{"id":"fde37fe4-d4cc-45ad-8780-9205fdf129bd","arxiv_id":"1908.04995","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For generic f(T) gravity, all static cylindrical vacuum solutions take the same simple metric form with a constant torsion fixing an effective cosmological constant, and charged solutions follow a five-step construction.","lead":"This paper builds exact cylindrically symmetric black hole and wormhole spacetimes for almost any version of f(T) gravity, in any dimension, with and without electric charge. A generalist should care because it shows that these modified gravity models generate an effective cosmological constant on their own and predict a universal distant correction to electric fields.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Generic-f(T) vacuum solution (20) may be gauge-restricted: the diagonal vielbein (4) is imposed, not derived, and f(T) lacks local Lorentz invariance.","rationale":"The reader's weakest assumption identifies the vielbein gauge issue, which is also the most structurally load-bearing concern in my reading. The algebra from (7) to (20) is internally consistent: starting from the diagonal tetrad (4) and assuming T=const via Eq. (8), the derivation of A=B and the master equation (16) is explicit and checkable. The quadratic charged example is plausibly correct, and the paper even notes a successful consistency check of (56) against (49). However, the paper uses language like 'most general solution' and 'generic case' without proving that the diagonal tetrad ansatz covers all static cylindrically symmetric solutions in f(T) gravity. Because f(T) is not local-Lorentz invariant, a metric can admit multiple physically inequivalent tetrad frames, and the field equations differ between frames; this is a genuine correctness risk for the exhaustiveness claim, not merely an unpalatable convention. The multipole expansion in Section IV is another flagged weakness ('Skipping the calculations'), but the core vacuum construction is the central claim, and the gauge restriction is the clearest load-bearing caveat. I therefore confirm the CONDITIONAL verdict: the paper's explicit solutions are likely valid as solutions, but the 'generic f(T)' exhaustiveness claim needs a gauge-completeness argument or an explicit restriction to the diagonal gauge.","tokens_in":9951,"tokens_out":1693,"duration_ms":15371,"concrete_test":"Re-derive the vacuum field equations starting from a general vielbein with the same metric (5) but allowing an arbitrary static rotation/boost parameter between the radial and time directions (e.g., e^0 = sqrt(A) dt + a(r) dz, e^1 = (1/sqrt(B)) dr, etc., or a Lorentz-boosted diagonal tetrad). Substitute the ansatz A = B = C r^2 - m/r^(n-3) into the resulting f(T) equations: if the same branch of solutions survives for all values of the rotation parameter and yields the same T, the gauge concern is benign; if the equations force specific relations between C and the rotation parameter or admit new solutions not of the form (20), the paper's 'most general' claim fails and must be restricted to the diagonal gauge.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central vacuum claim rests on the diagonal vielbein ansatz (4), introduced by fiat following Refs. [1,3,10]. The field equations (8)-(10) are obtained from this specific tetrad, and f(T) gravity is not invariant under local Lorentz transformations of the vielbein, so different tetrads representing the same metric generally yield different field equations and different torsion scalars. The paper never proves that every static cylindrically symmetric solution of a generic f(T) theory admits a diagonal vielbein, nor that a non-diagonal or rotated tetrad could not produce additional solutions for the same f(T). Thus Eq. (20) is rigorously a solution in this tetrad gauge, but the phrase 'most general solution in closed form for all f(T)' overstates the scope: the derivation establishes existence of this family, not exhaustiveness over all solutions of arbitrary f(T). The charged algorithm in Section III inherits the same restriction through Eq. (40). Additionally, the paper itself flags a second limitation: 'Skipping the calculations' in Section IV for the multipole expansion, meaning Eq. (59) is asserted without derivation; however, the consistency check for the quadratic charged solution (verified against Eq. (49)) supports the general pattern. The geometric interpretation as (A)dS also depends on the sign of T(Λ,...), which is theory-dependent and can disagree with the sign of Λ, as the paper acknowledges.