Squeeze any mass inside rₛ = 2GM/c² and escape velocity reaches the speed of light: it becomes a black hole, and that radius is its event horizon — the edge past which the void keeps everything, even light. Earth’s is 8.87 mm; the Sun’s is 2.95 km. Karl Schwarzschild solved Einstein’s equations for it in 1916, from a trench on the Eastern Front.
THE TECHNIQUE rₛ = 2GM/c²
The demo computes the Schwarzschild radius for Earth and the Sun: live demo
HISTORY & CREDIT Karl Schwarzschild · 1916
“A black hole sucks things in like a vacuum.” — outside rₛ its gravity is ordinary Newtonian; the horizon is a one-way surface, not a suction. cited
the threshold · when v_esc = c, light cannot leave. the radius · rₛ = 2GM/c² — the event horizon. 1916 · Karl Schwarzschild, the first exact solution of general relativity, written at the front; he died months later.
The size at which mass becomes a one-way door. physics
RECOMMEND FOR I-13 Earth and Sun, on the compiler
On i-13, Earth’s Schwarzschild radius is 8.87 mm; the Sun’s is 2.95 km:
$ i13 run gw_schwarzschild.i13 # r_s = 2*mu/c^2
RUN OK · 24 step(s)
rs_mm = 8.8696 -- Earth, millimetres
sun_rs_km = 2.9528 -- Sun, kilometres
Recommend as a NULL — a theorem (B39). rₛ = 2GM/c² is an exact GR result, a linear function of mass; any correct mechanism returns the same horizon. NULL — the edge of the void.