distance from a massive body where the escape velocity equals the speed of light

The Schwarzschild radius (sometimes erroneously referred to as the gravitational radius), is the radius of a sphere that has certain properties: if all the mass of an object is compressed within this sphere, the escape speed from the surface of the sphere would equal the speed of light. An example of an object smaller than its Schwarzschild radius is a black hole. Once a stellar remnant collapses below this radius, light can no longer escape and the object is no longer visible. 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.

This radius can be calculated using the equation:

$r_{s}={\frac {2GM}{c^{2}}}$ where the gravitational constant G is 6.67430×10−11 N⋅m2/kg2, M is the mass of the object, and c is the speed of light which is 299,792,458 m/s.

## Derivation

The Schwarzschild radius is found within the Schwarzschild metric, and originally was used to describe the gravitational field around a black hole, given the assumptions that it is spherical, non-rotating, without a magnetic field, and that the cosmological constant is zero; (it describes the path of a particle moving through this spacetime) however, this radius can be calculated for any object.