# Schwarzschild radius

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## Schwarzschild radius

The radius of the event horizon of a black hole: a critical radius that must be exceeded by a body if light from its surface is to reach an outside observer. For a body of mass M (but zero angular momentum and zero electric charge), the Schwarzschild radius, R S, is given by
R S = 2GM /c 2
where G is the gravitational constant and c the speed of light. If a body collapses so that its radius becomes less than this critical value, then the escape velocity becomes equal to the speed of light and the object becomes a black hole. The Schwarzschild radius is proportional to the mass of a body. For a star the size of the Sun, the Schwarzschild radius is some three km.

## Schwarzschild radius

[′shvärts‚shilt ‚rād·ē·əs]
(relativity)
Conventionally taken to be twice the black hole mass appearing in the general relativistic Schwarzschild solution times the gravitational constant divided by the square of the speed of light; the event horizon in a Schwarzschild solution is at the Schwarzschild radius.
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