{"id":"e2ca890b-77bb-4f05-b36f-7da926bfdd09","arxiv_id":"2411.09202","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A new three-parameter rotating wormhole spacetime is constructed and shown to have a regular throat, an asymptotically Kerr limit, and a shadow compatible with some EHT constraints.","lead":"The authors construct a rotating wormhole from a known static wormhole using the Azreg-Ainou method and show it has a throat, regular curvature, and a shadow that can mimic black holes. It adds a new model to the black hole mimicker catalogue and shows how weakly current EHT data constrain such alternatives.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The shadow calculation rests on an unproven and likely false Hamilton-Jacobi separability; the metric's Δ(r) does not match the Δ_std required for the separable Kerr-like form.","rationale":"The reader's formal weakest_assumption is the Azreg-Ainou ansatz and the choice Ψ=K+a²cos²θ. That concern is about uniqueness rather than correctness: even if Ψ is one of many admissible choices, the resulting metric (3.33) is still an explicit regular wormhole spacetime, so the geometric construction can stand. The more load-bearing defect is the claimed HJ separability, which the reader mentions in the rationale but does not make the primary weak point. The separability claim is directly used to produce every shadow image and the EHT constraints, including the headline bound p≤0.24. A concrete algebraic check shows the metric is not in the separable Kerr-like class: the Δ appearing in g^{rr} differs from the Δ_std appearing in the inverse t-φ metric. Thus the effective potential (5.6) is not the correct radial potential, and the angular equation (5.4) is just Kerr's rather than the one for this spacetime. This invalidates the shadow-based observational conclusions, although the new wormhole metric itself may remain correct. The ADM mass misidentification identified by the reader is a real but secondary error: it would shift the δ constraint even if separability held. Because the geometric core of the paper is likely salvageable and the shadow can in principle be recomputed numerically, the conditional verdict remains appropriate; the paper should not be accepted in its current form with the claimed analytical shadow and EHT match.","tokens_in":20182,"tokens_out":26842,"duration_ms":252272,"concrete_test":"Use a computer algebra system to form the null HJ expression H = g^{μν}p_μp_ν for the metric (3.33) with the ansatz p_μ=(-E, S_r'(r), S_θ'(θ), L), then multiply by Σ. Compute ∂²(Σ H)/∂r∂θ for generic nonzero p and a. If this mixed derivative does not vanish identically, no separated solution of the form (5.2) exists and the shadow equations are invalid. As a complementary check, construct the putative Killing tensor from (5.8) and evaluate ∇_(μK_{νρ}); nonzero value settles the absence of a Carter constant.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's shadow and EHT claims depend on the assertion that the null Hamilton-Jacobi equation separates as in Eq. (5.2). For the metric (3.33), the t-φ block has the Kerr-like form with q=2m(r)r, so its determinant D is -sin²θ Δ_std, where Δ_std = r² - 2m(r)r + a². The inverse components g^{tt}, g^{tφ}, g^{φφ} consequently contain denominators Δ_std. But the radial part has g^{rr} = Δ/Σ with Δ given by Eq. (3.35), and Δ ≠ Δ_std for p≠0 (e.g., M=1, p=0.5, a=0.5, r=3 gives Δ≈3.16 while Δ_std≈4.89). In the standard separable Kerr-like family, the same Δ appears in both g^{rr} and the t-φ block. Since that condition fails here, the HJ equation does not reduce to the Kerr angular equation (5.4) plus the radial equation (5.5)-(5.6). The text after Eq. (5.8) merely asserts that the construction in [71-73] applies, without verifying the required X^{ij}, Y^{ij} constraints. If separability fails, the shadow boundary conditions (5.9)-(5.10) and all derived shadow profiles and EHT bounds in §V are invalid, undermining the observational part of the central claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper applies the Azreg-Ainou algorithm to the static R=0 wormhole of Eq. (2.5) and obtains a new rotating, asymptotically flat, axially symmetric line element, Eq. (3.33), with mass function m(r) in Eq. (3.34) and radial function Δ(r) in Eq. (3.35). The authors argue that this metric reduces to the static R=0 wormhole for a=0 and to Kerr for p=0, that it has a throat at r=2M with regular curvature invariants on the wormhole domain, that the supporting matter in GR violates the energy conditions, and that the spacetime possesses no ergosphere. They then compute shadow profiles under