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arxiv: 2605.16413 · v2 · pith:IWSZPV4Qnew · submitted 2026-05-13 · 🌀 gr-qc

Image of a wormhole with an arbitrary throat profile

Valeria A. Ishkaeva , Sergey V. Sushkov This is my paper

Pith reviewed 2026-05-20 20:25 UTC · model grok-4.3

classification 🌀 gr-qc
keywords wormholeblack hole shadowaccretion diskthroat silhouetteDoppler effectgravitational redshiftstatic spherically symmetric metricphoton energy shift
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The pith

Wormholes can be tuned so their shadow and silhouette radii match a Schwarzschild black hole of equal mass, but their thin accretion disk images differ and appear brighter because the Doppler effect dominates over gravitational redshift.

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

The paper derives general expressions for the shadow radius, throat silhouette radius, and photon energy shift in any static spherically symmetric spacetime. It then specializes these formulas to a three-parameter family of wormholes whose throat profile is controlled by the radius a, the length λ, and the gravitational-well parameter u0. For selected values of these parameters the wormhole shadow and silhouette exactly coincide with those of a Schwarzschild black hole of the same mass. Despite this geometric match the images of a thin equatorial accretion disk around the wormhole are substantially brighter, because the energy shift is set mainly by the Doppler boost from orbital motion rather than by gravitational redshift.

Core claim

We find that there exist sets of parameters a, λ, u0 such that the wormhole shadow and throat silhouette radii coincide with the shadow and event horizon silhouette of a Schwarzschild black hole of the same mass. Nevertheless, the accretion disk images of these objects differ substantially. In wormhole images, the Doppler effect plays a major role, not the gravitational redshift. As a result, the accreting wormhole images appear brighter.

What carries the argument

A static spherically symmetric wormhole metric with three free parameters (throat radius a, throat length λ, gravitational-well depth u0) that governs null geodesics and photon energy shifts for shadow and accretion-disk calculations.

If this is right

  • Observers could distinguish these wormholes from black holes by the brightness of their accretion disks even when shadow sizes coincide.
  • The energy-shift calculation shows that Doppler boosting, not redshift, sets the observed intensity for the wormhole case.
  • Only a narrow range of the three parameters produces an exact match to the Schwarzschild shadow and silhouette.
  • The general expressions for shadow and silhouette radii apply to any static spherically symmetric metric, not just the wormhole family studied.

Where Pith is reading between the lines

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

  • Future Event Horizon Telescope or next-generation arrays might separate wormhole candidates from black holes by mapping disk brightness asymmetries rather than shadow size alone.
  • If the thin-disk model is replaced by a thick or radiatively inefficient flow, the relative importance of Doppler versus redshift effects could shift and weaken the brightness contrast.
  • The same parameter-tuning technique might be applied to other observables such as ring-down spectra or lensing of background stars.

Load-bearing premise

The analysis relies on one specific three-parameter static spherically symmetric wormhole metric together with the thin-disk approximation; if real wormholes have different throat shapes or thicker disks, the claimed brightness distinction would not necessarily appear.

What would settle it

High-resolution radio or infrared images of an accreting compact object whose shadow and silhouette radii match those of a Schwarzschild black hole but whose disk brightness profile is significantly brighter than expected from gravitational redshift alone would support the wormhole interpretation.

Figures

Figures reproduced from arXiv: 2605.16413 by Sergey V. Sushkov, Valeria A. Ishkaeva.

Figure 1
Figure 1. Figure 1: Embedding diagrams of the wormhole for different values of the throat length parameter [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Photon trajectories u(ϕ) in the wormhole spacetime for different λ and u0. Black curves (|l| > |lph|) cross the throat, blue curves (|l| < |lph|) are deflected back, and red curves (|l| = |lph|) correspond to the circular orbit. Before we consider the parameter dependence of the circular orbits, it is important to note the overall structure of photon spheres in this spacetime. Because the function N(u) is … view at source ↗
Figure 3
Figure 3. Figure 3: Location of the circular orbit uph as a function of λ (left) and u0 (right). E. Shadow and throat silhouette The presence of a wormhole can be found from a dark spot in its observed image. This spot can be either the shadow, if there is a luminous background behind the wormhole, or the throat silhouette, if the photons emitted near the throat. Both quantities were derived in full generality in Secs. II D a… view at source ↗
Figure 4
Figure 4. Figure 4: Shadow radius αsh (left column) and throat silhouette radius αsil (right column) as functions of λ (top) and u0 (bottom) [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Shadow radius αsh as a function of the throat radius a [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Images of the accreting Schwarzschild black hole (top left) and of the wormhole with [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
read the original abstract

We investigate the observable signatures -- the shadow, the throat silhouette, and the image of a thin accretion disk -- for a family of static, spherically symmetric wormholes with an arbitrary throat profile. First, we derive expressions for the shadow radius, the throat silhouette radius, and the photon energy shift for a general static, spherically symmetric metric. Then we apply these results to a specific wormhole metric containing three free parameters: the throat radius~$a$, the throat length~$\lambda$, and the parameter~$u_0$ that controls the depth of the gravitational well. We numerically obtain the shadow and silhouette radii as functions of $\lambda$, $u_0$, and $a$, construct accretion disk images for three representative parameter sets, and compare the results with those for a Schwarzschild black hole. We find that there exist sets of parameters $a$, $\lambda$, $u_0$ such that the wormhole shadow and throat silhouette radii coincide with the shadow and event horizon silhouette of a Schwarzschild black hole of the same mass. Nevertheless, the accretion disk images of these objects differ substantially. In wormhole images, the Doppler effect plays a major role, not the gravitational redshift. As a result, the accreting wormhole images appear brighter.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript derives general expressions for the shadow radius, throat silhouette radius, and photon energy shift factor g for static spherically symmetric metrics. It then specializes to a three-parameter wormhole family with throat radius a, throat length λ, and parameter u0 controlling the gravitational well depth. Numerical evaluation shows that parameter choices exist for which the wormhole shadow (~5.2M) and throat silhouette (~2M apparent size) match those of a Schwarzschild black hole of equal mass. Ray-traced thin equatorial accretion disk images, however, differ substantially, with the wormhole cases appearing brighter because the energy shift is dominated by Doppler boosting rather than gravitational redshift.

