Schwarzschild Radius
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It's the radius to which a given mass would need to be compressed for its escape velocity at that radius to equal the speed of light, forming a black hole. Any mass compressed within its own Schwarzschild radius becomes a black hole, since nothing, not even light, could escape from inside it.

The formula is r_s = 2GM/c², where G is the gravitational constant, M is the object's mass, and c is the speed of light. Notice it depends only on mass — it's a simple linear relationship, so doubling the mass exactly doubles the Schwarzschild radius.

Yes — every mass has a mathematically defined Schwarzschild radius, it just isn't physically meaningful unless the object is actually compressed that small. Earth's Schwarzschild radius is about 9 millimeters, and the Sun's is about 3 kilometers, both far smaller than their actual radii.

A black hole only forms if all of an object's mass is actually packed inside that radius; ordinary matter's internal pressure holds stars and planets at a far larger size. Only extreme processes, like the core collapse of a massive star, can compress matter down to within its own Schwarzschild radius.

Essentially yes — it defines the event horizon, the boundary beyond which nothing can escape and which appears as the black hole's dark silhouette to an outside observer. It is not a physical surface, though; it's a mathematical boundary in spacetime, not a solid edge.