an assumed Hamilton-Jacobi separability and compare them with EHT observations of M87* and SgrA*, deriving a bound p≲0.24 from the fractional deviation parameter δ.","tokens_in":20517,"tokens_out":5421,"duration_ms":63821,"significance":"If sound, the paper gives an explicit, regular rotating wormhole that interpolates between Kerr and a known static wormhole, with concrete observables (shadow, energy-condition violations) that could be tested against black-hole-shadow data. The geometric construction is largely self-contained: the limits p=0 and a=0 are correctly identified, the throat condition and embedding diagrams support the wormhole interpretation, and the displayed curvature invariants are finite on r≥2M. However, the observational part rests on two load-bearing assumptions: exact Hamilton-Jacobi separability of the null geodesic equation and the identification of M as the ADM mass. Both need to be established or corrected before the EHT comparison can be trusted.","major_comments":[{"comment":"The Hamilton-Jacobi separability of the metric (3.33) is asserted but not demonstrated, and the assertion is questionable. For the inverse metric, the g^{rr} component is Δ/Σ with Δ given by Eq. (3.35), while the t-φ sector contains the different combination Δ_std = r² − 2m(r)r + a². For p ≠ 0 these two quantities are not equal; for example, with M=1, p=0.5, a=0.5, r=3 one finds Δ≈3.16 while Δ_std≈4.89. The standard Kerr-like separable form requires the same Δ to appear in the radial and in the t-φ block. The paragraph after Eq. (5.8) merely claims that the construction of Refs. [71–73] applies and that the metric 'belongs to the same general class', without verifying the X^{ij}, Y^{ij} constraints for this specific Δ(r). Unless explicit verification is provided, the separated angular and radial equations (5.4)–(5.6), the critical parameters (5.10), and all shadow profiles and EHT bounds in §V B are unsupported. The authors should either prove separability for the line element (3.33) or remove the shadow/EHT section and temper the corresponding conclusions.","section":"§V, Eqs. (5.5)–(5.10)"},{"comment":"The parameter M is not the ADM mass of the spacetime. From Eq. (3.34), m(r) → M/(p+1) as r → ∞, so the asymptotic form of gtt is −1 + 2M/((p+1)r) + O(r⁻²). The correct ADM mass is therefore M_adm = M/(p+1), not M. The paper nevertheless calls M the ADM mass throughout, for example in the concluding paragraph of §VI, and uses M as the normalization scale in the shadow plots and in the fractional deviation parameter δ of Eq. (5.15). Since δ compares the shadow diameter with 3√3 M_adm, using M instead of M/(p+1) rescales δ by a factor (p+1) and changes the exclusion plot in Fig. 13 (right) and the stated bound p≲0.24. The mass interpretation must be corrected, or the EHT constraints must be recomputed using the actual ADM mass.","section":"§III C, Eq. (3.34); §V B; §VI"}],"minor_comments":[{"comment":"The choice Ψ = K + a² cos²θ is presented as a solution of the G_{rθ}=0 constraint, but the paper does not address whether the Azreg-Ainou construction with this Ψ is unique or whether other choices would change the resulting rotating geometry. A sentence acknowledging this limitation would help calibrate the claim that Eq. (3.33) is the rotating counterpart of the static wormhole.","section":"§III B, Eq. (3.29)"},{"comment":"The wormhole criteria are stated but the flare-out condition ∂b/∂r < 0 at the throat is not explicitly checked with the numerical or analytic expressions; the authors say 'one can easily verify' without showing the calculation. This is a short addition that would make the wormhole claim easier to check.","section":"§IV A, after Eq. (4.8)"},{"comment":"The text says ΔC reaches a maximum value of 0.005 for p=0, a=0.99, while the colorbar in Fig. 13 (left) appears to saturate at 0.004. Please make the value consistent.","section":"§V B, Fig. 13 caption and text"},{"comment":"The allowed domain of the parameter p is never stated explicitly. The metric and plots appear to assume p ≥ 0, and the discussion mentions extending p > 1.5; this should be stated and justified (e.g., for positivity of N² and regularity of the wormhole).","section":"General"},{"comment":"The celestial coordinates α and β are defined with a finite observer distance r0, but the shadow formulas (5.12) are taken in the limit r → ∞. The notation should make clear that the observer is asymptotically far, and the limit should be stated consistently.","section":"§V, Eq. (5.11)"}],"recommendation":"major_revision","confidential_remarks":"The geometric part of the paper — the new line element, the wormhole properties, the energy-condition analysis, and the invariant plots — appears to be a legitimate contribution to the rotating-wormhole literature. The central obstacle is the shadow section: the separability claim is not substantiated and is in fact doubtful for the given Δ(r), and the mass misidentification further compromises the EHT comparison. Both issues are fixable within the manuscript's scope (by rigorous separability verification and correction of the mass normalization, or by removing the observational claims). I do not see a need to reject, but the paper should not be accepted with the current shadow analysis."