Physics
General Relativity
Mass bends spacetime. The funnel is the real curved geometry of space around a black hole (Flamm's paraboloid), the clocks show time running slow deep in the well, and the ruler shows a proper 'meter' swallowing less and less coordinate distance as you fall toward the horizon.
r / rₛ2.00
Clock rate √(1−rₛ/r)0.707
Ruler stretch 1/√(1−rₛ/r)1.414
1 s here = distant1.41 s
Real distance from horizon— m
…yet coordinate r − rₛ—
Drag to orbit, scroll to zoom. The bright ring is the event horizon (r = rₛ); the white ring is your probe. The bar at the bottom lays equal real metres onto the flat coordinate-r axis. Colour runs red (slow clocks, near) to teal (normal, far).
What to observe
- Watch the row of clock hands. The far ones keep pace, but each clock deeper in the well runs slower, its rate is exactly √(1 − rₛ/r). Right at the horizon it freezes: time stops for a distant onlooker.
- The blocks on the bottom bar are all identical real meters, but placed by their r coordinate they pile up near the horizon: loads of real metres squeeze into a tiny change of r. A ruler you hold is always one metre, what grows is the real distance packed into each step of r, stretched by 1/√(1 − rₛ/r). Watch the readouts: "real distance from horizon" races ahead of "coordinate r − rₛ".
- Both effects blow up together at r = rₛ (clocks stop, the funnel goes vertical) and both fade to 1 far away, where the funnel flattens back into ordinary flat space.
- Grow rₛ (more mass) and the whole well deepens: the curvature, the time dilation and the stretching all reach farther out.
Shortcuts: space run/pause · s step · r reset · f fullscreen