{"id":"5e21f78a-40d6-4063-988a-05b345340c30","arxiv_id":"2512.19406","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Simpson–Visser regularization of null-singularity metrics yields core-controlled shadows without a photon sphere that can mimic Schwarzschild when the regularization length L≈4M.","lead":"This paper applies a known mathematical trick — replacing the singular center with a smoothed core — to two already-known naked-singularity spacetimes, and works out what their shadows would look like. It finds that these smoothed objects can produce a dark shadow-like region even with no photon sphere, and that tuning one free parameter makes the shadow look just like a Schwarzschild black hole's.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Wormhole 'shadow' is actually transmitted light from the other side; the central claim confuses a dark region with a gravitational shadow.","rationale":"The reader's weakest assumption is exactly the same: in a traversable wormhole, the b<b0 rays are not captured but traverse the throat, and the dark region may be an image of the other side. This is the most load-bearing concern because the entire novel claim — that these spacetimes 'can produce a shadow without a photon sphere' — depends on treating the throat as a trap. The manuscript itself is internally inconsistent: it describes the metrics as regular two-way traversable wormholes, yet refers to b<b0 photons as 'trapped near the singularity' (Sec. III). The geodesic equation shows no trapping: the effective potential at the throat is finite, and for b<b0 the square of the radial momentum is positive, so the photon crosses to the other universe. The intensity calculation artificially limits emission to the observer's side, excluding the natural background of the other asymptotic region. If that background is bright, the central dark region disappears entirely, revealing that the 'shadow' is not a property of the spacetime alone but a choice of source distribution. This is not a minor qualification; it overturns the central claim. The reader's CONDITIONAL verdict was appropriate given the ambiguity, but the analytic argument demonstrates the issue is real and foundational, so a REJECT is warranted unless the authors reframe the claim (e.g., as a 'dark region' under one-sided emission assumptions) and abandon the shadow terminology. Other issues, such as the 3√3M inconsistency, are secondary to this fundamental problem.","tokens_in":15901,"tokens_out":7795,"duration_ms":80830,"concrete_test":"Analytically integrate the radial null geodesic for the metric (5) with b<b0=(1+x)M from a distant point on the + side; show the solution reaches r=0 with positive radial velocity and then continues to r→-∞, demonstrating transmission. To confirm observability, ray-trace a uniform bright source at r=-∞ (or a thin disk extending through the throat) and compute the intensity on the observer's sky; if the region b<b0 is illuminated, the 'shadow' is not a shadow. A single numerical integration for e.g. x=2 and b=2.5M would show the geodesic crossing to negative r.","verdict_should_be":"REJECT","load_bearing_attack":"The central claim that the regularized null-singularity metrics (Eqs. 5 and 10) cast a shadow without a photon sphere rests on the statement in Sec. III that 'photons with b<b0 are trapped near the singularity, forming a shadow' (text after Eq. 13). But for L>0 these are two-way traversable wormholes with a regular throat at r=0 and r extending to -∞. The radial null geodesic equation (12) gives (1/h²)(dr/dλ)² = 1/b² - f(r)/(r²+L²). At r=0, f(0)/L² = 1/b0² with b0=(1+x)M (after correcting the typo in Eq. 13). For any b<b0, the right-hand side is strictly positive at r=0, so the photon reaches the throat with nonzero radial momentum and continues into the other asymptotic region; it is not trapped. The intensity model in Sec. IV includes emission only from infalling matter on the observer's side and implicitly discards rays that leave through the throat. A consistent treatment must include light from the other side (or from the same universe seen through the wormhole) inside b0, which fills the dark region. Thus the dark centers in Figs. 3(d) and 4(d) are not shadows caused by photon capture but boundary-imposed artifacts of the assumed source distribution. The central claim conflates 'dark region' with 'shadow' in the standard black-hole-shadow sense.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper applies the Simpson-Visser regularization to the null singularity metric (Eq. 4) and the charged null singularity metric (Eq. 9), producing regular two-way traversable wormholes (Eqs. 5 and 10). The authors study null geodesics via the effective potential V_eff = f/(r^2+L^2), identify a critical impact parameter b0 from V_eff(0), compute images under an infalling spherical accretion model, and compare the resulting shadow radii with EHT bounds for Sgr A* and M87. The central claim is that these regularized spacetimes can form a shadow without a (exterior) photon sphere and that the shadows closely mimic Schwarzschild/charged black-bounce shadows.","tokens_in":16308,"tokens_out":13453,"duration_ms":134392,"significance":"If the interpretation were correct, the result would be significant: it would strengthen the claim that EHT shadow-size measurements do not uniquely indicate a photon sphere or an event horizon, and it would extend the Simpson-Visser regularization program to null-singularity spacetimes. The algebraic derivation of b0 from V_eff is transparent, and the EHT comparison in Fig. 5 is clearly presented. However, the core physical interpretation is not supported. The metric is a two-way traversable wormhole, and the statement that photons with b<b0 are 'trapped' is false; such photons pass through the throat into the other asymptotic region. The dark region in Figs. 3(d) and 4(d) is therefore an artifact of the one-sided emission model rather than a gravitational shadow in the standard black-hole sense. The claimed mimicry of Schwarzschild is also a fitted statement, obtained by choosing L/M so that (1+x)M ≈ 3√3 M, rather than an independent prediction.","major_comments":[{"comment":"The statement that 'photons with b<b0 are trapped near the singularity, forming a shadow' is incorrect for the L>0 wormhole metrics (5) and (10). From Eq. (12), (1/h^2)(dr/dλ)^2 = 1/b^2 − V_eff(r). Since V_eff(0)=1/b0^2, for b<b0 the right-hand side is strictly positive at r=0, so the photon reaches the throat with nonzero radial momentum and continues into the region r<0. It is not trapped. The intensity model in Sec. IV, Eq. (29), integrates only over the observer-side branch and implicitly discards rays that pass through the throat. A consistent treatment would include light from the other asymptotic side; such light would fill the central dark region in Figs. 3(d) and 4(d). The abstract's central claim that these spacetimes 'can produce a shadow without a photon sphere' is therefore unsupported.","section":"Sec. III, after Eq. (13)"},{"comment":"The assertion that in the modified null singularity spacetime 'for all values of L photon sphere is absent' is inconsistent with the effective potential. For the uncharged case, V_eff(r)=1/(sqrt(r^2+L^2)+M)^2 has a global maximum at r=0; the charged case (10) has the same structure. This maximum corresponds to an unstable circular null orbit at the throat, i.e., a photon sphere located at the core, and it is precisely the quantity b0=1/sqrt(V_eff(0)) that sets the boundary of the dark region. The title and abstract use the qualifier 'exterior' photon sphere, but the body repeatedly claims 'without a photon sphere'. This distinction is load-bearing: a photon sphere at the throat is what produces the critical impact parameter. The paper should define 'exterior' consistently and either avoid the unqualified claim or prove that the throat maximum is not a photon sphere under the chosen defin","section":"Sec. III, around Eq. (22)"},{"comment":"The statement that the regularized null singularity shadows 'closely mimic' Schwarzschild is a fitted statement, not an independent outcome. For the uncharged case the shadow radius is b0=(1+x)M; it equals the Schwarzschild value 3√3 M only for x = 3√3−1 ≈ 4.2. The EHT compatibility bands in Fig. 5 are therefore constraints on L/M, and the resemblance to Schwarzschild is enforced by parameter choice. The text should state this explicitly and should not imply that the mimicry is a prediction of the model. This also applies to the charged case, where q/M is a second tunable parameter.","section":"Sec. IV.A and Fig. 5"}],"minor_comments":[{"comment":"Dimensional/unit error: b0 should be L/√f(0), not L^2/√f(0). The later formula b0=(1+x)M (and Eq. 22) is correct, so this appears to be a typo, but Eq. (13) is used in the central argument and should be corrected.","section":"Eq. (13)"},{"comment":"The text says the shadow size is 'around 3√3M' for the modified null singularity spacetime. Since b0=(1+x)M for the parameters plotted (L up to about 2M), the shadow radius is at most about 3M. Please clarify which parameter values give 3√3 M or correct the statement.","section":"Sec. III, text near Figs. 3 and 4"},{"comment":"The orbit equation is not derived, and the symbols ψ, ξ, and l are undefined. It also appears not to be used in the subsequent analysis. Please remove it or provide a proper derivation.","section":"Eq. (14)"},{"comment":"The integration range in Eq. (29) is not specified. For a two-way traversable wormhole, the author should state whether the integral runs from infinity to the throat on the observer's side, and whether a companion contribution from the other side is included. This is directly related to Major Comment 1.","section":"Sec. IV, Eq. (29)"},{"comment":"There are numerous typos and unclear phrases, including 'exterior exterior photon sphere' in the abstract, 'more then one times' in the Introduction, and inconsistent use of 'irrespective'/'irrespective of L'. A careful proofread is needed.","section":"General"}],"recommendation":"reject","confidential_remarks":"The reference list leans heavily on the authors' own previous work (e.g., Refs. [78], [79], [83], [85], [132]), but this is not the basis for my recommendation. The decision rests on the physical interpretation: the alleged 'trapping' of photons with b<b0 is false for a two-way traversable wormhole, so the central claim of a shadow without a photon sphere is not established. If the authors reframe the work as modeling the image of a one-sided accretion flow in a wormhole geometry, the paper would need to be substantially rewritten, and its title/abstract claims would no longer hold in the standard sense."