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take. The central geometric construction—the rotating wormhole metric (3.33) with mass function (3.34)—is new, explicit, and sound. The limits check out (Kerr at p=0, static R=0 wormhole at a=0), the throat sits at r=2M, the spacetime is regular on [2M,∞) with finite ZM invariants, and the energy-condition analysis is honest. The use of Azreg-Ainou rather than Newman-Janis is well justified; the explanation of why NJ fails is clear. That part of the paper is worth publishing.\n\nThe trouble is Section V. The shadow calculation assumes the null Hamilton-Jacobi equation separates in the standard Kerr-like way, but the metric doesn't belong to that separable family. For separability you need the same Δ(r) to appear in g^{rr} and in the t-φ block (via the determinant). Here g^{rr} uses Δ from (3.35), while the t-φ block gives Δ_std = r² − 2m(r)r + a². For p≠0 the two are different—for M=1, p=0.5, a=0.5, r=3, Δ≈3.16 and Δ_std≈4.89. So the reduction to Eqs (5.4)–(5.6) doesn't go through, and the appeal to Refs [71–73] doesn't apply without checking their constraints, which are not satisfied. The shadow profiles and the ΔC, δ bounds in Section V are therefore not valid for p≠0. This is a load-bearing flaw, not a cosmetic one.\n\nThere's also a mass normalization problem: m(r)→M/(p+1) as r→∞, so M is not the ADM mass. The paper treats M as the ADM mass when normalizing shadows and when comparing with SgrA*; that makes the p>0.24 exclusion unreliable. Minor: Eq (5.4) doesn't obviously reduce to the standard Kerr angular equation unless an a² factor is accounted for.\n\nBottom line: the geometry is a real contribution and should get a serious referee. But Section V needs to be rebuilt, presumably with numerical null geodesics, and the mass fixed. I'd send it to review, flagging that the observational section requires major revision.","headline":"The rotating wormhole metric is new and seems sound, but the shadow and EHT constraints rest on a Hamilton-Jacobi separability that fails for p≠0, plus an ADM mass normalization error; the geometry deserves review, the observational section does not.","tokens_in":21034,"tokens_out":20754,"would_cite":true,"duration_ms":215006,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83C15","83C20","83C57"],"pacs":[],"model":"deepseek-v4-flash","headline":"A new rotating Lorentzian wormhole, built from the static zero-Ricci wormhole, is shown to be regular, asymptotically flat, and consistent with EHT shadow bounds.","keywords":["rotating wormhole","Lorentzian wormhole","Newman-Janis algorithm","Azreg-Ainou method","wormhole shadow","energy conditions","Kerr-like spacetime","zero Ricci scalar"],"falsifier":"Solve Eq. (3.28) for $\\Psi$ without imposing Eq. (3.29) and check for other regular solutions that reduce to $h(r)$ as $a\\to0$ and satisfy the wormhole conditions; if any exist, the metric (3.33) is not the uniquely determined rotating counterpart. A cleaner settle would be an independent derivation of the same metric from a specified axisymmetric matter source in an explicit gravity theory.","tokens_in":1996,"feed_emoji":"🕳️","tokens_out":2560,"duration_ms":111938,"temperature":0.7,"pith_summary":"This paper tries to establish that the static, spherically symmetric zero-Ricci wormhole has a rotating counterpart, and that the new line element is a genuine wormhole rather than a disguised black hole. It argues that the Newman-Janis algorithm and its generalized version fail for this seed, while the Azreg-Ainou method succeeds and yields an explicit metric with three parameters: mass $M$, rotation $a$, and a dimensionless $p$. The authors show the metric reduces to the known static wormhole at $a=0$, to Kerr at $p=0$, has a throat at $r=2M$, no horizon or ergosphere, and finite curvature invariants on and outside the throat. They then compute the shadow and find it compatible with M87* and SgrA* observations, with the SgrA* fractional deviation bound selecting $p\\leq0.24$. A