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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

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2026-08-03 14:42 UTC pith:TFETECXV

load-bearing objection 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. the 3 major comments →

arxiv 2512.19406 v3 pith:TFETECXV submitted 2025-12-22 gr-qc

Optical appearance of regularized compact objects without an exterior photon sphere

Ashok B. Joshi , Vishva Patel , Parth C. Varasani This is my paper
classification gr-qc
keywords black hole shadowsphoton sphereregularized compact objectstraversable wormholesnull geodesicseffective potentialobservational constraintsnaked singularity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

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.

Core claim

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

What carries the argument

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

Load-bearing premise

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.

What would settle it

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).

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • 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.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

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.

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 (3)
  1. [Sec. III, after Eq. (13)] 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.
  2. [Sec. III, around Eq. (22)] 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
  3. [Sec. IV.A and Fig. 5] 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.
minor comments (5)
  1. [Eq. (13)] 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.
  2. [Sec. III, text near Figs. 3 and 4] 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.
  3. [Eq. (14)] 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.
  4. [Sec. IV, Eq. (29)] 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.
  5. [General] 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.

Circularity Check

0 steps flagged

No significant circularity: the shadow boundary is computed from the given metrics and the EHT comparisons are parameter constraints, not fitted predictions.

full rationale

The derivation chain is self-contained. The shadow boundary for the regularized null-singularity spacetimes is obtained by direct use of the null geodesic equation, Eq. (12), with Veff = f(r)/(r^2+L^2). The critical impact parameter b0 is then fixed algebraically by Veff(0)=1/b^2, giving Eqs. (13), (20), and (22) for the respective metrics. The absence of a photon sphere is checked by the effective-potential conditions, not assumed. No fitted parameter is renamed as a prediction: the Schwarzschild-like mimicry is not a free-standing prediction, because b0=(1+x)M retains the free SV parameter x, and the paper explicitly uses EHT angular-diameter bounds in Fig. 5 to delimit the allowed parameter ranges. Self-citations to prior null-singularity and shadow-without-photon-sphere work [78,79,83] are contextual background and are not load-bearing; the present geodesic and intensity integrals are computed from the stated metrics without invoking a uniqueness theorem or an imported ansatz from the same authors. The main interpretive caveat—whether a two-way traversable wormhole's dark center should be called a shadow when photons with b<b0 pass through the throat rather than being captured—depends on the assumed emission model in Sec. IV (Eqs. 23-29) and on the definition of 'shadow'. That is a physical/interpretational concern about the source distribution, not a circular reduction of the derived result to its own inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 0 invented entities

The central claims rest on two free parameters (L and q), plus assumptions that the regularized metrics admit the assumed matter source, that the b0 boundary acts as a shadow, and that EHT diameter bounds apply directly to non-rotating spherical models.

free parameters (2)
  • L (Simpson-Visser regularization parameter) = L/M ≈ 3.55–4.22 for neutral model under Sgr A* 1σ; ≈3.75–5.25 for M87 1σ
    Introduced ad hoc to smooth the singularity; shadow radius b0=(1+x)M; EHT comparison constrains it, so the match to Schwarzschild is a fit, not a prediction.
  • q (charge of charged null singularity) = explored q/M = 0, 0.5, 1.0, 1.5; no tight bound reported
    Free charge parameter of the charged metric; enters Eq (22) for b0 and shifts shadow radius slightly.
axioms (3)
  • domain assumption SV substitution r→√(r²+L²) yields a valid spacetime solution of Einstein(-Maxwell) equations for some (exotic) matter source
    Paper computes curvature invariants and NEC violation but does not construct the matter source; for black-bounce metrics it cites [134,135].
  • domain assumption Shadow boundary is set by impact parameter b0 where photons reach r=0; such photons are assumed not to contribute to observed intensity
    Used in Section III Eq (13) and Section IV intensity model; requires that the other side of the wormhole is dark/opaque.
  • domain assumption EHT shadow-diameter bounds from [64,137] apply directly to these spherically symmetric, non-rotating metrics
    Used in Section IV A; ignores spin, inclination, and detailed accretion physics.

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read the original abstract

Recent observations by the Event Horizon Telescope (EHT) indicate that the shadow of the compact object at our Galaxy's center (Sgr A*) closely resembles that of a Schwarzschild black hole. However, identifying the presence and exact location of unstable circular null geodesics outside the compact object (hereafter referred to as an exterior exterior photon sphere) observationally remains challenging. Motivated by this, we investigate shadow formation in spacetimes that lack an exterior photon sphere by applying the Simpson--Visser (SV) regularization technique (originally designed to smooth black hole singularities) to null singularity and charged null singularity metrics. Apart from the shadow-like dark region without an exterior photon sphere in the charged SV spacetime, our investigation shows that, for a specific range of parameters, the shadow boundary (dark region) is controlled by the regular core rather than by an exterior photon sphere. Our results reveal that shadows arising from these regularized null singularity spacetimes closely mimic those of Schwarzschild and charged black-bounce spacetimes, even though no exterior exterior photon sphere exists. We also perform a phenomenological comparison of the predicted shadow sizes with the EHT observations of Sgr A* and M87, identifying parameter ranges compatible with the observed angular diameters.

Figures

Figures reproduced from arXiv: 2512.19406 by Ashok B. Joshi, Parth C. Varasani, Vishva Patel.

Figure 1
Figure 1. Figure 1: FIG. 1: In Figs. ( [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: In Figs. ( [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: In Figs. ( [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: In Figs. ( [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Shadow radius in null regular geometry compared with Sgr [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

discussion (0)

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Reference graph

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