Schwarzschild radius

The Schwarzschild radius or gravitational radius is a characteristic radius associated with every mass. The term is used in physics and astronomy, especially in the theory of gravitation, general relativity. It was found in 1916 by Karl Schwarzschild and results from his discovery of an exact solution for the gravitational field outside a static, spherically symmetric star (see Schwarzschild metric, which is a solution of the Einstein field equations).

Formula for the Schwarzschild radius

The Schwarzschild radius is proportional to the mass, with a proportionality constant involving the gravitational constant and the speed of light.

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The formula for the Schwarzschild radius can be found by setting the escape velocity to the speed of light, and is

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: r_s = rac{2Gm}{c^2}

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where

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: r_s is the Schwarzschild radius

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: G is the gravitational constant, that is 6.67 × 10-11 N m2 / kg2;

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: m is the mass of the gravitating object; and

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: c² is the speed of light squared, that is (299,792,458 m/s)² = 8.98755 × 1016 m²/s².

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The proportionality constant, 2G/c^2, can be approximated as 1.48 × 10-27 m / kg.

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