sympathetic reader would care because this gives a concrete, observationally testable wormhole that mimics Kerr at large distances and sharpens the black-hole-mimicker program.","feed_headline":"Rotating wormhole metric fits EHT shadow bounds","feed_subtitle":"Built from a zero-Ricci static wormhole, the rotating metric matches SgrA* shadow data for p≤0.24.","key_machinery":"The load-bearing mechanism is the Azreg-Ainou procedure: rather than complexifying the radial coordinate as in the Newman-Janis method, it promotes the seed functions $f(r),g(r),h(r)$ to three-variable functions $A,B,\\Psi$, fixes them by requiring the Boyer-Lindquist components $g_{tr}=g_{r\\phi}=0$, and then solves the constraint $G_{r\\theta}=0$. The crucial step is the solution $\\Psi=K+a^2\\cos^2\\theta$, where $K(r)=h\\sqrt{g/f}$; this choice is what converts the static seed into the explicit metric (3.33). The Hamilton-Jacobi equation for null geodesics is separable for this Kerr-like form, which is what makes the shadow computation possible.","core_discovery":"The central discovery is the line element (3.33), with $\\Sigma = r^2 + a^2\\cos^2\\theta$, $m(r)$ as in (3.34), and $\\Delta(r)$ as in (3.35). In the $a\\to0$ limit it returns the static $R=0$ wormhole, in the $p\\to0$ limit it returns Kerr, and for $a\\neq0$, $p\\neq0$ it is a Kerr-like rotating wormhole: the throat sits at $r=2M$ with throat radius $S|_{r=2M} = [4M^2 + a^2(p^2+4p+2)/(p+1)^2]^{1/2}$, the spacetime is asymptotically flat, and the six independent Zakhary-McIntosh curvature invariants are finite and smooth on $r\\in[2M,\\infty)$. The metric has no ergosphere because $g_{tt}<0$ everywhere, it is not of Teo type but belongs to the Damour-Solodukhin-inspired Kerr-like class, and the matter required in general relativity violates all energy conditions, as expected for a wormhole. The null Hamilton-Jacobi equation separates, giving an analytic shadow; the shadow satisfies the EHT circularity bound for all allowed parameters and satisfies the SgrA* fractional-deviation bound only for $p\\lesssim0.24$.","pith_inferences":["A natural extension the authors leave open is to derive (3.33) from a specific axisymmetric scalar-field solution in the braneworld; if that succeeds, the GR energy-condition violation would be reinterpreted as geometric stress, and the rotating wormhole would gain a dynamical field-theoretic status.","The success of $\\Psi=K+a^2\\cos^2\\theta$ suggests testing whether the Azreg-Ainou method with this ansatz generates Kerr-like rotating families for other static seeds whose Newman-Janis transform is obstructed; uniqueness of the ansatz is not established, so each such construction needs independent verification.","The shadow analysis assumes the standard wormhole-shadow convention: all light sources are on the observer's side and the other mouth is dark. If sources exist inside the far mouth or near the throat, the observable image could differ qualitatively from the dark spot computed here.","The $p\\le0.24$ bound is testable with next-generation very-long-baseline interferometry; a measured $\\delta$ outside that interval for SgrA* would single out Kerr-like models and rule out this specific wormhole."],"forward_implications":["The $R=0$ static wormhole now has an explicit rotating extension, and the obstruction that blocked the Newman-Janis route is understood: the transformation functions $\\chi_1,\\chi_2$ become $\\theta$-dependent.","The spacetime is a black-hole mimicker: it approaches Kerr asymptotically and its shadow for $p\\lesssim0.24$ is consistent with SgrA* and M87* data, so current observations cannot exclude it.","Because $\\Delta(r)$ has no zero on $r\\ge2M$ and $g_{tt}<0$ everywhere, there is no horizon and no ergosphere; this gives concrete differences from Kerr in photon orbits, lensing, and accretion signatures near the throat.","The energy-condition violation, while expected, is severe in GR; any physical realization must live in an alternative theory such as braneworld gravity, where the effective geometric stress may satisfy the null energy condition.","The SgrA* bound $p\\le0.24$ is a sharp prediction: future measurements of shadow fractional deviation outside this range would eliminate the wormhole as a model for SgrA*."],"supporting_citations":[{"why":"Introduces the static R=0 wormhole that is the seed for the rotating construction.","marker":"[37]"},{"why":"Documents the earlier unsuccessful Newman-Janis attempt to rotate this seed, which motivates the Azreg-Ainou route.","marker":"[45]"},{"why":"Supplies the Azreg-Ainou method for generating rotating metrics from static seeds without the