues affect the central claims of the paper, and the manuscript therefore requires substantial revision.","major_comments":[{"comment":"The entire static solution is derived from the diagonal vielbein (17), but the paper does not demonstrate that this is a 'good tetrad' for the f(T) field equations. The introduction explicitly cites Refs. [59,60] for the statement that diagonal ansatze are unsuitable in spherically symmetric f(T) setups and Ref. [61] for a non-diagonal good tetrad. Equations (21)-(24) report only diagonal components of (13); the off-diagonal components are never shown to vanish for the resulting A(r), g(r), q(r), and \\aleph(r). Since f(T) gravity is not local-Lorentz invariant, a different vielbein for the same metric satisfies different equations, so unless the full set of components of (13) is checked, the metric (18) with (33) cannot be claimed to be a solution of the theory. The rotating vielbein (38) inherits the same problem.","section":"Section III, Eq. (17)"},{"comment":"The claim that the central singularity is 'much milder' than in GR/TEGR contradicts the paper's own exponents. For the new solution the invariants are reported to behave as (K, R_{\\mu\\nu}R^{\\mu\\nu}) ~ r^{-4(d-2)} and (R, T) ~ r^{-2(d-2)}, while the GR/TEGR Maxwell values are given as r^{-2d} and r^{-d}. At d = 4 these exponents coincide, and for d > 4 one has 4(d-2) > 2d and 2(d-2) > d, so the new singularity is in fact more singular, not milder. The comparison should be redone with the correct d-dimensional GR exponents and the claim corrected or removed.","section":"Section III, paragraph after Eq. (34)"},{"comment":"The entropy calculation has an internal coefficient mismatch. For d = 4, Eq. (42) gives S = \\pi r_b^2 f_T, whereas the leading term of Eq. (43) is (\\Omega_2/6) r_b^2 a1 = (2\\pi/3) r_b^2 a1. In addition, Eq. (43) uses \\Omega_{d-2} r_b^{d-2} as the horizon area, but the line element (18) is written in cylindrical coordinates with infinite \\xi directions, so the horizon area is not the volume of a unit (d-2)-sphere unless compactification is assumed. The positivity constraint on q1 and the negative-entropy conclusion depend on this approximate formula and need to be re-examined.","section":"Eqs. (42) and (43)"},{"comment":"The physical content attributed to the nonlinear electrodynamics is largely inherited from the ansatz rather than derived. The dual function \\aleph(r) is fixed by hand to the sech form (30), and the constraints N = 0 and 2 a2 c1^2 c2 = a1 P are imposed to obtain the simplified solution; the higher-order terms Q14 and Q24 and the q1 corrections in (34) are therefore direct consequences of this input. The abstract's statement that these higher-order terms have 'their source' in the NLED field should be qualified, since the theory does not single out the chosen \\aleph(r).","section":"Section III.A, Eqs. (30)-(33)"}],"minor_comments":[{"comment":"The angular component is garbled as '... = \\zeta_{\\xi_{d-n-2}}^{\\xi_{d-n-2}} = f_{TT}[...]'; the equation should be typeset cleanly with all indices explicit.","section":"Eq. (21)"},{"comment":"The sentence 'Eq. (22) is a second-order algebraic equation and it gives T = T0 = const' is confusing because the later non-constant-T solution also uses Eq. (22) through the relation (32); the logical structure of the two branches should be clarified.","section":"Section III.A, text near Eq. (22)"},{"comment":"The rotating solution is presented as a coordinate transformation of the static vielbein, but the paper does not state explicitly how the field equations behave under this transformation in f(T) theory; in particular the sentence at the end of Section IV that 'the torsion components are vanishing' is unexplained and should be removed or expanded.","section":"Section IV, Eqs. (35)-(40)"},{"comment":"The heat capacity is written with symbols \\alpha and c that are not defined consistently in the surrounding text; the calculation should be checked for notational consistency.","section":"Eq. (49)"},{"comment":"There are several typographical and grammatical issues, including 'this inanition' in the abstract, which should be corrected in a careful revision.","section":"Abstract and general text"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is largely an incremental extension of Ref. [1], and the title overstates the rotating part, which is only a coordinate transformation of the static solution. The main reason for requesting a major revision is the unresolved good-tetrad issue; if it turns out that the diagonal vielbein (17) is not a legitimate tetrad for the f(T) field equations, the central solution and all derived physical statements would not hold."