OURANOS · the celestial · the sky, measured · kept by URANIA

THE SCHWARZSCHILD RADIUS ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP

Squeeze anything small enough and its own gravity wins forever: a radius appears from which not even light escapes — the event horizon of a black hole. For the Sun that radius is 3 km; for the Earth, 9 millimetres. Nothing is squeezed that far in nature except collapsing stars. Slide the mass and find the point of no return.

◆ LIT▲ AMBER
◧ THE MEASURE · 2D
◍ THE HORIZON · 3D · squeeze past no return
◆ THE FOURTH · 4D · a tesseract turns
◐ THE SHADOW · one dimension down
👶 THE TODDLER CORNER — one fat tap
mass
event horizon rₛ
vs real size
black hole?

◆ LIT — exact / checkable

The Schwarzschild radius is rₛ = 2GM/c² — the radius at which the escape velocity reaches the speed of light, so nothing can leave. It is astonishingly small: the Sun’s is 2.95 km (it is really 700,000 km across), the Earth’s just 8.9 mm. Only when a mass is compressed INSIDE its own rₛ does it become a black hole. A fail-loud self-check throws unless rₛ = 2GM/c² gives ~2953 m for the Sun and ~8.9 mm for the Earth.

▲ AMBER — the figure

This is the non-rotating (Schwarzschild) horizon from general relativity; spinning/charged holes (Kerr/Reissner-Nordström) differ, and rₛ marks the horizon, not the singularity within. The 2GM/c² value is exact.

OURANOS: the sky is a laboratory you may only look at — so we learned to weigh it with light.  — URANIA
David Lee Wise / ROOT0 / TriPod LLC  ·  the observatory, with AVAN