schwarzschild geometry · real general relativity · verified, not faked

Where light itself runs out of road.

A black hole isn't a cosmic vacuum cleaner — it's a place where spacetime curves so steeply that straight lines bend into spirals and, past a certain edge, every path leads inward. Fire beams of light past this one and watch them follow real curved-spacetime geodesics: distant rays barely bend, closer ones swing hard, and any ray that crosses the critical line can never leave. The rings mark the true geometry — the event horizon, the photon sphere where light can orbit, the last stable orbit for matter — and the clock shows time itself freezing as it falls in.

Fire light

beam spread15 rays

The geometry

event horizon (Rs)r = 1.0 Rs

photon sphere1.5 Rs

ISCO (last orbit)3.0 Rs

capture threshold2.60 Rs

Infalling clock

100%

far from the hole

drop clock at5.0 Rs

Legend

event horizon — nothing escapes

photon sphere — light orbits

ISCO — last stable matter orbit

ray escapes

ray captured

Everything here is exact, not artistic. The

event horizon

sits at the Schwarzschild radius Rs = 2GM/c² — for our Sun that's 2.95 km, for Earth about 9 millimetres; squeeze any mass inside its Rs and it becomes a black hole. Just outside, at 1.5 Rs, is the

photon sphere

, where gravity is exactly strong enough that light can circle in an orbit — a ray aimed just right will loop the hole several times before flying off, which is why beams near that radius fan out so wildly. The ISCO at 3 Rs is the innermost stable circular orbit: matter can orbit outside it but must plunge in once it drifts inside, which is why accretion disks have a sharp inner edge. The capture threshold at 2.598 Rs (exactly 3√3⁄2) is the impact parameter below which a light ray is doomed — and every ray you fire is integrated through the real geodesic equation d²u/dφ² + u = 3M·u², the same maths used to render the Event Horizon Telescope's images. The clock is the strangest part: time runs at √(1 − Rs/r) of the far-away rate, so a clock lowered toward the horizon visibly slows, and at the horizon itself appears — to us, safely distant — to stop forever. Not a metaphor. The geometry simply runs out of future.