Wormholes
Mathematical solutions to general relativity that connect distant regions of spacetime. None has ever been observed. Included for completeness — they are NOT used for spaceflight.
A wormhole — formally an Einstein-Rosen bridge — is a topological feature of spacetime that the equations of general relativity permit but the universe has never been observed to actually instantiate. The mathematics is real (Einstein and Rosen worked it out in 1935); the physics is uncertain (no candidate has been seen); the engineering does not exist (and may be physically impossible). Treat them the way you'd treat tachyons or time-travel paradoxes: interesting puzzles in the equations, not flight hardware.
The original Schwarzschild solution to Einstein's equations describes a non-rotating black hole, and inside the geometry there's a second "universe" connected by a tube of spacetime. The catch: the tube isn't traversable. To cross it you'd have to move faster than light. Kip Thorne and others worked out in the 1980s that adding "exotic matter" — material with negative energy density, of which we have no examples — could in principle hold a wormhole open long enough to cross. Stephen Hawking pushed back: quantum effects probably destroy any traversable wormhole as soon as you try to use one.
Observationally, we have no candidates. No gravitational-lensing signature, no astrophysical source has yet been identified that requires a wormhole interpretation. If they exist in nature, they're either very small (sub-atomic, quantum gravity domain) or very far away. The popular-culture wormhole — a stable, traversable, instant-shortcut between solar systems — would require physics we have no example of, and would carry the same causality-violation paradoxes that make time travel philosophically uncomfortable.
So why include them in a science encyclopedia at all? Because they're a beautiful illustration of the limits of general relativity: the equations admit solutions that the universe doesn't seem to use, and figuring out *why* is one of the live frontiers of theoretical physics. Quantum gravity, AdS/CFT correspondence, the ER=EPR conjecture — all of it touches wormhole geometry. They are real mathematics. They are not real spacecraft.