Schwarzschild radius

The Schwarzschild radius, named after the German astronomer Karl Schwarzschild, is a critical radius associated with a non-rotating black hole. It defines the boundary within which the escape velocity is equal to the speed of light, and anything that passes this radius is predicted to be unable to escape the gravitational pull of the black hole.

For a non-rotating (static and spherically symmetric) black hole, the Schwarzschild radius is given by the formula:

\[R_s = \frac{2GM}{c^2}\]

where:

• ( G ) is the gravitational constant,
• ( M ) is the mass of the black hole,
• ( c ) is the speed of light.

This radius is a fundamental parameter in the description of a non-rotating black hole's geometry and is sometimes referred to as the gravitational radius. It represents the boundary of the black hole's event horizon, the region from which nothing, not even light, can escape.

Objects or radiation that come closer to the black hole than the Schwarzschild radius are effectively within the gravitational grasp of the black hole and are destined to be pulled inexorably toward the singularity at the center of the black hole. The concept of the Schwarzschild radius is a key aspect of the theory of general relativity, describing the extreme gravitational effects near a massive object.