Two sheets,
joined at the throat
The Ellis wormhole is the simplest geometry with two asymptotically flat regions and no horizon between them. The embedding shows why the shortcut is a shortcut: through the throat the distance is a few multiples of b, while around the outside it is unbounded.
lawr(ℓ) = √(ℓ² + b²) with the embedding z = b·arcsinh(ℓ/b). The throat radius b never shrinks to zero, so nothing is crushed.
tryDrag the traveller from one sheet through to the other.
noticeThe proper distance through the throat grows only linearly, while the two mouths can sit arbitrarily far apart in the embedding space. Holding this open needs exotic matter — the honest caveat this picture cannot draw.
in lifeNo known example. It stays a solution on paper, useful mainly for testing what general relativity permits.
found byEinstein and Rosen described the bridge in 1935; Ellis gave this horizon-free version in 1973.