usual complexification.","marker":"[51]"},{"why":"Provides the Boyer-Lindquist reduction equations and the $G_{r\\theta}=0$ constraint whose solution $\\Psi=K+a^2\\cos^2\\theta$ is used to build the metric.","marker":"[52]"},{"why":"Defines the general rotating wormhole form and the Teo-type class that the new metric is shown not to belong to.","marker":"[14]"},{"why":"Defines the Kerr-like wormhole class, as rotating generalizations of Damour-Solodukhin wormholes, into which the new solution falls.","marker":"[54]"},{"why":"Supplies the Zakhary-McIntosh curvature invariants whose finiteness establishes that the spacetime is non-singular.","marker":"[62]"},{"why":"Identifies the general class of axisymmetric metrics with separable Hamilton-Jacobi equations, which justifies the shadow computation for this wormhole.","marker":"[73]"},{"why":"Provides the M87* circularity bound $\\Delta C\\le0.1$ that leaves the full parameter space allowed.","marker":"[75]"},{"why":"Provides the SgrA* fractional deviation bound on $\\delta$ that restricts the wormhole parameter to $p\\le0.24$.","marker":"[79]"}],"fun_headline_variants":["New rotating wormhole matches EHT shadow","Kerr-like wormhole passes SgrA* shadow test","Spin makes wormhole fit black hole images","Rotating wormhole fits SgrA* for p≤0.24","Wormhole shadow matches EHT with spin"],"cache_read_input_tokens":23168,"weakest_assumption_plain":"The whole construction depends on an assumed shortcut for how the metric functions depend on angle under rotation, namely $\\Psi=K+a^2\\cos^2\\theta$; the paper does not prove that this shortcut is the unique one that the physics requires, so if it is wrong the new metric is just one of many hand-built rotating spacetimes rather than the rotating version of the original wormhole.","fun_headline_variants_meta":{"raw":{"variants":["New rotating wormhole matches EHT shadow","Kerr-like wormhole passes SgrA* shadow test","Spin makes wormhole fit black hole images","Rotating wormhole fits SgrA* for p≤0.24","Wormhole shadow matches EHT with spin"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000232,"raw_usage":{"total_tokens":1495,"prompt_tokens":956,"completion_tokens":539,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":572,"completion_tokens_details":{"reasoning_tokens":461}},"tokens_in":572,"tokens_out":539,"duration_ms":6366,"temperature":1.0,"reasoning_tokens":461,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T20:57:19.548192+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Solve Eq. (3.28) for $\\Psi$ without imposing Eq. (3.29) and check for other regular solutions that reduce to $h(r)$ as $a\\to0$ and satisfy the wormhole conditions; if any exist, the metric (3.33) is not the uniquely determined rotating counterpart. A cleaner settle would be an independent derivation of the same metric from a specified axisymmetric matter source in an explicit gravity theory.","supporting_citations":[{"cited_title":"Dadhich, S","cited_arxiv_id":null,"evidence_quote":"Introduces the static R=0 wormhole that is the seed for the rotating construction."},{"cited_title":"Biswas, M","cited_arxiv_id":null,"evidence_quote":"Documents the earlier unsuccessful Newman-Janis attempt to rotate this seed, which motivates the Azreg-Ainou route."},{"cited_title":"Azreg-A ¨ ınou, Phys","cited_arxiv_id":null,"evidence_quote":"Supplies the Azreg-Ainou method for generating rotating metrics from static seeds without the usual complexification."},{"cited_title":"Azreg-A ¨ ınou, Eur","cited_arxiv_id":null,"evidence_quote":"Provides the Boyer-Lindquist reduction equations and the $G_{r\\theta}=0$ constraint whose solution $\\Psi=K+a^2\\cos^2\\theta$ is used to build the metric."},{"cited_title":"Bueno, P","cited_arxiv_id":null,"evidence_quote":"Defines the Kerr-like wormhole class, as rotating generalizations of Damour-Solodukhin wormholes, into which the new solution falls."},{"cited_title":"Zakhary and C.B.G","cited_arxiv_id":null,"evidence_quote":"Supplies the Zakhary-McIntosh curvature invariants whose finiteness establishes that the spacetime is non-singular."},{"cited_title":"Gal’tsov and A","cited_arxiv_id":null,"evidence_quote":"Identifies the general class of axisymmetric metrics with separable Hamilton-Jacobi equations, which justifies the shadow computation for this wormhole."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the M87* circularity bound $\\Delta C\\le0.1$ that leaves the full parameter space allowed."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the SgrA* fractional deviation bound on $\\delta$ that restricts the wormhole parameter to $p\\le0.24$."}],"review_version":1}