02 / General relativity

Curved-Space Gravity

Follow freely falling matter and light through Schwarzschild spacetime.

Geodesics around a nonrotating black hole

Ready

Gold: trajectory · cyan: photon sphere r = 3M · dashed: ISCO r = 6M

A coordinate map of the equatorial plane—not an embedding surface. Radius is areal radius; drawn distances are not proper radial distances.

Quantitative comparison

Measured & predicted

Initializing model…
Explore the geometry

Curvature intuition

Surface analogy
Ball’s pathFlat-surface reference

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A ball follows a path on a curved surface. Mass adjusts this illustrative surface; it does not change the Schwarzschild experiment or its mass-normalized measurements.

Interpretation

What the model establishes

The spacetime is the exact exterior vacuum solution for a spherical, nonrotating source. The trajectories are numerical test-particle solutions, with no self-gravity, spin, radiation reaction, or horizon-interior evolution.