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper constructs static cylindrically symmetric solutions of n-dimensional f(T) gravity. In the uncharged case, the field equations for a diagonal vielbein imply that the torsion scalar is constant, equal to a root T of the algebraic equation 2T f_T - 2Λ - f = 0 (Eq. 8); the resulting metric is A = B = T/((n-2)(n-1)) r^2 - m/r^{n-3} (Eq. 20). The charged case is treated by an algorithm that reduces the field equations to an algebraic equation for T(r), a first-order equation for A(r), and quadratures for A, B, and the electrostatic potential V; the quadratic model f(T)=T+αT^2 is worked out explicitly, including large-r series. A generic multipole expansion for the electric potential is stated in Section IV, and the paper discusses applications to quadratic and cubic models, including the generation of an effective cosmological constant from a nonvanishing torsion root.","tokens_in":10204,"tokens_out":9223,"duration_ms":89289,"significance":"If the derivation is taken at face value, Eq. (20) is a valuable exact result: it provides, for every f(T) admitting a real root of Eq. (8), a closed-form uncharged cylindrical solution with an effective cosmological constant determined by that root, with no fitted parameters. The charged algorithm is coherent and the quadratic example is checked against the consistency equation (49). The paper also makes the interesting observation that the effective cosmological constant can have a sign opposite to the explicit Λ, and that f(T) can generate an effective cosmological constant even when Λ=0. These features are worth publishing, provided the scope of the claims is made precise with respect to the vielbein ansatz and the asserted generic expansion is supported by the derivation.","major_comments":[{"comment":"The claim of the 'most general solution in closed form for all f(T)' is not established. The derivation starts from the diagonal vielbein ansatz (4), and the field equations (8)-(10) are obtained from that specific tetrad. Since f(T) gravity is not invariant under local Lorentz transformations of the vielbein, one cannot assume without argument that every static cylindrically symmetric solution admits this diagonal tetrad, nor that a non-diagonal or rotated tetrad would not lead to additional solutions for the same f(T). Thus Eq. (20) is rigorously a solution in the chosen tetrad gauge, but the paper overstates the exhaustiveness of this family. Please either prove that the diagonal vielbein captures all static cylindrically symmetric solutions in generic f(T) gravity, or explicitly reformulate the claims as applying to the diagonal-vielbein sector.","section":"Introduction, Eq. (4), Eqs. (8)-(10), Eq. (20)"},{"comment":"The generic multipole expansion is introduced with 'Skipping the calculations'. Equation (59) is the basis of the Section IV conclusion that the first nonvanishing higher-order moment is generically of order 1/r^5 and that the shape of f(T) does not affect the order of that term. As written, the only evidence offered for the generic expansion is its consistency with the quadratic example, which is insufficient to establish a generic statement about arbitrary f(T). The derivation should be included, or the claim should be downgraded to a conjecture supported by the quadratic example.","section":"Section IV, Eq. (59)"}],"minor_comments":[{"comment":"The terminology 'anti-de Sitter' for a positive effective cosmological constant and 'de Sitter' for a negative one is opposite to the most common convention in general relativity; please add an explicit sentence fixing the sign convention used in the paper.","section":"Eqs. (21)-(22)"},{"comment":"The object denoted F_{tr} in Eq. (42) appears to be the contravariant component F^{tr} rather than the covariant component F_{tr} = -V'; please correct the index placement or the definition to avoid confusion in the integration leading to Eq. (43).","section":"Eq. (42)"},{"comment":"The abstract mentions wormholes as part of the solution family, but the paper only notes that a wormhole may occur for certain parameter ranges and does not construct or analyze an explicit wormhole solution; please adjust the wording to match the actual content.","section":"Abstract and Section III"}],"recommendation":"major_revision","confidential_remarks":"The main substantive risk is the vielbein-gauge dependence of the 'generic' conclusions; the other major point is the missing derivation of Eq. (59). Both are fixable in revision. The self-citations to Refs. [19,20] are used only for standard root-finding and elliptic-integral material and do not raise concerns."