Geometry's Verdict: Why Wormholes Are Doomed to Exoticity ✦

Original: "A No-Go Theorem for Topological Bridges with Matter-Vacuum Coupling"

arXiv:2605.14027v1 · 2026-05-13 · CC BY · ⏱ 1 min · General Relativity

Interaction with dark energy does not turn a wormhole into a legitimate creation — the energy law remains relentless.

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Spacetime geometry presents a bill for any miracle. Even if you force dark energy to work for a wormhole, the meter will show negative pressure — and the Universe will refuse to pay. Like a judge exposing a forgery, Einstein's equations discard the illusory props and demand a direct violation of energy conditions. The verdict is final for now, but quantum appeal is unpredictable.

🎯 Keeping a wormhole open is like trying to preserve a tunnel in a bottomless sponge that immediately sucks in its pores at the slightest attempt to expand. Adding a 'helper' in the form of vacuum interaction is analogous to bringing in a crew from a parallel universe: they pour in water, but the sponge shrinks even faster, pushing everything out.

🎬 In 'Star Trek,' wormholes are commonplace, but that would require filling the holds with exotic matter of negative mass, overriding the Standard Model. And stabilizing a wormhole according to [scientist:Kip Thorne]Kip Thorne's[/scientist] recipe from 'Contact,' though it relies on quantum fluctuations, demands energy control in the Planckian froth — something even more out of reach than starships.

\frac{d^2 r}{dz^2} = \frac{b - r b'}{2b^2} > 0

Geometric flaring requirement: the second derivative of the embedding function must be positive, which is impossible without negative pressure.

\tau - \rho = \frac{b - r b'}{\kappa^2 r^3} > 0

The effective radial tension exceeds the energy density, which directly contradicts the hypothesis of no exotic matter.

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Geometry's Verdict: Why Wormholes Are Doomed to Exoticity ✦