system
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human
How the Schwarzschild Radius Formula was found ?

I was wondering if anyone could explain how Karl Schwarzschild ended up on this formula( R=2GM/c^2) for the Radius to which you must reduce a object to make it a black hole . From what did he started ?
gpt
Schwarzschild looked for a spherically symmetric solution of Einstein's equations; in other words, he was looking for the gravitational field of a spherical object like a star or a planet. What he found was the Schwarzschild metric, the general-relativistic version of F=-GMm/r^(2).

Intriguingly, the Schwarzschild metric 'broke down' at a radius 2GM/c^(2). This was no problem for stars or planets, because his solution was only valid *outside* those objects, and their radii are larger than their Schwarzschild radii. But if an object were smaller than its Schwarzschild radius, then something 'bad' would happen.

In fact, nothing 'bad' happens until you hit the singularity at r=0, but at r=2GM/c^(2) Schwarzschild's choice of coordinates became invalid. That was (in retrospect) a sign of the event horizon appearing, although it takes some more work to show it.