General relativity simulator

See how mass curves spacetime and how everything moving through it responds. Three views cover the curved geometry around a mass, orbits and light paths computed from the Schwarzschild geodesic equation, and the gravitational waves sent out by two merging black holes.

This interactive simulation runs in your browser with WebGL. Free, no account needed.

What you can explore

Curvature

A grid of spacetime dips around a central mass. Increase the mass and the well deepens, with the event horizon and photon sphere marked as the curvature becomes extreme.

Geodesics

Bodies orbit a black hole along true Schwarzschild geodesics, so their orbits rotate a little on every lap: the effect that explained Mercury’s perihelion. A dashed Newtonian ellipse stays fixed beside them for comparison, and light rays bend as they pass the mass.

Gravitational waves

Two black holes spiral together, speed up and merge, then the remnant rings down. A two-armed spiral of waves ripples outward across spacetime, a ring of test masses stretches and squeezes as it passes, and a strain plot shows the characteristic chirp detected by LIGO.

Key equations

  • G_μν + Λg_μν = 8πG T_μν / c⁴
  • d²u/dφ² = M/L² − u + 3Mu²
  • Δφ = 6πGM / c²a(1 − e²)

Curriculum

Enrichment beyond A-level, IB Physics A.5.

Common questions

Why do orbits precess in general relativity?

The extra 3Mu² term in the geodesic equation slightly strengthens gravity close to the mass, so the orbit does not quite close and its closest point advances a little each time around.

What is a gravitational-wave chirp?

As two black holes lose energy to gravitational waves they spiral closer, orbit faster and radiate more strongly, so the signal rises in both frequency and amplitude until they merge.

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