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague, worth a look if you work on exact solutions in f(T) gravity. The paper gives an explicit closed-form static cylindrical vacuum solution, Eq. (20), for arbitrary f(T) and arbitrary dimension n, with torsion a constant root of Eq. (8). That collapse of a whole family of theories to one metric form is genuinely new relative to prior work that only treated quadratic/cubic cases under parameter restrictions. The charged section is also useful: a five-step algorithm, a quadratic example with integrals reduced to series, and a consistency check against Eq. (49) that appears to hold. The paper states the multipole expansion 'skipping the calculations'; that is a real gap, but the quadratic check gives some confidence.\n\nThe soft spot the stress-test flagged is real and not minor: the diagonal vielbein ansatz, Eq. (4), is imposed, not derived. f(T) gravity is not invariant under local Lorentz transformations of the vielbein, so the field equations obtained from this tetrad need not cover all static cylindrically symmetric solutions of a given f(T). The text says 'most general solution in closed form for all f(T)' — that overstates the scope. What is established is existence of this family: every f(T) with a suitable root admits this metric. Exhaustiveness would require either a proof that a diagonal gauge is always reachable or an explicit discussion of tetrad choice. The charged algorithm inherits the same restriction through Eq. (40).\n\nOther soft spots: the multipole expansion (59) is asserted without derivation, and the paper explicitly excludes the degenerate p=0 double-root case, though it points to prior treatment. Both are flagged by the author, which is good, but the 'most general' language should be tuned. The citation pattern is fine; the self-citations are to standard root-finding and elliptic-integral references, not to the author's own unrelated work.\n\nOverall: the central algebra is explicit and I found no internal contradictions. The paper is a useful tool for the f(T) solutions community, and the one-over-r-to-the-fifth leading correction is a concrete, checkable claim. It deserves a serious referee. The referee should require the authors to either justify the vielbein gauge claim or visibly restrict the statement to the diagonal tetrad class, and to fill in or relegate the multipole calculation.","headline":"Useful and mostly sound generic f(T) exact-solutions paper whose 'most general' claim needs a vielbein-gauge caveat.","tokens_in":10749,"tokens_out":1750,"would_cite":true,"duration_ms":17277,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83C57","83D05"],"pacs":["04.50.-h","04.20.Jb","04.20.-q"],"model":"deepseek-v4-flash","headline":"Generic f(T) gravity admits closed-form static cylindrical AdS/dS black holes in every dimension.","keywords":["f(T) gravity","teleparallel gravity","static cylindrical symmetry","exact black hole solutions","effective cosmological constant","constant torsion","charged black holes","exact solutions"],"falsifier":"Compute the vacuum field equations for the metric (5) using a Lorentz-rotated, non-diagonal vielbein (frame field) for a concrete model such as $f(T)=T+\\alpha T^2$ and look for a solution with $A\\neq B$ or with $r$-dependent torsion. Any such counterexample would show that the diagonal ansatz was not exhaustive and that (20) is not the most general generic solution; equivalently, the universal claim fails if the rotated-frame equations do not force $G=F$.","tokens_in":9720,"feed_emoji":"🕳️","tokens_out":13012,"duration_ms":111093,"temperature":0.7,"pith_summary":"The paper aims to show that teleparallel $f(T)$ gravity has a universal static, cylindrically symmetric sector: for any function $f$, the uncharged vacuum metric is fixed by one constant torsion value, and the same construction extends to charged solutions through an explicit algorithm. In vacuum the torsion $T$ is forced to be a constant root of $2T f_T - 2\\Lambda - f = 0$, so the metric is $A = B = \\frac{T}{(n-2)(n-1)}r^2 - \\frac{m}{r^{n-3}}$, with