Gravity well fabric
The classic “rubber sheet” analogy for general relativity. A flat grid represents spacetime — place masses on it and watch the fabric deform into gravity wells. Fire test particles and watch them follow curved geodesics around the wells, just as planets orbit stars.
Gμν + Λgμν = (8πG/c4) Tμν | Click to place masses, drag to fire particles
The rubber sheet analogy
Einstein’s general theory of relativity (1915) describes gravity not as a force but as the curvature of spacetime caused by mass and energy. The “rubber sheet” analogy imagines spacetime as a stretched elastic membrane. A heavy object placed on it creates a depression — a gravity well. Nearby objects naturally roll toward the depression, mimicking gravitational attraction. This simulation implements that analogy directly.
Geodesics
In curved spacetime, objects follow paths called geodesics — the straightest possible paths through curved geometry. On a flat surface, geodesics are straight lines. On a curved surface (like our deformed grid), geodesics curve toward the wells. A particle moving fast enough will orbit the well; too slow, and it spirals in. Too fast, and it deflects but escapes — like a hyperbolic orbit.
Limitations of the analogy
The rubber sheet is a useful teaching tool but has important limitations. Real spacetime is four-dimensional (three space + one time), not two-dimensional. The sheet analogy also requires an external “gravity” pulling objects down into the wells, which is circular reasoning. And it only shows spatial curvature, not the more important time curvature that dominates most gravitational effects. Still, it captures the essential insight: mass curves geometry, and curved geometry guides motion.
Einstein’s field equations
The full theory is expressed by the Einstein field equations: Gμν + Λgμν = (8πG/c4) Tμν. The left side describes the curvature of spacetime; the right side describes the distribution of matter and energy. John Wheeler summarized it: “Spacetime tells matter how to move; matter tells spacetime how to curve.” This simulation is a two-dimensional visual echo of that profound relationship.
What you see here
The wireframe grid represents a 2D slice of spacetime. Each mass creates a depression proportional to its size. The depth coloring — gold at the surface fading to deep dark in the wells — helps convey the three-dimensional shape. Test particles are launched with initial velocities and then follow Newtonian gravity as an approximation of geodesic motion. Try placing two masses close together and firing a particle between them to see figure-eight orbits.