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague — quick read of 1908.07381.\n\nThe paper does add something real: a d-dimensional family of charged AdS black holes in quadratic f(T) gravity with nonlinear electrodynamics, parametrized by q1, which reduces to the authors' earlier Maxwell solution [1] when q1→0. That is a legitimate extension, and the asymptotic expansion for A(r) and the gauge field is explicit. The dual-formulation method is standard and the reductions to known limits are useful checks. The rotating version via coordinate transformation is the usual trick.\n\nThe soft spots are in the interpretation, not the algebra (as far as I can tell). First and most serious: the diagonal vielbein (17) is adopted without showing it is a 'good tetrad' for f(T). The paper's own introduction cites [59,60] noting diagonal ansätze are unsuitable in spherically symmetric f(T); cylindrical coordinates may be different, but the authors report only the non-vanishing components (21)-(24) and never state the off-diagonal components of (13) vanish. If those don't vanish, the solution isn't a solution of the same f(T) theory. That is a load-bearing gap and needs an explicit check.\n\nSecond, the 'milder singularity' claim contradicts the paper's own exponents: for the solution, (K, RμνRμν) ~ r^{-4(d-2)}; for GR/TEGR charged black holes they give r^{-2d}. At d=4 these are equal, and for d>4 the solution's singularities are stronger, not milder. The comparison in the text as written is wrong.\n\nThird, the thermodynamics has internal inconsistencies: (42) gives S ∝ r_b^2 f_T, but (43) has a different normalization with Ω_{d-2} r_b^{d-2}/6 and terms that don't look like f_T expanded; there are also typographical problems in (51) with an undefined c. The q1→0 limit also looks singular for the mass parameter M, which conflicts with the claim that this limit returns to the Maxwell solution.\n\nThe circularity from choosing the sech ansatz (30) and the constraints is mild; that's how these constructions work, and it doesn't invalidate the solution.\n\nBottom line: the derivation is plausible and the literature will want to know whether the diagonal tetrad passes a full check. A serious referee should demand that check, plus corrections to the singularity comparison, entropy normalization, and q1 limit. I'd send it to review with a request for major revision, not desk-reject it. For a reading group, maybe, mainly if someone is actively working on f(T) black holes. I wouldn't cite it until the tetrad and thermodynamics issues are cleared up.","headline":"New family of AdS black holes in f(T)+NLED, but the singularity and entropy claims need correction and the diagonal vielbein needs a good-tetrad check.","tokens_in":20848,"tokens_out":4238,"would_cite":false,"duration_ms":41261,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["04.50.Kd","97.60.Lf","98.80.-k"],"model":"deepseek-v4-flash","headline":"The paper derives exact d-dimensional AdS black holes in quadratic f(T) teleparallel gravity with nonlinear electrodynamics, with a milder central singularity than in General Relativity and entropy not proportional to horizon area.","keywords":["f(T) gravity","teleparallel gravity","nonlinear electrodynamics","AdS black holes","exact solutions","black hole thermodynamics","torsion","entropy"],"falsifier":"Take the same quadratic f(T) action and the same nonlinear electrodynamics potential, but solve the field equations in a non-diagonal cylindrical tetrad of the type recommended for f(T) gravity by refs [59,60], and check whether the metric function (33) still satisfies them; if the equations change, the claimed solution, milder singularity, and non-area entropy are frame artifacts.","tokens_in":19768,"feed_emoji":"🕳️","tokens_out":18124,"duration_ms":138834,"temperature":0.7,"pith_summary":"The paper derives exact d-dimensional anti-de Sitter black hole solutions in quadratic f(T) teleparallel gravity coupled to nonlinear electrodynamics, with $f(T)=a_0+a_1T+a_2T^2$, where $T$ is the torsion scalar. These solutions generalize the previously known charged f(T) black holes with linear electrodynamics by adding higher-order charge terms controlled by a single nonlinearity parameter $q_1$, and they reduce to the earlier solutions when $q_1$ vanishes. The central singularity is milder than the corresponding singularity in General Relativity. The entropy, computed from the f(T) area formula, is not proportional to the horizon area and can be negative unless $q_1$ is constrained. Rotating versions are obtained by a global coordinate transformation, and the paper studies heat capacity, phase transitions, and Gibbs free energy.","feed_headline":"New black holes soften the singularity and entropy-area law","feed_subtitle":"Exact solutions in quadratic teleparallel gravity show entropy is no longer tied to horizon area.","key_machinery":"The argument rides on three pieces: the quadratic action $f(T)=a_0+a_1T+a_2T^2$; the diagonal vielbein ansatz (17) in cylindrical coordinates, which fixes the metric (18); and nonlinear electrodynamics in the dual Legendre representation, with the chosen potential $\\aleph(r) = -P \\,\\mathrm{sech}^2(q_1/((d-3)m r^{d-3}))/r^{2(d-2)}$. The hyperbolic-secant form is what produces the higher-order charge terms and the deviation from linear electrodynamics; taking $q_1=0$ eliminates them. The field equations then fix $A(r)$, $g(r)$, and the gauge potential $q(r)$ self-consistently. The thermodynamic conclusion follows from the f(T) entropy formula $S=(1/4)A f_T$ with $f_T=a_1+2a_2T$, which makes the entropy depend on the torsion corrections rather than on area alone.","core_discovery":"The paper's central claim is that new exact charged black hole solutions exist in quadratic teleparallel equivalent gravity with nonlinear electrodynamics. For the metric (18) in d dimensions, the field equations yield the metric function $A(r)$ with the asymptotic expansion $A(r) \\approx \\Lambda_{\\mathrm{eff}} r^2 - M/r^{d-3} + Q^2/r^{2(d-3)} + Q_{14}/r^{3d-8} + Q_{24}/r^{4(d-3)}$, where the monopole and quadrupole terms are accompanied by higher-order terms sourced by the nonlinear electromagnetic field. Setting the parameter $q_1=0$ returns the linear-electrodynamics solution of ref [1], so the family is a one-parameter nonlinear electrodynamics deformation. Near $r=0$ the invariants $(K, R_{\\mu\\nu}R^{\\mu\\nu})$ behave as $r^{-4(d-2)}$ and $(R, T)$ as $r^{-2(d-2)}$, instead of the steeper GR/TEGR falloffs $r^{-2d}$ and $r^{-d}$, so the singularity is milder. The entropy, defined as $S=(1/4)A f_T$, is not proportional to the area and can be negative for some $q_1$ unless a constraint is imposed. The rotating counterpart is generated by a global coordinate transformation, preserving local geometry but changing global properties.","pith_inferences":["If the diagonal frame is legitimate, the softened singularity suggests that nonlinear electrodynamics in f(T) gravity can act as a low-energy mechanism for regularizing black hole interiors, though the invariants still diverge and the paper does not prove regularity.","In the TEGR limit ($a_1\\to 1$, $a_2\\to 0$), $f_T\\to 1$ and the entropy formula reverts to the area law; verifying that the derived expression (43) has this limit would be a consistency test the paper leaves implicit.","The higher-order charge terms $Q_{14}$ and $Q_{24}$ are not universal features of f(T) plus nonlinear electrodynamics but are inherited from the hand-chosen hyperbolic-secant form of $\\aleph$; testing other NLED functions would reveal which singularity-softening effects are robust.","Because the rotating metric comes from a global coordinate transformation, the thermodynamics of the rotating family may differ from the static one; a direct computation of rotating horizon quantities would settle whether the non-area entropy persists there."],"forward_implications":["Setting $q_1=0$ reproduces the linear-electrodynamics charged AdS black holes of ref [1], so the new family is a one-parameter nonlinear electrodynamics deformation of that baseline.","The curvature and torsion invariants diverge near $r=0$ as $r^{-4(d-2)}$ and $r^{-2(d-2)}$ rather than $r^{-2d}$ and $r^{-d}$, so the central singularity is softer in every dimension.","The entropy is proportional to $f_T$ rather