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Schwarzschild Radius

(Gravitational Radius)
(radius of a black hole's event horizon)

The Schwarzschild Radius (or Gravitational Radius) is the radius of a Black Hole's Event Horizon, according to Karl Schwarzschild's solution to Einstein's Field Equation. It is a function of mass and is directly proportional to it.

rS = 2GM/c²

This applies to a non-rotating black hole. Rotation or electric charge would modify it.

It places a limit on how small an object of a given mass can be without becoming a black hole, but somewhat larger objects can collapse into black holes if their structure is insufficiently "strong" to support the given mass (i.e., they produce insufficient pressure), or if some spherical sub-portion of the object exceeds that portion's Schwarzschild Density, the density that implies a mass is within its Schwarzschild radius.

The Sun's mass has a Schwarzschild radius of about 3km, and the Earth's is about 9 millimeters.

The term Schwarzschild Diameter naturally means twice the Schwarzschild radius.

(limit,black holes)