Black Hole Embedding Diagrams Explained
What an embedding diagram is
An embedding diagram is a visualization method: you take a 2D spatial slice of a curved geometry and represent it as a surface embedded in 3D Euclidean space. The “funnel” shape is an analogy for curvature, not a literal hole in space.
What it is not
- Not the “real shape of spacetime in space” (spacetime is not embedded in ordinary space in this picture).
- Not a picture of time; it is typically a spatial slice.
- Not a guarantee about what you would see in an image—visual appearance depends on light geodesics and emission.
How to connect embedding intuition to lensing
Embedding diagrams help you think about “distances and curvature” in a slice. Lensing and ray tracing are about how light paths behave in the full spacetime. Together, they provide complementary intuition: geometry‑as‑shape and geometry‑as‑light‑bending.
FAQ
- Does the funnel mean gravity “pulls downward”? No. The “down” direction is a visualization axis; it’s not a physical direction in space.
- Is an embedding diagram the same as a wormhole throat diagram? They’re related visualization ideas, but the underlying geometries differ.
- Why do these diagrams show a pinch? They encode how the spatial slice’s distance metric changes with radius in the model.