the sign of $T$ deciding whether the solution is asymptotically anti-de Sitter or de Sitter, independent of the sign of the bare $\\Lambda$. This matters because it turns a nonlinear theory into a single algebraic root problem: the shape of $f$ fixes only the value of $T$, not the structure of the solution. The charged solutions share the same effective cosmological constant, set by the value $T_0$ at infinity, and their leading correction to the Coulomb potential is generically order $1/r^5$. If correct, the paper shows that nonlinear $f(T)$ models can generate an effective cosmological constant even when the bare $\\Lambda$ is zero.","feed_headline":"Every f(T) theory gives closed-form cylindrical AdS/dS black holes","feed_subtitle":"One constant torsion value fixes an effective cosmological constant in every f(T) model; charge adds a 1/r^5 correction.","key_machinery":"The load-bearing identity is the algebraic torsion condition $2T f_T - 2\\Lambda - f = 0$, where $f_T$ is the derivative of $f$ with respect to $T$; it forces $T$ to be constant in vacuum. Once all $T'$ terms vanish, the first-order equations imply $G = F$ (so $A$ can be rescaled to equal $B$) and reduce the system to the master equation $r^2 F' + (n-4) r F + r^2 F^2 + 6 - 2n = 0$, whose direct integration produces the closed metric (20). In the charged case the analogous identity is $G = F - 2(\\ln f_T)'$, which ties $B$ to $A$ through $f_T(T(r))$, and Maxwell's equation fixes $V' = -\\frac{(n-3)q\\, f_T(T(r))}{f_T(T_0)\\, r^{n-2}}$. This mechanism is what converts a complicated nonlinear $f$ into a single fixed effective cosmological constant.","core_discovery":"The central discovery is that in vacuum the torsion is not dynamical: equation (8), $2T f_T - 2\\Lambda - f = 0$, fixes $T$ to a constant depending only on $\\Lambda$ and the parameters of $f$. All $T'$ terms then drop out, and the remaining field equations reduce to $G = F$ and the master equation $r^2 F' + (n-4) r F + r^2 F^2 + 6 - 2n = 0$, whose integration gives $A = B = \\frac{T}{(n-2)(n-1)}r^2 - \\frac{m}{r^{n-3}}$. Thus every $f(T)$ model, within this diagonal frame-field (vielbein) ansatz, admits the same two-parameter family of static cylindrical black holes (or regular/wormhole solutions when $A$ has no zero), with the constant torsion acting as an effective cosmological constant. For the charged case $T$ is no longer constant, but the paper reduces the field equations to a five-step procedure: solve (8) for $T_0$ at infinity, solve (44) for $T(r)$, integrate (45) for $A(r)$, obtain $B(r)$ from (40), and obtain $V(r)$ from (48). The same $T_0$ sets the effective cosmological constant in the charged and uncharged solutions, and the generic multipole expansion shows the first non-Coulomb correction to $V$ is proportional to $1/r^5$.","pith_inferences":["Editorial inference: because $f(T)$ gravity is not invariant under local Lorentz rotations of the frame, the diagonal-tetrad solution (20) is best read as a tetrad-gauge statement; a non-diagonal frame could in principle support additional static cylindrical solutions outside this family.","Editorial inference: the same constant-torsion mechanism that produces $\\Lambda_{\\rm eff}$ here might work in spherical or planar symmetric $f(T)$ solutions, so observational constraints on $f(T)$ models may need to account for an induced cosmological constant even when the bare $\\Lambda$ vanishes.","Editorial inference: for $f(T) = T + \\alpha T^2$ with $\\Lambda = 0$ and $\\alpha < 0$, the paper's branch analysis predicts an anti-de Sitter end state; following this branch in a numerical time evolution of the same symmetry would test whether the algebraic-root classification survives outside the original static ansatz."],"forward_implications":["Any nonlinear $f(T)$ with bare $\\Lambda = 0$ can still generate a non-zero effective cosmological constant through a non-trivial constant torsion root, so the trivial $T = 0$ vacuum is not the only possibility.","The de Sitter or anti-de Sitter character of a solution is decided by the sign of the constant torsion $T$, not by the sign of the bare cosmological constant, and the same $f(T)$ can yield both end behaviors in different parameter ranges.","Charged solutions inherit the same effective cosmological constant as the uncharged solution, fixed by $T_0$ at infinity, and their first non-Coulomb electric correction is generically order $1/r^5$.","In