Schwarzschild radius
The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is the radius of a sphere such that, if all the mass of an object were to be compressed within that sphere, the escape velocity from the surface of the sphere would equal the speed of light. An example of an object where the mass is within its Schwarzschild radius is a black hole. Once a stellar remnant collapses to or below this radius, light cannot escape and the object is no longer directly visible outside, thereby forming a black hole. It is a characteristic radius associated with every quantity of mass. The Schwarzschild radius was named after the German astronomer Karl Schwarzschild, who calculated this exact solution for the theory of general relativity in 1916.
The Schwarzschild radius is given as
where G is the gravitational constant, M is the object mass and c is the speed of light.
In 1916, Karl Schwarzschild obtained the exact solution to Einstein's field equations for the gravitational field outside a non-rotating, spherically symmetric body (see Schwarzschild metric). Using the definition M = Gm/c2, the solution contained a term of the form 1/2M − r; where the value of making this term singular has come to be known as the Schwarzschild radius. The physical significance of this singularity, and whether this singularity could ever occur in nature, was debated for many decades; a general acceptance of the possibility of a black hole did not occur until the second half of the 20th century.
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