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the two metrics are new and the geodesic algebra is mostly right, but the headline “shadow without a photon sphere” doesn’t survive close reading. For the modified null singularity, V_eff = 1/(sqrt(r^2+L^2)+M)^2 has a maximum at r=0; the throat is an unstable photon sphere. The same happens in the charged version. So the honest claim is “no exterior photon sphere,” not “no photon sphere.” The text itself computes r_ph = 0 and then the figure caption says “for all values of L photon sphere is absent” — that is an internal inconsistency, not a semantic quibble.\n\nWhat is genuinely new: applying the Simpson–Visser replacement to the null singularity and charged null singularity metrics is a natural extension that I don’t think is in the earlier literature, and the shadow-radius formulas b0 = (1+x)M and Eq. (22) are correctly derived from the effective potential. The curvature invariants are finite, the NEC violation is shown, and the comparison with Schwarzschild and charged black-bounce spacetimes is useful. The EHT constraints on L/M and q/M are also reasonable as parameter bounds.\n\nThe soft spots are real. Eq. (13) has a units typo: it should be L/sqrt(f(0)), not L^2/sqrt(f(0)). More importantly, the statement that photons with b < b0 are “trapped near the singularity” is false for L>0: these are two-way traversable wormholes, and a photon reaches the throat with nonzero radial momentum and passes into the other asymptotic region. The dark regions in Figs. 3(d) and 4(d) are therefore not gravitational shadows in the standard black-hole sense; they are consequences of the intensity model only including infalling matter on the observer’s side. Light from the other side, or continued geodesics, would fill the supposed shadow.\n\nThere is also a numerical inconsistency in the text: the claim that the shadow size is “around 3√3M” conflicts with b0 = (1+x)M, since 3√3M requires x ≈ 4.196, while the figures use L/M ≤ 2, where b0 ≤ 3M. The later “mimicry” of Schwarzschild is achieved by choosing L/M ≈ 4, which is fine as a constraint but not an independent prediction.\n\nThe heavy self-citation is not a red flag here — most of it points to the null-singularity papers that this work directly regularizes.\n\nBottom line: this deserves a serious referee, but the referee should push the authors to either drop the no-photon-sphere claim or restrict it to “no exterior photon sphere,” and to reframe the wormhole dark region as a source-boundary effect rather than a shadow. With that revision it would be a modest but citeable addition to the shadow phenomenology catalogue.","headline":"New SV-regularized null-singularity metrics with mostly correct geodesics, but the claim of a shadow without a photon sphere collapses because the throat itself is a photon sphere and the dark disk is a source-boundary artifact.","tokens_in":16744,"tokens_out":6540,"would_cite":false,"duration_ms":65753,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Regularized null-singularity spacetimes — traversable wormholes with no horizon and no photon sphere — can still cast shadows, with the boundary set by the regular core, closely mimicking the shadows of standard black holes within current o","keywords":["black hole shadows","photon sphere","regularized compact objects","traversable wormholes","null geodesics","effective potential","observational constraints","naked singularity"],"falsifier":"Ray-trace the full null geodesic congruence with emission included from both asymptotic regions (or from a screen placed at the far side) and compute the observed intensity inside b0: if significant light appears there, the central dark region is an artifact of the one-sided infall model rather than a shadow. Alternatively, high-resolution imaging that resolves the photon-ring subring structure at the shadow edge would distinguish a core-transmission boundary (no subring cascade) from a photon-sphere shadow (cascade present).","tokens_in":15852,"feed_emoji":"🕳️","tokens_out":11209,"duration_ms":101240,"temperature":0.7,"pith_summary":"Dark shadow-like images of compact objects are usually taken as evidence for an event horizon and a surrounding photon sphere. This paper argues that neither is required. It applies a radius-smoothing regularization — replacing the radial coordinate r by sqrt(r^2+L^2) — to two naked-singularity metrics, producing two-way traversable wormholes whose effective potential for light has no local maximum and hence no photon sphere, yet whose finite core value produces a critical impact parameter b0 below which light crosses the throat and never returns to the observer. That core-controlled boundary produces a dark disk that can closely match the shadow size of an ordinary black hole of the same mass, for a range of the regularization parameter L. Using the measured shadow diameters of the supermassive objects at the Galactic center and in M87, the paper constrains L and the charge parameter. If correct, the result means a measured shadow does not identify a photon sphere or an