the limit where the nonlinear parameters vanish, the quadratic and cubic solutions reduce to the general-relativity result $T = 2\\Lambda$, with $\\Lambda_{\\rm eff} = \\Lambda$ in four dimensions, giving a controlled GR limit."],"supporting_citations":[{"why":"Derives the quadratic f(T)=T+αT^2 solution in the special case 24αΛ=-1, which the paper generalizes and checks against.","marker":"[2]"},{"why":"Constructs cylindrical solutions for quadratic and cubic f(T) under restricted conditions, setting up the problem the paper solves generically.","marker":"[1]"},{"why":"One source of the diagonal vielbein ansatz for static cylindrical symmetry used in Eq. (4).","marker":"[3]"},{"why":"Another source of the same diagonal vielbein and metric form.","marker":"[10]"},{"why":"Provides the self-contained review of f(T) gravity whose field-equation framework the paper uses.","marker":"[8]"},{"why":"Reference for the n=4, k=3 anti-de Sitter metric A=B=r^2/ℓ^2 used to interpret the torsion value T=6/ℓ^2.","marker":"[13]"},{"why":"Reference for the torsion value corresponding to de Sitter or anti-de Sitter spacetime.","marker":"[14]"}],"fun_headline_variants":["Universal cylindrical black holes in any f(T) model","Closed-form AdS/dS black holes for all f(T) gravities","f(T) gravity yields universal static cylindrical black holes","Every f(T) theory admits closed-form cylindrical black holes"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the diagonal choice of frame field used in Eq. (4) is not missing any static cylindrically symmetric solutions; because $f(T)$ gravity changes its form under frame rotations, the paper does not prove that every solution of a given $f(T)$ can be represented this way.","fun_headline_variants_meta":{"raw":{"variants":["Universal cylindrical black holes in any f(T) model","Closed-form AdS/dS black holes for all f(T) gravities","f(T) gravity yields universal static cylindrical black holes","Every f(T) theory admits closed-form cylindrical black holes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000726,"raw_usage":{"total_tokens":3243,"prompt_tokens":922,"completion_tokens":2321,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":538,"completion_tokens_details":{"reasoning_tokens":2252}},"tokens_in":538,"tokens_out":2321,"duration_ms":16293,"temperature":1.0,"reasoning_tokens":2252,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:27:29.200327+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the vacuum field equations for the metric (5) using a Lorentz-rotated, non-diagonal vielbein (frame field) for a concrete model such as $f(T)=T+\\alpha T^2$ and look for a solution with $A\\neq B$ or with $r$-dependent torsion. Any such counterexample would show that the diagonal ansatz was not exhaustive and that (20) is not the most general generic solution; equivalently, the universal claim fails if the rotated-frame equations do not force $G=F$.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Derives the quadratic f(T)=T+αT^2 solution in the special case 24αΛ=-1, which the paper generalizes and checks against."},{"cited_title":"(27) This constraint is always satisfied if α and Λ have the same sign","cited_arxiv_id":null,"evidence_quote":"Constructs cylindrical solutions for quadratic and cubic f(T) under restricted conditions, setting up the problem the paper solves generically."},{"cited_title":"As we noticed earlier even in the case Λ ≡ 0, the f (T) theory generates a non vanishing effective cosmological constant","cited_arxiv_id":null,"evidence_quote":"One source of the diagonal vielbein ansatz for static cylindrical symmetry used in Eq. (4)."},{"cited_title":"Nashed and E.N","cited_arxiv_id":null,"evidence_quote":"Another source of the same diagonal vielbein and metric form."},{"cited_title":"The latter is brought to the following form once we eliminate T, Λ and G using (7), (34) and(39) r2F′ + (n − 4)rF + r2 F2 + 6 − 2n = 4r2V′2 fT(T(r)) A","cited_arxiv_id":null,"evidence_quote":"Provides the self-contained review of f(T) gravity whose field-equation framework the paper uses."},{"cited_title":"Gonz´ alez, E.N","cited_arxiv_id":null,"evidence_quote":"Reference for the n=4, k=3 anti-de Sitter metric A=B=r^2/ℓ^2 used to interpret the torsion value T=6/ℓ^2."},{"cited_title":"Bengochea and R","cited_arxiv_id":null,"evidence_quote":"Reference for the torsion value corresponding to de Sitter or anti-de Sitter spacetime."}],"review_version":1}