Wormhole Embedded Diagrams Explained
What is an embedding diagram?
An embedding diagram is a visualization trick. You take a 2D slice of a curved space (often an equatorial slice) and draw it as a surface embedded in 3D Euclidean space so our intuition can “see” curvature as shape.
The benefit is intuition: a “throat” can look like a smooth bottleneck connecting two regions.
What it means (and what it doesn’t)
The embedded surface is not literally what the wormhole “looks like” in a sci‑fi sense. It’s a representation of distances within a particular spatial slice.
It also doesn’t automatically tell you whether a wormhole is physically realizable, stable, or traversable. Those questions depend on the full spacetime geometry and the matter/energy assumptions used to construct it.
Throat radius vs minimum radius
Many wormhole models have a “throat”: a location where the areal radius reaches a minimum. Depending on the chosen model and coordinates, parameters like “throat radius” and “minimum radius” can appear separately.
If you’re using this site’s generator, the best practical approach is: change one parameter at a time and watch how the throat width and the flare-out shape respond.
How changing parameters changes the diagram
The embedding shape typically changes in a few intuitive ways:
- Wider throat: the narrowest part of the surface becomes “less pinched”.
- Longer wormhole: the surface extends further along the embedding direction before opening out.
- More/less flaring: the transition from the throat to the asymptotic region becomes sharper or gentler.
These are geometric intuitions; the precise relationship depends on the model.
Try it: generate your own wormhole embedding
- Wormhole embedded diagram generator
- Chapter notes: producing embedded diagrams
- How altering wormhole length changes appearance