event horizon.","feed_headline":"Wormhole cores cast black-hole-like shadows with no photon sphere","feed_subtitle":"Horizonless, photon-sphere-free models match the measured shadow size of the Galactic center's supermassive object.","key_machinery":"The mechanism is the effective potential for null geodesics, V_eff(r) = f(r)/(r^2+L^2), on the regularized spacetimes obtained by substituting sqrt(r^2+L^2) for the radial coordinate in the null singularity and charged null singularity metrics. After regularization, f(r) is positive everywhere, so V_eff has no local maximum (no photon sphere) but takes a finite value at the throat r=0. This finite core value defines a critical impact parameter b0 — for the neutral case, b0 = L + M — that separates rays which cross the throat and disappear from the observer's sky (b < b0) from rays that scatter back (b > b0). The shadow boundary is thus set by the regular core, not by any unstable circular nu","core_discovery":"The paper's central claim is that the regularized null singularity and charged null singularity metrics — L>0 versions of naked singularities — describe regular, two-way traversable wormholes with no horizon and no photon sphere that nonetheless cast shadows. The metric function f(r) remains everywhere positive, so the effective potential V_eff(r)=f(r)/(r^2+L^2) has no local maximum and no circular photon orbit; instead, V_eff is finite at the throat r=0, giving a critical impact parameter b0. Photons with impact parameter below b0 pass through the regular core and re-emerge on the far side of the wormhole, so a distant observer on the original side sees a dark disk of radius b0; photons wit","pith_inferences":["The dark disk is only a shadow if light from the wormhole's far side is absent or negligible; a two-sided ray-tracing calculation that includes emission from the other asymptotic region could turn the dark region into an image of that far side, which would be a decisive check of the interpretation.","The same regularization applied to other naked-singularity metrics with positive f(0) should generically produce core-controlled shadows of size b0 = L/sqrt(f(0)), offering a simple criterion for when horizonless spacetimes cast shadows.","High-resolution images that resolve the photon-ring subring structure near the shadow edge could distinguish these models from black holes: here the edge is the throat-crossing boundary and should lack the nested demagnified subring cascade characteristic of a photon sphere."],"forward_implications":["A detected shadow does not by itself establish the presence of a photon sphere or an event horizon; the regularized wormhole models reproduce black-hole-like shadow sizes.","The shadow radius in these models is determined by the regular core's critical impact parameter b0, so shadow size and the existence of a bright photon ring are decoupled.","For the neutral model the shadow radius grows linearly with L/M as b0 = M + L, so the observed Galactic center and M87 shadow diameters translate directly into allowed ranges for L/M (and for q/M in the charged model).","Because these horizonless, photon-sphere-free spacetimes fall within the current observational bounds, alternative compact-object models remain viable explanations of the existing shadow images."],"fun_headline_variants":["No photon sphere, but shadows still appear","Regular cores mimic black hole shadows","Wormholes without photon spheres cast shadows","Photon-sphere-free objects still show shadows","Charged regular cores fake EHT shadows"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The central dark region counts as a shadow on the assumption that rays with impact parameter below b0 cross the wormhole throat and never return to the observer; if light from the far side of the wormhole reaches the observer inside b0, the dark region would instead be an image of the other side, and the claim that these spacetimes cast shadows would lose its meaning.","fun_headline_variants_meta":{"raw":{"variants":["No photon sphere, but shadows still appear","Regular cores mimic black hole shadows","Wormholes without photon spheres cast shadows","Photon-sphere-free objects still show shadows","Charged regular cores fake EHT shadows"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000125,"raw_usage":{"total_tokens":953,"prompt_tokens":765,"completion_tokens":188,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":509,"completion_tokens_details":{"reasoning_tokens":122}},"tokens_in":509,"tokens_out":188,"duration_ms":3240,"temperature":1.0,"reasoning_tokens":122,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T14:42:49.860074+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Ray-trace the full null geodesic congruence with emission included from both asymptotic regions (or from a screen placed at the far side) and compute the observed intensity inside b0: if significant light appears there, the central dark region is an artifact of the one-sided infall model rather than a shadow. Alternatively, high-resolution imaging that resolves the photon-ring subring structure at the shadow edge would distinguish a core-transmission boundary (no subring cascade) from a photon-sphere shadow (cascade present).","supporting_citations":[],"review_version":1}