Long-Throat Wormholes: How Doppler Notes Give Them Away ✦

Original: "Image of a wormhole with an arbitrary throat profile"

· Valeria A. Ishkaeva, Sergey V. Sushkov

arXiv:2605.16413v2 · 2026-05-13 · CC BY 4.0 · ⏱ 1 min · General Relativity

The shadow match is a mirage—wormhole accretion disks burn 1.5 times brighter: here, Doppler beats gravitational redshift.

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Two objects, one shadow. A black hole—a gravitational trap. A wormhole—a tunnel where spacetime is curved like a guitar neck. Their accretion disks give them away: for a black hole, photons redden and dim; for a wormhole, they surge to violet frequencies. The Doppler effect shouts over gravity: 1.45 vs. 0.74. Perhaps at the heart of Sagittarius A*, it's not a monster hiding, but a portal.

🎯 The name 'wormhole' came from John Wheeler's imagination, picturing a worm eating through an apple, bypassing the skin. And the idea of interstellar travel through such tunnels was seriously grounded by Kip Thorne and Michael Morris in the late 1980s.

🎬 In 'Interstellar,' a traversable wormhole—a portal to a distant galaxy—serves as a fictional embodiment of theoretical dreams of interstellar tunnels.

\alpha_{\text{sh}} = \left| \frac{r(u_{\text{ph}})}{N(u_{\text{ph}})} \right|

The angular shadow radius α_sh is given by the ratio of the radial coordinate r to the lapse function N at the photon sphere—the very place where light is caught in a gravitational carousel.

\int_0^{\infty} \frac{du}{r^2(u) \sqrt{N^{-2}(u) - \alpha_{\text{sil}}^2 / r^2(u)}} = \frac{\pi}{\alpha_{\text{sil}}}

This equation links the angular size of the throat silhouette α_sil to the full geometry of spacetime—it 'feels out' the entire wormhole.

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Long-Throat Wormholes: How Doppler Notes Give Them Away ✦