than to the horizon area alone, and it can become negative unless the nonlinearity parameter $q_1$ satisfies the bound derived at the event horizon.","The heat capacity is negative below the degenerate horizon and positive above it, with an infinite discontinuity at the degenerate horizon, indicating a second-order phase transition.","The rotating AdS solutions are generated by a global coordinate transformation of the static solution, so they preserve local geometry while changing global properties such as horizon identification."],"supporting_citations":[{"why":"Supplies the baseline charged AdS black hole in f(T) gravity with linear electrodynamics; the new solution reduces to it when q1 vanishes.","marker":"[1]"},{"why":"Provides the diagonal vielbein ansatz in d dimensions that the paper uses to set up the metric and field equations.","marker":"[49]"},{"why":"Identifies the good-tetrad problem in f(T) gravity, the premise that the chosen diagonal frame must satisfy.","marker":"[59]"},{"why":"Shows that the diagonal ansatz is not always a suitable vielbein, the caution that motivates checking the frame choice.","marker":"[60]"},{"why":"Gives the rotating AdS black hole construction in f(T) gravity that the paper adapts by global coordinate transformation.","marker":"[62]"},{"why":"Supplies the hyperbolic-secant nonlinear electrodynamics potential that the paper generalizes to d dimensions.","marker":"[64]"},{"why":"Provides the Legendre dual representation of nonlinear electrodynamics used to derive the exact solutions.","marker":"[65]"},{"why":"Supplies the f(T) entropy-area relation S=(1/4) A f_T that underlies the non-area entropy conclusion.","marker":"[85]"}],"fun_headline_variants":["Teleparallel black holes soften singularity, alter entropy","New AdS black holes defy entropy-area law","Quadratic teleparallel gravity yields milder singularities","Entropy not tied to area in new teleparallel black holes","Rotating and static black holes with softened singularity"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper's conclusions stand or fall on whether the diagonal cylindrical coordinate frame used for the calculation is an allowed frame for f(T) gravity, since f(T) is not invariant under local frame rotations and an unallowed frame would make the resulting metric and its thermodynamic properties artifacts of that choice.","fun_headline_variants_meta":{"raw":{"variants":["Teleparallel black holes soften singularity, alter entropy","New AdS black holes defy entropy-area law","Quadratic teleparallel gravity yields milder singularities","Entropy not tied to area in new teleparallel black holes","Rotating and static black holes with softened singularity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000666,"raw_usage":{"total_tokens":3115,"prompt_tokens":1099,"completion_tokens":2016,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":715,"completion_tokens_details":{"reasoning_tokens":1942}},"tokens_in":715,"tokens_out":2016,"duration_ms":12904,"temperature":1.0,"reasoning_tokens":1942,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:53:22.553091+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the same quadratic f(T) action and the same nonlinear electrodynamics potential, but solve the field equations in a non-diagonal cylindrical tetrad of the type recommended for f(T) gravity by refs [59,60], and check whether the metric function (33) still satisfies them; if the equations change, the claimed solution, milder singularity, and non-area entropy are frame artifacts.","supporting_citations":[{"cited_title":"Schwarzschild solution in extended teleparallel gravity","cited_arxiv_id":"1501.00974","evidence_quote":"Shows that the diagonal ansatz is not always a suitable vielbein, the caution that motivates checking the frame choice."},{"cited_title":"$f(T)$ gravity: effects on astronomical observation and Solar System experiments and upper-bounds","cited_arxiv_id":"1312.4103","evidence_quote":"Gives the rotating AdS black hole construction in f(T) gravity that the paper adapts by global coordinate transformation."},{"cited_title":"Anomaly and Hawking radiation from regular black holes","cited_arxiv_id":"0803.3849","evidence_quote":"Supplies the f(T) entropy-area relation S=(1/4) A f_T that underlies the non-area entropy conclusion."}],"review_version":1}