Spacetime Curvature for Beginners
Start with Minkowski spacetime
In special relativity, spacetime is flat. Minkowski spacetime is a geometric way of describing that flat structure with a metric. It already teaches the key lesson: “distance” in spacetime is not the same as Euclidean distance in ordinary 3D space.
What is a metric?
A metric tells you how to compute intervals (spacetime “distances”) between nearby events. Different metrics encode different gravitational environments. In GR, the metric is the main object you solve for.
What is a geodesic?
A geodesic is the “straightest possible” path in a curved geometry. Free-falling objects follow timelike geodesics; light follows null geodesics. This idea connects directly to ray tracing around black holes and wormholes.
Curvature: how to say “spacetime is bent” mathematically
Curvature shows up in tensors (like the Riemann curvature tensor). You don’t need the full formalism to understand the intuition: curvature changes which paths are geodesics and how nearby geodesics converge/diverge.
Try visuals on this site
- Black hole image simulation (see light bending)
- Black hole embedding diagram (geometry intuition)
- Wormhole embedding diagram
FAQ
- Is spacetime curvature the same as “a force”? In GR, gravity is modeled as geometry; “force” language is often a useful approximation in weak fields.
- Why does light bend? Light follows null geodesics; in curved spacetime, those paths are not straight lines in Euclidean space.
- Do embedding diagrams show real shape of spacetime? They show an embedding of a slice; they’re a visualization tool, not literal “shape in space”.