Significance. If the results hold, the work supplies a concrete mechanism for distinguishing wormholes from black holes via accretion imaging even when shadows and silhouettes coincide, which is directly relevant to strong-field tests with instruments such as the Event Horizon Telescope. The general expressions for arbitrary throat profiles constitute a reusable technical contribution. The explicit numerical comparisons and the identification of Doppler dominance provide falsifiable, observationally oriented predictions.

major comments (2)
  1. [§3] §3 (specific metric): the three-parameter family fixes the redshift function via u0 while allowing an arbitrary throat profile; the central claim that Doppler dominates the energy shift g in the disk images is therefore tied to this particular choice of Φ(r) and may not extend to other redshift functions that could be paired with the same throat shape.
  2. [§5] §5 (accretion disk images): the reported brightness difference assumes identical Keplerian orbital velocities and the same emissivity profile for the wormhole and Schwarzschild thin disks; without a quantitative decomposition of the gravitational versus Doppler contributions to g (e.g., separate plots or tables) or tests with non-Keplerian flow, the assertion that “the Doppler effect plays a major role, not the gravitational redshift” remains under-supported.
minor comments (2)
  1. [Figures 4–6] Figure captions and axis labels should explicitly state the normalization used for brightness so that direct visual comparison between wormhole and Schwarzschild panels is unambiguous.
  2. [§2] The general expression for the silhouette radius in §2 would benefit from an explicit statement of the condition used to locate the unstable photon orbit for the arbitrary metric functions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight important aspects of our analysis that we will clarify in the revised manuscript. We respond to each major comment below.

read point-by-point responses

  1. Referee: [§3] §3 (specific metric): the three-parameter family fixes the redshift function via u0 while allowing an arbitrary throat profile; the central claim that Doppler dominates the energy shift g in the disk images is therefore tied to this particular choice of Φ(r) and may not extend to other redshift functions that could be paired with the same throat shape.

    Authors: We agree with the referee that our results are specific to the chosen parametrization of the redshift function Φ(r) through the parameter u0. This choice allows us to control the depth of the gravitational well independently of the throat profile. The observed dominance of the Doppler effect in the energy shift for the accretion disk images holds for this family. In the revised manuscript, we will add a statement in Section 3 clarifying that the conclusions regarding the energy shift and image brightness are tied to this specific form of Φ(r), and that different choices of the redshift function could lead to different balances between gravitational and Doppler contributions. revision: partial

  2. Referee: [§5] §5 (accretion disk images): the reported brightness difference assumes identical Keplerian orbital velocities and the same emissivity profile for the wormhole and Schwarzschild thin disks; without a quantitative decomposition of the gravitational versus Doppler contributions to g (e.g., separate plots or tables) or tests with non-Keplerian flow, the assertion that “the Doppler effect plays a major role, not the gravitational redshift” remains under-supported.

    Authors: We used the standard thin-disk model with Keplerian orbits and a fixed emissivity profile to focus on the geometric differences between the wormhole and Schwarzschild spacetimes. The energy shift g is calculated from the metric and the four-velocity, incorporating both gravitational redshift (via Φ(r)) and Doppler boosting. Our numerical results show brighter wormhole images due to weaker gravitational redshift in the chosen parameter sets. To better support the claim, we will include in the revision a quantitative decomposition, such as plots of the separate gravitational and Doppler factors contributing to g at different disk radii for the compared cases. Regarding non-Keplerian flows, this would require additional modeling assumptions and is left for future work; we will note this limitation in the discussion. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper first derives general expressions for shadow radius, throat silhouette radius, and photon energy shift directly from an arbitrary static spherically symmetric metric. These expressions are then specialized to the three-parameter wormhole metric with throat radius a, length λ, and well-depth parameter u0. Numerical evaluation produces the radii as functions of those parameters, after which specific values are selected so the radii numerically coincide with the Schwarzschild values; this is an explicit search over parameter space rather than a fitted input renamed as a prediction. Accretion-disk images are subsequently obtained by ray-tracing the thin-disk model in each spacetime, revealing differences attributable to the distinct redshift factors g. No self-citation chain, no self-definitional loop, and no ansatz smuggled via prior work; the central comparison rests on independent numerical evaluation of the two metrics under identical thin-disk assumptions.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central results rest on a three-parameter family of static spherically symmetric wormhole metrics whose explicit form is not given in the abstract; the free parameters a, λ, and u0 are introduced to control throat size, length, and gravitational depth, and the analysis assumes the standard geodesic equation in general relativity.

free parameters (3)
  • throat radius a
    Controls the minimum radius of the wormhole throat.
  • throat length λ
    Sets the proper length of the throat region.
  • u0
    Determines the depth of the gravitational potential well.
axioms (2)
  • domain assumption The spacetime is static and spherically symmetric
    Invoked to reduce the metric to a single radial function and to simplify the geodesic equations for shadow and silhouette calculations.
  • standard math Null geodesics determine the shadow and photon ring
    Standard assumption in general relativity for computing unstable photon orbits.

pith-pipeline@v0.9.0 · 5755 in / 1608 out tokens · 60344 ms · 2026-05-20T20:25:33.548251+00:00 · methodology

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Reference graph

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